From da6a98c415d34917285cec2e24d8c3d9debde8c8 Mon Sep 17 00:00:00 2001 From: GitHub CI Documentation builder Date: Thu, 9 Jan 2025 16:25:28 +0000 Subject: [PATCH] Update docs --- ...tion__2d__rp_2test__cases_8hpp_source.html | 4 +- advection__field__rp_8hpp_source.html | 2 +- annotated.html | 14 +- bsl__predcorr_8hpp_source.html | 77 +- ...__second__order__explicit_8hpp_source.html | 263 +- ...__second__order__implicit_8hpp_source.html | 530 ++-- cartesian__to__circular_8hpp_source.html | 4 +- cartesian__to__czarny_8hpp_source.html | 4 +- circular__to__cartesian_8hpp_source.html | 4 +- classBslExplicitPredCorrRTheta-members.html | 2 +- classBslExplicitPredCorrRTheta.html | 12 +- classBslExplicitPredCorrRTheta.js | 2 +- classBslImplicitPredCorrRTheta-members.html | 2 +- classBslImplicitPredCorrRTheta.html | 12 +- classBslImplicitPredCorrRTheta.js | 2 +- classBslPredCorrRTheta-members.html | 2 +- classBslPredCorrRTheta.html | 12 +- classBslPredCorrRTheta.js | 2 +- ...larSplineFEMPoissonLikeSolver-members.html | 28 +- classPolarSplineFEMPoissonLikeSolver.html | 1053 +++++++- classPolarSplineFEMPoissonLikeSolver.js | 20 +- classVortexMergerEquilibria-members.html | 2 +- classVortexMergerEquilibria.html | 12 +- classVortexMergerEquilibria.js | 2 +- czarny__to__cartesian_8hpp_source.html | 4 +- discrete__mapping__builder_8hpp_source.html | 4 +- discrete__to__cartesian_8hpp_source.html | 4 +- docs_DDC_in_gyselalibxx.html | 8 +- ...Theta_2geometry_2geometry_8hpp_source.html | 307 ++- ...ryXVx_2geometry_2geometry_8hpp_source.html | 8 +- ...YVxVy_2geometry_2geometry_8hpp_source.html | 16 +- ...tryXY_2geometry_2geometry_8hpp_source.html | 8 +- inv__jacobian__o__point_8hpp_source.html | 4 +- math__tools_8hpp_source.html | 2 +- navtreedata.js | 6 +- navtreeindex0.js | 6 +- navtreeindex3.js | 2 +- navtreeindex4.js | 40 +- navtreeindex5.js | 18 +- navtreeindex6.js | 18 +- navtreeindex7.js | 8 + onion__patch__locator_8hpp_source.html | 4 +- polar__bsplines_8hpp_source.html | 1240 ++++----- polar__poisson_2test__cases_8hpp_source.html | 4 +- polarpoissonlikesolver_8hpp_source.html | 2391 +++++++++-------- search/all_12.js | 2 +- search/all_13.js | 2 +- search/all_15.js | 2 +- search/all_17.js | 186 +- search/all_19.js | 2 +- search/all_1a.js | 11 +- search/all_5.js | 6 +- search/all_6.js | 87 +- search/all_8.js | 106 +- search/all_9.js | 111 +- search/all_a.js | 97 +- search/all_c.js | 287 +- search/classes_4.js | 34 +- search/functions_1.js | 6 +- search/functions_13.js | 16 +- search/functions_15.js | 2 +- search/functions_16.js | 7 +- search/functions_17.js | 9 + search/functions_2.js | 27 +- search/functions_5.js | 21 +- search/functions_6.js | 27 +- search/functions_8.js | 2 +- search/functions_e.js | 2 +- search/functions_f.js | 2 +- search/searchdata.js | 2 +- search/typedefs_7.js | 79 +- search/typedefs_d.js | 2 +- search/typedefs_f.js | 2 +- ...lineFEMPoissonLikeSolver_1_1QDimRMesh.html | 10 +- ...plineFEMPoissonLikeSolver_1_1QDimRMesh.png | Bin 1958 -> 1911 bytes ...FEMPoissonLikeSolver_1_1QDimThetaMesh.html | 10 +- ...eFEMPoissonLikeSolver_1_1QDimThetaMesh.png | Bin 2005 -> 1959 bytes test__cases__adv__field_8hpp_source.html | 4 +- vector__mapper_8hpp_source.html | 4 +- vortex__merger__equilibrium_8hpp_source.html | 161 +- 80 files changed, 4351 insertions(+), 3146 deletions(-) create mode 100644 search/functions_17.js diff --git a/advection__2d__rp_2test__cases_8hpp_source.html b/advection__2d__rp_2test__cases_8hpp_source.html index 2d80e6442..a8c357d8a 100644 --- a/advection__2d__rp_2test__cases_8hpp_source.html +++ b/advection__2d__rp_2test__cases_8hpp_source.html @@ -513,8 +513,8 @@
RotationSimulation::RotationSimulation
RotationSimulation(Mapping const &mapping, double const rmin, double const rmax)
Instantiate a RotationSimulation simulation.
Definition test_cases.hpp:545
TranslationSimulation
Simulation of a translated Gaussian.
Definition test_cases.hpp:482
TranslationSimulation::TranslationSimulation
TranslationSimulation(Mapping const &mapping, double const rmin, double const rmax)
Instantiate a TranslationSimulation simulation.
Definition test_cases.hpp:494
-
Vx
Define non periodic real X velocity dimension.
Definition geometry.hpp:300
-
Vy
Define non periodic real Y velocity dimension.
Definition geometry.hpp:311
+
Vx
Define non periodic real X velocity dimension.
Definition geometry.hpp:341
+
Vy
Define non periodic real Y velocity dimension.
Definition geometry.hpp:352
diff --git a/advection__field__rp_8hpp_source.html b/advection__field__rp_8hpp_source.html index 7759fa909..4bcc0d3b1 100644 --- a/advection__field__rp_8hpp_source.html +++ b/advection__field__rp_8hpp_source.html @@ -504,7 +504,7 @@
AdvectionFieldFinder::operator()
void operator()(host_t< Spline2D > electrostatic_potential_coef, host_t< DVectorFieldRTheta< R, Theta > > advection_field_rp, CoordXY &advection_field_xy_center) const
Compute the advection field from a spline representation of .
Definition advection_field_rp.hpp:388
InverseJacobianMatrix
A class to calculate the inverse of the Jacobian matrix.
Definition inverse_jacobian_matrix.hpp:18
MetricTensor
An operator for calculating the metric tensor.
Definition metric_tensor.hpp:15
-
PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
static int constexpr continuity
The continuity enforced by the bsplines at the singular point.
Definition polar_bsplines.hpp:61
+
PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
static int constexpr continuity
The continuity enforced by the bsplines at the singular point.
Definition polar_bsplines.hpp:62
PolarSplineEvaluator
Define an evaluator on polar B-splines.
Definition polar_spline_evaluator.hpp:13
VectorField
A class which holds multiple (scalar) fields in order to represent a vector field.
Definition vector_field.hpp:64
NullExtrapolationRule
Define null extrapolation rule commun to all geometries.
Definition null_extrapolation_rules.hpp:17
diff --git a/annotated.html b/annotated.html index c2f883f49..3baac2614 100644 --- a/annotated.html +++ b/annotated.html @@ -424,12 +424,14 @@  CPolarSplineA structure containing the two Chunks necessary to define a spline on a set of polar basis splines  CPolarSplineEvaluatorDefine an evaluator on polar B-splines  ►CPolarSplineFEMPoissonLikeSolverDefine a polar PDE solver for a Poisson-like equation - CQDimRMeshTag the first dimension for the quadrature mesh - CQDimThetaMeshTag the second dimension for the quadrature mesh - CRBasisSubset - CRCellDim - CThetaBasisSubset - CThetaCellDim + CEvalDeriv1DTypeObject storing a value and a value of the derivative of a 1D function + CEvalDeriv2DTypeObject storing a value and a value of the derivatives in each direction of a 2D function + CQDimRMeshTag the first dimension for the quadrature mesh + CQDimThetaMeshTag the second dimension for the quadrature mesh + CRBasisSubset + CRCellDim + CThetaBasisSubset + CThetaCellDim  CPolarSplineSpanA structure containing the two ChunkSpans necessary to define a reference to a spline on a set of polar basis splines  CPolarSplineViewA structure containing the two ChunkViews necessary to define a constant reference to a spline on a set of polar basis splines  CPreallocatableLagrangeInterpolatorA class which stores information necessary to create an instance of the LagrangeInterpolator class diff --git a/bsl__predcorr_8hpp_source.html b/bsl__predcorr_8hpp_source.html index 81a9bca46..21612ebef 100644 --- a/bsl__predcorr_8hpp_source.html +++ b/bsl__predcorr_8hpp_source.html @@ -144,7 +144,7 @@
66 GridR,
67 GridTheta,
68 PolarBSplinesRTheta,
-
69 SplineRThetaEvaluatorNullBound_host> const& m_poisson_solver;
+
69 SplineRThetaEvaluatorNullBound> const& m_poisson_solver;
70
71 SplineRThetaBuilder_host const& m_builder;
72 SplineRThetaEvaluatorNullBound_host const& m_spline_evaluator;
@@ -152,7 +152,7 @@
74
75public:
-
93 BslPredCorrRTheta(
+
93 BslPredCorrRTheta(
94 Mapping const& mapping,
95 BslAdvectionRTheta<FootFinder, Mapping> const& advection_solver,
96 SplineRThetaBuilder_host const& builder,
@@ -161,7 +161,7 @@
99 GridR,
100 GridTheta,
101 PolarBSplinesRTheta,
-
102 SplineRThetaEvaluatorNullBound_host> const& poisson_solver)
+
102 SplineRThetaEvaluatorNullBound> const& poisson_solver)
103 : m_mapping(mapping)
104 , m_advection_solver(advection_solver)
105 , m_poisson_solver(poisson_solver)
@@ -198,19 +198,19 @@
134 polar_spline_evaluator(extrapolation_rule);
135
136
-
137 host_t<DFieldMemRTheta> electrical_potential0(grid);
-
138
+
137 host_t<DFieldMemRTheta> electrical_potential0_host(grid);
+
138 DFieldMemRTheta electrical_potential0(grid);
139 host_t<Spline2DMem> allfdistribu_coef(get_spline_idx_range(m_builder));
140 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
141 PoissonLikeRHSFunction const
142 charge_density_coord(get_const_field(allfdistribu_coef), m_spline_evaluator);
143 m_poisson_solver(charge_density_coord, get_field(electrical_potential0));
-
144
+
144 ddc::parallel_deepcopy(electrical_potential0, electrical_potential0_host);
145 ddc::PdiEvent("iteration")
146 .with("iter", 0)
147 .and_with("time", 0)
148 .and_with("density", allfdistribu)
-
149 .and_with("electrical_potential", electrical_potential0);
+
149 .and_with("electrical_potential", electrical_potential0_host);
150
151
152 std::function<void(host_t<DVectorFieldRTheta<X, Y>>, host_t<DConstFieldRTheta>)>
@@ -238,50 +238,51 @@
174 host_t<DVectorFieldMemRTheta<X, Y>>,
175 Kokkos::DefaultHostExecutionSpace>
176 time_stepper(grid);
-
177 host_t<DFieldMemRTheta> electrical_potential(grid);
-
178 start_time = std::chrono::system_clock::now();
-
179 for (int iter(0); iter < steps; ++iter) {
-
180 time_stepper
-
181 .update(Kokkos::DefaultHostExecutionSpace(),
-
182 allfdistribu,
-
183 dt,
-
184 define_advection_field,
-
185 advect_allfdistribu);
-
186
+
177 DFieldMemRTheta electrical_potential(grid);
+
178 host_t<DFieldMemRTheta> electrical_potential_host(grid);
+
179 start_time = std::chrono::system_clock::now();
+
180 for (int iter(0); iter < steps; ++iter) {
+
181 time_stepper
+
182 .update(Kokkos::DefaultHostExecutionSpace(),
+
183 allfdistribu,
+
184 dt,
+
185 define_advection_field,
+
186 advect_allfdistribu);
187
-
188 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
-
189 PoissonLikeRHSFunction const
-
190 charge_density_coord(get_const_field(allfdistribu_coef), m_spline_evaluator);
-
191 m_poisson_solver(charge_density_coord, get_field(electrical_potential));
-
192
-
193 ddc::PdiEvent("iteration")
-
194 .with("iter", iter + 1)
-
195 .and_with("time", iter * dt)
-
196 .and_with("density", allfdistribu)
-
197 .and_with("electrical_potential", electrical_potential);
-
198 }
-
199 end_time = std::chrono::system_clock::now();
-
200
+
188
+
189 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
+
190 PoissonLikeRHSFunction const
+
191 charge_density_coord(get_const_field(allfdistribu_coef), m_spline_evaluator);
+
192 m_poisson_solver(charge_density_coord, get_field(electrical_potential));
+
193 ddc::parallel_deepcopy(electrical_potential_host, electrical_potential);
+
194 ddc::PdiEvent("iteration")
+
195 .with("iter", iter + 1)
+
196 .and_with("time", iter * dt)
+
197 .and_with("density", allfdistribu)
+
198 .and_with("electrical_potential", electrical_potential_host);
+
199 }
+
200 end_time = std::chrono::system_clock::now();
201
-
202 display_time_difference("Iterations time: ", start_time, end_time);
-
203
+
202
+
203 display_time_difference("Iterations time: ", start_time, end_time);
204
-
205 return allfdistribu;
-
206 }
+
205
+
206 return allfdistribu;
+
207 }
-
207};
+
208};
AdvectionFieldFinder
Solve the Poisson-like equation and return the electric field for the coupled Vlasov equation.
Definition advection_field_rp.hpp:92
BslAdvectionRTheta
Define an advection operator on 2D index range.
Definition bsl_advection_rp.hpp:59
BslPredCorrRTheta
Predictor-corrector for the Vlasov-Poisson equations.
Definition bsl_predcorr.hpp:59
-
BslPredCorrRTheta::BslPredCorrRTheta
BslPredCorrRTheta(Mapping const &mapping, BslAdvectionRTheta< FootFinder, Mapping > const &advection_solver, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver)
Instantiate a BslPredCorrRTheta.
Definition bsl_predcorr.hpp:93
+
BslPredCorrRTheta::BslPredCorrRTheta
BslPredCorrRTheta(Mapping const &mapping, BslAdvectionRTheta< FootFinder, Mapping > const &advection_solver, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver)
Instantiate a BslPredCorrRTheta.
Definition bsl_predcorr.hpp:93
BslPredCorrRTheta::operator()
host_t< DFieldRTheta > operator()(host_t< DFieldRTheta > allfdistribu, double const dt, int const steps) const
Solves on the equations system.
Definition bsl_predcorr.hpp:111
ITimeSolverRTheta
Base class for the time solvers.
Definition itimesolver.hpp:11
ITimeSolverRTheta::display_time_difference
void display_time_difference(std::string const &title, std::chrono::time_point< std::chrono::system_clock > const &start_time, std::chrono::time_point< std::chrono::system_clock > const &end_time) const
Displays the time difference between two given times and a title.
Definition itimesolver.hpp:47
PoissonLikeRHSFunction
Type of right-hand side (rhs) function of the Poisson equation.
Definition poisson_like_rhs_function.hpp:17
-
PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
static int constexpr continuity
The continuity enforced by the bsplines at the singular point.
Definition polar_bsplines.hpp:61
+
PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
static int constexpr continuity
The continuity enforced by the bsplines at the singular point.
Definition polar_bsplines.hpp:62
PolarSplineEvaluator
Define an evaluator on polar B-splines.
Definition polar_spline_evaluator.hpp:13
-
PolarSplineFEMPoissonLikeSolver
Define a polar PDE solver for a Poisson-like equation.
Definition polarpoissonlikesolver.hpp:50
+
PolarSplineFEMPoissonLikeSolver
Define a polar PDE solver for a Poisson-like equation.
Definition polarpoissonlikesolver.hpp:51
RK2
A class which provides an implementation of a second-order Runge-Kutta method.
Definition rk2.hpp:37
RK2::update
void update(ExecSpace const &exec_space, ValField y, double dt, std::function< void(DerivField, ValConstField)> dy_calculator, std::function< void(ValField, DerivConstField, double)> y_update) const final
Carry out one step of the Runge-Kutta scheme.
Definition rk2.hpp:77
VectorField
A class which holds multiple (scalar) fields in order to represent a vector field.
Definition vector_field.hpp:64
diff --git a/bsl__predcorr__second__order__explicit_8hpp_source.html b/bsl__predcorr__second__order__explicit_8hpp_source.html index 41cfe7e90..f580f0b9f 100644 --- a/bsl__predcorr__second__order__explicit_8hpp_source.html +++ b/bsl__predcorr__second__order__explicit_8hpp_source.html @@ -156,7 +156,7 @@
85 GridR,
86 GridTheta,
87 PolarBSplinesRTheta,
-
88 SplineRThetaEvaluatorNullBound_host> const& m_poisson_solver;
+
88 SplineRThetaEvaluatorNullBound> const& m_poisson_solver;
89
90 SplineRThetaBuilder_host const& m_builder;
91 SplineRThetaEvaluatorConstBound_host const& m_evaluator;
@@ -165,7 +165,7 @@
94
95public:
-
120 BslExplicitPredCorrRTheta(
+
120 BslExplicitPredCorrRTheta(
121 AdvectionDomain const& advection_domain,
122 Mapping const& mapping,
123 BslAdvectionRTheta<SplineFootFinderType, Mapping>& advection_solver,
@@ -176,7 +176,7 @@
128 GridR,
129 GridTheta,
130 PolarBSplinesRTheta,
-
131 SplineRThetaEvaluatorNullBound_host> const& poisson_solver,
+
131 SplineRThetaEvaluatorNullBound> const& poisson_solver,
132 SplineRThetaEvaluatorConstBound_host const& advection_evaluator)
133 : m_mapping(mapping)
134 , m_advection_solver(advection_solver)
@@ -212,155 +212,156 @@
162 IdxRangeBSTheta polar_idx_range(ddc::discrete_space<BSplinesTheta>().full_domain());
163
164 // --- Electrostatic potential (phi). -------------------------------------------------------------
-
165 host_t<DFieldMemRTheta> electrical_potential(grid);
-
166
-
167 host_t<SplinePolar> electrostatic_potential_coef(
-
168 PolarBSplinesRTheta::singular_idx_range<PolarBSplinesRTheta>(),
-
169 IdxRangeBSRTheta(radial_bsplines, polar_idx_range));
-
170
-
171 ddc::NullExtrapolationRule extrapolation_rule;
-
172 PolarSplineEvaluator<PolarBSplinesRTheta, ddc::NullExtrapolationRule, Kokkos::HostSpace>
-
173 polar_spline_evaluator(extrapolation_rule);
-
174
-
175 // --- For the computation of advection field from the electrostatic potential (phi): -------------
-
176 host_t<DVectorFieldMemRTheta<X, Y>> electric_field_alloc(grid);
-
177 host_t<DVectorFieldMemRTheta<X, Y>> electric_field_predicted_alloc(grid);
-
178 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_alloc(grid);
-
179 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_predicted_alloc(grid);
-
180
-
181 host_t<DVectorFieldRTheta<X, Y>> electric_field(electric_field_alloc);
-
182 host_t<DVectorFieldRTheta<X, Y>> electric_field_predicted(electric_field_predicted_alloc);
-
183 host_t<DVectorFieldRTheta<X, Y>> advection_field(advection_field_alloc);
-
184 host_t<DVectorFieldRTheta<X, Y>> advection_field_predicted(advection_field_predicted_alloc);
-
185
-
186 AdvectionFieldFinder advection_field_computer(m_mapping);
-
187
+
165 DFieldMemRTheta electrical_potential(grid);
+
166 host_t<DFieldMemRTheta> electrical_potential_host(grid);
+
167
+
168 host_t<SplinePolar> electrostatic_potential_coef(
+
169 PolarBSplinesRTheta::singular_idx_range<PolarBSplinesRTheta>(),
+
170 IdxRangeBSRTheta(radial_bsplines, polar_idx_range));
+
171
+
172 ddc::NullExtrapolationRule extrapolation_rule;
+
173 PolarSplineEvaluator<PolarBSplinesRTheta, ddc::NullExtrapolationRule, Kokkos::HostSpace>
+
174 polar_spline_evaluator(extrapolation_rule);
+
175
+
176 // --- For the computation of advection field from the electrostatic potential (phi): -------------
+
177 host_t<DVectorFieldMemRTheta<X, Y>> electric_field_alloc(grid);
+
178 host_t<DVectorFieldMemRTheta<X, Y>> electric_field_predicted_alloc(grid);
+
179 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_alloc(grid);
+
180 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_predicted_alloc(grid);
+
181
+
182 host_t<DVectorFieldRTheta<X, Y>> electric_field(electric_field_alloc);
+
183 host_t<DVectorFieldRTheta<X, Y>> electric_field_predicted(electric_field_predicted_alloc);
+
184 host_t<DVectorFieldRTheta<X, Y>> advection_field(advection_field_alloc);
+
185 host_t<DVectorFieldRTheta<X, Y>> advection_field_predicted(advection_field_predicted_alloc);
+
186
+
187 AdvectionFieldFinder advection_field_computer(m_mapping);
188
189
-
190 // --- Parameter for linearisation of advection field: --------------------------------------------
-
191 start_time = std::chrono::system_clock::now();
-
192 for (int iter(0); iter < steps; ++iter) {
-
193 double const time = iter * dt;
-
194 // STEP 1: From rho^n, we compute phi^n: Poisson equation
-
195 host_t<Spline2DMem> allfdistribu_coef(get_spline_idx_range(m_builder));
-
196 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
-
197 PoissonLikeRHSFunction const
-
198 charge_density_coord_1(get_const_field(allfdistribu_coef), m_evaluator);
-
199 m_poisson_solver(charge_density_coord_1, electrostatic_potential_coef);
-
200
-
201 polar_spline_evaluator(
-
202 get_field(electrical_potential),
-
203 get_const_field(coords),
-
204 electrostatic_potential_coef);
-
205
-
206 ddc::PdiEvent("iteration")
-
207 .with("iter", iter)
-
208 .and_with("time", time)
-
209 .and_with("density", allfdistribu)
-
210 .and_with("electrical_potential", electrical_potential);
-
211
-
212 // STEP 2: From phi^n, we compute A^n:
-
213 advection_field_computer(electrostatic_potential_coef, advection_field);
-
214
+
190
+
191 // --- Parameter for linearisation of advection field: --------------------------------------------
+
192 start_time = std::chrono::system_clock::now();
+
193 for (int iter(0); iter < steps; ++iter) {
+
194 double const time = iter * dt;
+
195 // STEP 1: From rho^n, we compute phi^n: Poisson equation
+
196 host_t<Spline2DMem> allfdistribu_coef(get_spline_idx_range(m_builder));
+
197 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
+
198 PoissonLikeRHSFunction const
+
199 charge_density_coord_1(get_const_field(allfdistribu_coef), m_evaluator);
+
200 m_poisson_solver(charge_density_coord_1, electrostatic_potential_coef);
+
201
+
202 polar_spline_evaluator(
+
203 get_field(electrical_potential_host),
+
204 get_const_field(coords),
+
205 electrostatic_potential_coef);
+
206
+
207 ddc::PdiEvent("iteration")
+
208 .with("iter", iter)
+
209 .and_with("time", time)
+
210 .and_with("density", allfdistribu)
+
211 .and_with("electrical_potential", electrical_potential_host);
+
212
+
213 // STEP 2: From phi^n, we compute A^n:
+
214 advection_field_computer(electrostatic_potential_coef, advection_field);
215
-
216 // STEP 3: From rho^n and A^n, we compute rho^P: Vlasov equation
-
217 // --- Copy rho^n because it will be modified:
-
218 host_t<DFieldMemRTheta> allfdistribu_predicted(grid);
-
219 ddc::parallel_deepcopy(get_field(allfdistribu_predicted), allfdistribu);
-
220 m_advection_solver(get_field(allfdistribu_predicted), get_field(advection_field), dt);
-
221
-
222 // --- advect also the feet because it is needed for the next step
-
223 host_t<FieldMemRTheta<CoordRTheta>> feet_coords(grid);
-
224 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
225 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
-
226 });
-
227 m_find_feet(get_field(feet_coords), get_field(advection_field), dt);
-
228
+
216
+
217 // STEP 3: From rho^n and A^n, we compute rho^P: Vlasov equation
+
218 // --- Copy rho^n because it will be modified:
+
219 host_t<DFieldMemRTheta> allfdistribu_predicted(grid);
+
220 ddc::parallel_deepcopy(get_field(allfdistribu_predicted), allfdistribu);
+
221 m_advection_solver(get_field(allfdistribu_predicted), get_field(advection_field), dt);
+
222
+
223 // --- advect also the feet because it is needed for the next step
+
224 host_t<FieldMemRTheta<CoordRTheta>> feet_coords(grid);
+
225 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
226 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
+
227 });
+
228 m_find_feet(get_field(feet_coords), get_field(advection_field), dt);
229
-
230 // STEP 4: From rho^P, we compute phi^P: Poisson equation
-
231 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu_predicted));
-
232 PoissonLikeRHSFunction const
-
233 charge_density_coord_4(get_const_field(allfdistribu_coef), m_evaluator);
-
234 m_poisson_solver(charge_density_coord_4, electrostatic_potential_coef);
-
235
-
236 // STEP 5: From phi^P, we compute A^P:
-
237 advection_field_computer(electrostatic_potential_coef, advection_field_predicted);
-
238
+
230
+
231 // STEP 4: From rho^P, we compute phi^P: Poisson equation
+
232 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu_predicted));
+
233 PoissonLikeRHSFunction const
+
234 charge_density_coord_4(get_const_field(allfdistribu_coef), m_evaluator);
+
235 m_poisson_solver(charge_density_coord_4, electrostatic_potential_coef);
+
236
+
237 // STEP 5: From phi^P, we compute A^P:
+
238 advection_field_computer(electrostatic_potential_coef, advection_field_predicted);
239
-
240 // --- we evaluate the advection field A^n at the characteristic feet X^P
-
241 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_evaluated(grid);
-
242 host_t<VectorSplineCoeffsMem2D<X, Y>> advection_field_coefs(
-
243 get_spline_idx_range(m_builder));
-
244
-
245 m_builder(
-
246 ddcHelper::get<X>(advection_field_coefs),
-
247 ddcHelper::get<X>(get_const_field(advection_field)));
-
248 m_builder(
-
249 ddcHelper::get<Y>(advection_field_coefs),
-
250 ddcHelper::get<Y>(get_const_field(advection_field)));
-
251
-
252 m_evaluator(
-
253 get_field(ddcHelper::get<X>(advection_field_evaluated)),
-
254 get_const_field(feet_coords),
-
255 ddcHelper::get<X>(get_const_field(advection_field_coefs)));
-
256 m_evaluator(
-
257 get_field(ddcHelper::get<Y>(advection_field_evaluated)),
-
258 get_const_field(feet_coords),
-
259 ddcHelper::get<Y>(get_const_field(advection_field_coefs)));
-
260
+
240
+
241 // --- we evaluate the advection field A^n at the characteristic feet X^P
+
242 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_evaluated(grid);
+
243 host_t<VectorSplineCoeffsMem2D<X, Y>> advection_field_coefs(
+
244 get_spline_idx_range(m_builder));
+
245
+
246 m_builder(
+
247 ddcHelper::get<X>(advection_field_coefs),
+
248 ddcHelper::get<X>(get_const_field(advection_field)));
+
249 m_builder(
+
250 ddcHelper::get<Y>(advection_field_coefs),
+
251 ddcHelper::get<Y>(get_const_field(advection_field)));
+
252
+
253 m_evaluator(
+
254 get_field(ddcHelper::get<X>(advection_field_evaluated)),
+
255 get_const_field(feet_coords),
+
256 ddcHelper::get<X>(get_const_field(advection_field_coefs)));
+
257 m_evaluator(
+
258 get_field(ddcHelper::get<Y>(advection_field_evaluated)),
+
259 get_const_field(feet_coords),
+
260 ddcHelper::get<Y>(get_const_field(advection_field_coefs)));
261
-
262 // STEP 6: From rho^n and (A^n(X^P) + A^P(X^n))/2, we compute rho^{n+1}: Vlasov equation
-
263 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
264 ddcHelper::get<X>(advection_field)(irp)
-
265 = (ddcHelper::get<X>(advection_field_evaluated)(irp)
-
266 + ddcHelper::get<X>(advection_field_predicted)(irp))
-
267 / 2.;
-
268 ddcHelper::get<Y>(advection_field)(irp)
-
269 = (ddcHelper::get<Y>(advection_field_evaluated)(irp)
-
270 + ddcHelper::get<Y>(advection_field_predicted)(irp))
-
271 / 2.;
-
272 });
-
273
+
262
+
263 // STEP 6: From rho^n and (A^n(X^P) + A^P(X^n))/2, we compute rho^{n+1}: Vlasov equation
+
264 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
265 ddcHelper::get<X>(advection_field)(irp)
+
266 = (ddcHelper::get<X>(advection_field_evaluated)(irp)
+
267 + ddcHelper::get<X>(advection_field_predicted)(irp))
+
268 / 2.;
+
269 ddcHelper::get<Y>(advection_field)(irp)
+
270 = (ddcHelper::get<Y>(advection_field_evaluated)(irp)
+
271 + ddcHelper::get<Y>(advection_field_predicted)(irp))
+
272 / 2.;
+
273 });
274
-
275 m_advection_solver(allfdistribu, get_field(advection_field), dt);
-
276 }
-
277
-
278 // STEP 1: From rho^n, we compute phi^n: Poisson equation
-
279 host_t<Spline2DMem> allfdistribu_coef(get_spline_idx_range(m_builder));
-
280 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
-
281 PoissonLikeRHSFunction const
-
282 charge_density_coord(get_const_field(allfdistribu_coef), m_evaluator);
-
283 m_poisson_solver(charge_density_coord, get_field(electrical_potential));
-
284
-
285 ddc::PdiEvent("last_iteration")
-
286 .with("iter", steps)
-
287 .and_with("time", steps * dt)
-
288 .and_with("density", allfdistribu)
-
289 .and_with("electrical_potential", electrical_potential);
-
290
+
275
+
276 m_advection_solver(allfdistribu, get_field(advection_field), dt);
+
277 }
+
278
+
279 // STEP 1: From rho^n, we compute phi^n: Poisson equation
+
280 host_t<Spline2DMem> allfdistribu_coef(get_spline_idx_range(m_builder));
+
281 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
+
282 PoissonLikeRHSFunction const
+
283 charge_density_coord(get_const_field(allfdistribu_coef), m_evaluator);
+
284 m_poisson_solver(charge_density_coord, get_field(electrical_potential));
+
285 ddc::parallel_deepcopy(electrical_potential_host, electrical_potential);
+
286 ddc::PdiEvent("last_iteration")
+
287 .with("iter", steps)
+
288 .and_with("time", steps * dt)
+
289 .and_with("density", allfdistribu)
+
290 .and_with("electrical_potential", electrical_potential_host);
291
-
292 end_time = std::chrono::system_clock::now();
-
293 display_time_difference("Iterations time: ", start_time, end_time);
-
294
+
292
+
293 end_time = std::chrono::system_clock::now();
+
294 display_time_difference("Iterations time: ", start_time, end_time);
295
-
296 return allfdistribu;
-
297 }
+
296
+
297 return allfdistribu;
+
298 }
-
298};
+
299};
AdvectionDomain
Define a domain for the advection.
Definition advection_domain.hpp:40
AdvectionFieldFinder
Solve the Poisson-like equation and return the electric field for the coupled Vlasov equation.
Definition advection_field_rp.hpp:92
BslAdvectionRTheta
Define an advection operator on 2D index range.
Definition bsl_advection_rp.hpp:59
BslExplicitPredCorrRTheta
A second order explicit predictor-corrector for the Vlasov-Poisson equations.
Definition bsl_predcorr_second_order_explicit.hpp:67
-
BslExplicitPredCorrRTheta::BslExplicitPredCorrRTheta
BslExplicitPredCorrRTheta(AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)
Instantiate a BslExplicitPredCorrRTheta.
Definition bsl_predcorr_second_order_explicit.hpp:120
BslExplicitPredCorrRTheta::operator()
host_t< DFieldRTheta > operator()(host_t< DFieldRTheta > allfdistribu, double const dt, int const steps) const final
Solves on the equations system.
Definition bsl_predcorr_second_order_explicit.hpp:146
+
BslExplicitPredCorrRTheta::BslExplicitPredCorrRTheta
BslExplicitPredCorrRTheta(AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)
Instantiate a BslExplicitPredCorrRTheta.
Definition bsl_predcorr_second_order_explicit.hpp:120
Euler
A class which provides an implementation of an explicit Euler method.
Definition euler.hpp:33
ITimeSolverRTheta
Base class for the time solvers.
Definition itimesolver.hpp:11
ITimeSolverRTheta::display_time_difference
void display_time_difference(std::string const &title, std::chrono::time_point< std::chrono::system_clock > const &start_time, std::chrono::time_point< std::chrono::system_clock > const &end_time) const
Displays the time difference between two given times and a title.
Definition itimesolver.hpp:47
PoissonLikeRHSFunction
Type of right-hand side (rhs) function of the Poisson equation.
Definition poisson_like_rhs_function.hpp:17
-
PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
static int constexpr continuity
The continuity enforced by the bsplines at the singular point.
Definition polar_bsplines.hpp:61
+
PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
static int constexpr continuity
The continuity enforced by the bsplines at the singular point.
Definition polar_bsplines.hpp:62
PolarSplineEvaluator
Define an evaluator on polar B-splines.
Definition polar_spline_evaluator.hpp:13
-
PolarSplineFEMPoissonLikeSolver
Define a polar PDE solver for a Poisson-like equation.
Definition polarpoissonlikesolver.hpp:50
+
PolarSplineFEMPoissonLikeSolver
Define a polar PDE solver for a Poisson-like equation.
Definition polarpoissonlikesolver.hpp:51
SplineFootFinder
Define a base class for all the time integration methods used for the advection.
Definition spline_foot_finder.hpp:26
GridR
Definition geometry.hpp:116
GridTheta
Definition geometry.hpp:119
diff --git a/bsl__predcorr__second__order__implicit_8hpp_source.html b/bsl__predcorr__second__order__implicit_8hpp_source.html index fe04a150a..977a65784 100644 --- a/bsl__predcorr__second__order__implicit_8hpp_source.html +++ b/bsl__predcorr__second__order__implicit_8hpp_source.html @@ -154,7 +154,7 @@
84 GridR,
85 GridTheta,
86 PolarBSplinesRTheta,
-
87 SplineRThetaEvaluatorNullBound_host> const& m_poisson_solver;
+
87 SplineRThetaEvaluatorNullBound> const& m_poisson_solver;
88
89 SplineRThetaBuilder_host const& m_builder;
90 SplineRThetaEvaluatorConstBound_host const& m_evaluator;
@@ -163,7 +163,7 @@
93
94public:
-
119 BslImplicitPredCorrRTheta(
+
119 BslImplicitPredCorrRTheta(
120 AdvectionDomain const& advection_domain,
121 Mapping const& mapping,
122 BslAdvectionRTheta<SplineFootFinderType, Mapping> const& advection_solver,
@@ -174,7 +174,7 @@
127 GridR,
128 GridTheta,
129 PolarBSplinesRTheta,
-
130 SplineRThetaEvaluatorNullBound_host> const& poisson_solver,
+
130 SplineRThetaEvaluatorNullBound> const& poisson_solver,
131 SplineRThetaEvaluatorConstBound_host const& advection_evaluator)
132 : m_mapping(mapping)
133 , m_advection_solver(advection_solver)
@@ -210,288 +210,290 @@
161 IdxRangeBSTheta polar_idx_range(ddc::discrete_space<BSplinesTheta>().full_domain());
162
163 // --- Electrostatic potential (phi). -------------------------------------------------------------
-
164 host_t<DFieldMemRTheta> electrical_potential(grid);
-
165
-
166 host_t<SplinePolar> electrostatic_potential_coef(
-
167 PolarBSplinesRTheta::singular_idx_range<PolarBSplinesRTheta>(),
-
168 IdxRangeBSRTheta(radial_bsplines, polar_idx_range));
-
169
-
170 ddc::NullExtrapolationRule extrapolation_rule;
-
171 PolarSplineEvaluator<PolarBSplinesRTheta, ddc::NullExtrapolationRule, Kokkos::HostSpace>
-
172 polar_spline_evaluator(extrapolation_rule);
-
173
-
174 // --- For the computation of advection field from the electrostatic potential (phi): -------------
-
175 host_t<DVectorFieldMemRTheta<X, Y>> electric_field_alloc(grid);
-
176 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_alloc(grid);
-
177 host_t<DVectorFieldRTheta<X, Y>> electric_field(electric_field_alloc);
-
178 host_t<DVectorFieldRTheta<X, Y>> advection_field(advection_field_alloc);
-
179
-
180 AdvectionFieldFinder advection_field_computer(m_mapping);
-
181
-
182 start_time = std::chrono::system_clock::now();
-
183 for (int iter(0); iter < steps; ++iter) {
-
184 // STEP 1: From rho^n, we compute phi^n: Poisson equation
-
185 host_t<Spline2DMem> allfdistribu_coef(get_spline_idx_range(m_builder));
-
186 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
-
187 PoissonLikeRHSFunction const
-
188 charge_density_coord_1(get_const_field(allfdistribu_coef), m_evaluator);
-
189 m_poisson_solver(charge_density_coord_1, electrostatic_potential_coef);
-
190
-
191 polar_spline_evaluator(
-
192 get_field(electrical_potential),
-
193 get_const_field(coords),
-
194 electrostatic_potential_coef);
-
195
-
196 ddc::PdiEvent("iteration")
-
197 .with("iter", iter)
-
198 .and_with("time", iter * dt)
-
199 .and_with("density", allfdistribu)
-
200 .and_with("electrical_potential", electrical_potential);
-
201
+
164 DFieldMemRTheta electrical_potential(grid);
+
165 host_t<DFieldMemRTheta> electrical_potential_host(grid);
+
166
+
167 host_t<SplinePolar> electrostatic_potential_coef(
+
168 PolarBSplinesRTheta::singular_idx_range<PolarBSplinesRTheta>(),
+
169 IdxRangeBSRTheta(radial_bsplines, polar_idx_range));
+
170
+
171 ddc::NullExtrapolationRule extrapolation_rule;
+
172 PolarSplineEvaluator<PolarBSplinesRTheta, ddc::NullExtrapolationRule, Kokkos::HostSpace>
+
173 polar_spline_evaluator(extrapolation_rule);
+
174
+
175 // --- For the computation of advection field from the electrostatic potential (phi): -------------
+
176 host_t<DVectorFieldMemRTheta<X, Y>> electric_field_alloc(grid);
+
177 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_alloc(grid);
+
178 host_t<DVectorFieldRTheta<X, Y>> electric_field(electric_field_alloc);
+
179 host_t<DVectorFieldRTheta<X, Y>> advection_field(advection_field_alloc);
+
180
+
181 AdvectionFieldFinder advection_field_computer(m_mapping);
+
182
+
183 start_time = std::chrono::system_clock::now();
+
184 for (int iter(0); iter < steps; ++iter) {
+
185 // STEP 1: From rho^n, we compute phi^n: Poisson equation
+
186 host_t<Spline2DMem> allfdistribu_coef(get_spline_idx_range(m_builder));
+
187 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
+
188 PoissonLikeRHSFunction const
+
189 charge_density_coord_1(get_const_field(allfdistribu_coef), m_evaluator);
+
190 m_poisson_solver(charge_density_coord_1, electrostatic_potential_coef);
+
191
+
192 polar_spline_evaluator(
+
193 get_field(electrical_potential_host),
+
194 get_const_field(coords),
+
195 electrostatic_potential_coef);
+
196
+
197 ddc::PdiEvent("iteration")
+
198 .with("iter", iter)
+
199 .and_with("time", iter * dt)
+
200 .and_with("density", allfdistribu)
+
201 .and_with("electrical_potential", electrical_potential_host);
202
-
203 // STEP 2: From phi^n, we compute A^n:
-
204 advection_field_computer(electrostatic_potential_coef, advection_field);
-
205
+
203
+
204 // STEP 2: From phi^n, we compute A^n:
+
205 advection_field_computer(electrostatic_potential_coef, advection_field);
206
-
207 // STEP 3: From rho^n and A^n, we compute rho^P: Vlasov equation
-
208 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_k(grid);
-
209 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_k_tot(grid);
-
210
-
211 host_t<VectorSplineCoeffsMem2D<X, Y>> advection_field_coefs_k(
-
212 get_spline_idx_range(m_builder));
-
213 m_builder(
-
214 ddcHelper::get<X>(advection_field_coefs_k),
-
215 ddcHelper::get<X>(get_const_field(advection_field)));
-
216 m_builder(
-
217 ddcHelper::get<Y>(advection_field_coefs_k),
-
218 ddcHelper::get<Y>(get_const_field(advection_field)));
-
219
-
220 host_t<FieldMemRTheta<CoordRTheta>> feet_coords(grid);
-
221 host_t<FieldMemRTheta<CoordRTheta>> feet_coords_tmp(grid);
-
222
+
207
+
208 // STEP 3: From rho^n and A^n, we compute rho^P: Vlasov equation
+
209 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_k(grid);
+
210 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_k_tot(grid);
+
211
+
212 host_t<VectorSplineCoeffsMem2D<X, Y>> advection_field_coefs_k(
+
213 get_spline_idx_range(m_builder));
+
214 m_builder(
+
215 ddcHelper::get<X>(advection_field_coefs_k),
+
216 ddcHelper::get<X>(get_const_field(advection_field)));
+
217 m_builder(
+
218 ddcHelper::get<Y>(advection_field_coefs_k),
+
219 ddcHelper::get<Y>(get_const_field(advection_field)));
+
220
+
221 host_t<FieldMemRTheta<CoordRTheta>> feet_coords(grid);
+
222 host_t<FieldMemRTheta<CoordRTheta>> feet_coords_tmp(grid);
223
-
224 // initialisation:
-
225 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
226 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
-
227 });
-
228
-
229 const double tau = 1e-6;
-
230 implicit_loop(
-
231 advection_field,
-
232 get_const_field(advection_field_coefs_k),
-
233 get_field(feet_coords),
-
234 dt / 4.,
-
235 tau);
-
236
-
237 // Evaluate A^n at X^P:
-
238 m_evaluator(
-
239 get_field(ddcHelper::get<X>(advection_field_k)),
-
240 get_const_field(feet_coords),
-
241 ddcHelper::get<X>(get_const_field(advection_field_coefs_k)));
-
242 m_evaluator(
-
243 get_field(ddcHelper::get<Y>(advection_field_k)),
-
244 get_const_field(feet_coords),
-
245 ddcHelper::get<Y>(get_const_field(advection_field_coefs_k)));
-
246
-
247 // Compute the new advection field (E^n(X^n) + E^n(X^P)) /2:
-
248 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
249 ddcHelper::get<X>(advection_field_k_tot)(irp)
-
250 = (ddcHelper::get<X>(advection_field)(irp)
-
251 + ddcHelper::get<X>(advection_field_k)(irp))
-
252 / 2.;
-
253 ddcHelper::get<Y>(advection_field_k_tot)(irp)
-
254 = (ddcHelper::get<Y>(advection_field)(irp)
-
255 + ddcHelper::get<Y>(advection_field_k)(irp))
-
256 / 2.;
-
257 });
-
258
+
224
+
225 // initialisation:
+
226 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
227 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
+
228 });
+
229
+
230 const double tau = 1e-6;
+
231 implicit_loop(
+
232 advection_field,
+
233 get_const_field(advection_field_coefs_k),
+
234 get_field(feet_coords),
+
235 dt / 4.,
+
236 tau);
+
237
+
238 // Evaluate A^n at X^P:
+
239 m_evaluator(
+
240 get_field(ddcHelper::get<X>(advection_field_k)),
+
241 get_const_field(feet_coords),
+
242 ddcHelper::get<X>(get_const_field(advection_field_coefs_k)));
+
243 m_evaluator(
+
244 get_field(ddcHelper::get<Y>(advection_field_k)),
+
245 get_const_field(feet_coords),
+
246 ddcHelper::get<Y>(get_const_field(advection_field_coefs_k)));
+
247
+
248 // Compute the new advection field (E^n(X^n) + E^n(X^P)) /2:
+
249 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
250 ddcHelper::get<X>(advection_field_k_tot)(irp)
+
251 = (ddcHelper::get<X>(advection_field)(irp)
+
252 + ddcHelper::get<X>(advection_field_k)(irp))
+
253 / 2.;
+
254 ddcHelper::get<Y>(advection_field_k_tot)(irp)
+
255 = (ddcHelper::get<Y>(advection_field)(irp)
+
256 + ddcHelper::get<Y>(advection_field_k)(irp))
+
257 / 2.;
+
258 });
259
-
260 // X^P = X^n - dt/2 * ( E^n(X^n) + E^n(X^P) )/2:
-
261 // --- Copy phi^n because it will be modified:
-
262 host_t<DFieldMemRTheta> allfdistribu_predicted(grid);
-
263 ddc::parallel_deepcopy(allfdistribu_predicted, allfdistribu);
-
264 m_advection_solver(
-
265 get_field(allfdistribu_predicted),
-
266 get_const_field(advection_field_k_tot),
-
267 dt / 2.);
-
268
-
269 // --- advect also the feet because it is needed for the next step
-
270 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
271 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
-
272 });
-
273 m_foot_finder(get_field(feet_coords), get_const_field(advection_field_k_tot), dt / 2.);
-
274
+
260
+
261 // X^P = X^n - dt/2 * ( E^n(X^n) + E^n(X^P) )/2:
+
262 // --- Copy phi^n because it will be modified:
+
263 host_t<DFieldMemRTheta> allfdistribu_predicted(grid);
+
264 ddc::parallel_deepcopy(allfdistribu_predicted, allfdistribu);
+
265 m_advection_solver(
+
266 get_field(allfdistribu_predicted),
+
267 get_const_field(advection_field_k_tot),
+
268 dt / 2.);
+
269
+
270 // --- advect also the feet because it is needed for the next step
+
271 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
272 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
+
273 });
+
274 m_foot_finder(get_field(feet_coords), get_const_field(advection_field_k_tot), dt / 2.);
275
-
276 // STEP 4: From rho^P, we compute phi^P: Poisson equation
-
277 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
-
278 PoissonLikeRHSFunction const
-
279 charge_density_coord_4(get_const_field(allfdistribu_coef), m_evaluator);
-
280 m_poisson_solver(charge_density_coord_4, electrostatic_potential_coef);
-
281
-
282 // STEP 5: From phi^P, we compute A^P:
-
283 advection_field_computer(electrostatic_potential_coef, advection_field);
-
284
+
276
+
277 // STEP 4: From rho^P, we compute phi^P: Poisson equation
+
278 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
+
279 PoissonLikeRHSFunction const
+
280 charge_density_coord_4(get_const_field(allfdistribu_coef), m_evaluator);
+
281 m_poisson_solver(charge_density_coord_4, electrostatic_potential_coef);
+
282
+
283 // STEP 5: From phi^P, we compute A^P:
+
284 advection_field_computer(electrostatic_potential_coef, advection_field);
285
-
286 // STEP 6: From rho^n and A^P, we compute rho^{n+1}: Vlasov equation
-
287 m_builder(
-
288 ddcHelper::get<X>(advection_field_coefs_k),
-
289 ddcHelper::get<X>(get_const_field(advection_field)));
-
290 m_builder(
-
291 ddcHelper::get<Y>(advection_field_coefs_k),
-
292 ddcHelper::get<Y>(get_const_field(advection_field)));
-
293
+
286
+
287 // STEP 6: From rho^n and A^P, we compute rho^{n+1}: Vlasov equation
+
288 m_builder(
+
289 ddcHelper::get<X>(advection_field_coefs_k),
+
290 ddcHelper::get<X>(get_const_field(advection_field)));
+
291 m_builder(
+
292 ddcHelper::get<Y>(advection_field_coefs_k),
+
293 ddcHelper::get<Y>(get_const_field(advection_field)));
294
-
295 // initialisation:
-
296 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
297 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
-
298 });
-
299
-
300 implicit_loop(
-
301 advection_field,
-
302 get_const_field(advection_field_coefs_k),
-
303 get_field(feet_coords),
-
304 dt / 2.,
-
305 tau);
-
306
-
307 // Evaluate A^P at X^P:
-
308 m_evaluator(
-
309 get_field(ddcHelper::get<X>(advection_field_k)),
-
310 get_const_field(feet_coords),
-
311 ddcHelper::get<X>(get_const_field(advection_field_coefs_k)));
-
312 m_evaluator(
-
313 get_field(ddcHelper::get<Y>(advection_field_k)),
-
314 get_const_field(feet_coords),
-
315 ddcHelper::get<Y>(get_const_field(advection_field_coefs_k)));
-
316
-
317 // Computed advection field (A^P(X^n) + A^P(X^P)) /2:
-
318 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
319 ddcHelper::get<X>(advection_field_k_tot)(irp)
-
320 = (ddcHelper::get<X>(advection_field)(irp)
-
321 + ddcHelper::get<X>(advection_field_k)(irp))
-
322 / 2.;
-
323 ddcHelper::get<Y>(advection_field_k_tot)(irp)
-
324 = (ddcHelper::get<Y>(advection_field)(irp)
-
325 + ddcHelper::get<Y>(advection_field_k)(irp))
-
326 / 2.;
-
327 });
-
328 // X^k = X^n - dt * ( A^P(X^n) + A^P(X^P) )/2
-
329 m_advection_solver(allfdistribu, get_const_field(advection_field_k_tot), dt);
-
330 }
-
331
-
332 // STEP 1: From rho^n, we compute phi^n: Poisson equation
-
333 host_t<Spline2DMem> allfdistribu_coef(get_spline_idx_range(m_builder));
-
334 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
-
335 PoissonLikeRHSFunction const
-
336 charge_density_coord(get_const_field(allfdistribu_coef), m_evaluator);
-
337 m_poisson_solver(charge_density_coord, get_field(electrical_potential));
-
338
-
339 ddc::PdiEvent("last_iteration")
-
340 .with("iter", steps)
-
341 .and_with("time", steps * dt)
-
342 .and_with("density", allfdistribu)
-
343 .and_with("electrical_potential", electrical_potential);
-
344
-
345 end_time = std::chrono::system_clock::now();
-
346 display_time_difference("Iterations time: ", start_time, end_time);
-
347
-
348
+
295
+
296 // initialisation:
+
297 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
298 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
+
299 });
+
300
+
301 implicit_loop(
+
302 advection_field,
+
303 get_const_field(advection_field_coefs_k),
+
304 get_field(feet_coords),
+
305 dt / 2.,
+
306 tau);
+
307
+
308 // Evaluate A^P at X^P:
+
309 m_evaluator(
+
310 get_field(ddcHelper::get<X>(advection_field_k)),
+
311 get_const_field(feet_coords),
+
312 ddcHelper::get<X>(get_const_field(advection_field_coefs_k)));
+
313 m_evaluator(
+
314 get_field(ddcHelper::get<Y>(advection_field_k)),
+
315 get_const_field(feet_coords),
+
316 ddcHelper::get<Y>(get_const_field(advection_field_coefs_k)));
+
317
+
318 // Computed advection field (A^P(X^n) + A^P(X^P)) /2:
+
319 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
320 ddcHelper::get<X>(advection_field_k_tot)(irp)
+
321 = (ddcHelper::get<X>(advection_field)(irp)
+
322 + ddcHelper::get<X>(advection_field_k)(irp))
+
323 / 2.;
+
324 ddcHelper::get<Y>(advection_field_k_tot)(irp)
+
325 = (ddcHelper::get<Y>(advection_field)(irp)
+
326 + ddcHelper::get<Y>(advection_field_k)(irp))
+
327 / 2.;
+
328 });
+
329 // X^k = X^n - dt * ( A^P(X^n) + A^P(X^P) )/2
+
330 m_advection_solver(allfdistribu, get_const_field(advection_field_k_tot), dt);
+
331 }
+
332
+
333 // STEP 1: From rho^n, we compute phi^n: Poisson equation
+
334 host_t<Spline2DMem> allfdistribu_coef(get_spline_idx_range(m_builder));
+
335 m_builder(get_field(allfdistribu_coef), get_const_field(allfdistribu));
+
336 PoissonLikeRHSFunction const
+
337 charge_density_coord(get_const_field(allfdistribu_coef), m_evaluator);
+
338 m_poisson_solver(charge_density_coord, get_field(electrical_potential));
+
339 ddc::parallel_deepcopy(electrical_potential_host, electrical_potential);
+
340
+
341 ddc::PdiEvent("last_iteration")
+
342 .with("iter", steps)
+
343 .and_with("time", steps * dt)
+
344 .and_with("density", allfdistribu)
+
345 .and_with("electrical_potential", electrical_potential_host);
+
346
+
347 end_time = std::chrono::system_clock::now();
+
348 display_time_difference("Iterations time: ", start_time, end_time);
349
-
350 return allfdistribu;
-
351 }
+
350
+
351
+
352 return allfdistribu;
+
353 }
-
352
-
353
354
-
355private:
-
356 double compute_square_polar_distance(CoordRTheta const& coord1, CoordRTheta const& coord2) const
-
357 {
-
358 CoordXY coord_xy1(m_mapping(coord1));
-
359 CoordXY coord_xy2(m_mapping(coord2));
-
360
-
361 const double x1 = ddc::select<X>(coord_xy1);
-
362 const double y1 = ddc::select<Y>(coord_xy1);
-
363 const double x2 = ddc::select<X>(coord_xy2);
-
364 const double y2 = ddc::select<Y>(coord_xy2);
-
365
-
366 return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
-
367 }
-
368
-
369
-
370 void implicit_loop(
-
371 host_t<DVectorFieldRTheta<X, Y>> advection_field,
-
372 host_t<ConstVectorSplineCoeffs2D<X, Y>> advection_field_coefs_k,
-
373 host_t<FieldRTheta<CoordRTheta>> feet_coords,
-
374 double const dt,
-
375 double const tau) const
-
376 {
-
377 IdxRangeRTheta const grid = get_idx_range(advection_field);
-
378 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_k(grid);
-
379 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_k_tot(grid);
-
380 host_t<FieldMemRTheta<CoordRTheta>> feet_coords_tmp(grid);
-
381
-
382 double square_difference_feet = 0.;
-
383 int count = 0;
-
384 const int max_count = 50;
-
385 do {
-
386 count++;
-
387
-
388 // Evaluate A at X^{k-1}:
-
389 m_evaluator(
-
390 get_field(ddcHelper::get<X>(advection_field_k)),
-
391 get_const_field(feet_coords),
-
392 ddcHelper::get<X>(advection_field_coefs_k));
-
393 m_evaluator(
-
394 get_field(ddcHelper::get<Y>(advection_field_k)),
-
395 get_const_field(feet_coords),
-
396 ddcHelper::get<Y>(advection_field_coefs_k));
-
397
-
398 // Compute the new advection field A(X^n) + A(X^{k-1}):
-
399 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
400 ddcHelper::get<X>(advection_field_k_tot)(irp)
-
401 = ddcHelper::get<X>(advection_field)(irp)
-
402 + ddcHelper::get<X>(advection_field_k)(irp);
-
403 ddcHelper::get<Y>(advection_field_k_tot)(irp)
-
404 = ddcHelper::get<Y>(advection_field)(irp)
-
405 + ddcHelper::get<Y>(advection_field_k)(irp);
-
406 });
-
407
-
408 // X^{k-1} = X^k:
-
409 ddc::parallel_deepcopy(feet_coords_tmp, feet_coords);
-
410
-
411 // X^k = X^n - dt* X^k:
-
412 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
413 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
-
414 });
-
415 m_foot_finder(feet_coords, get_const_field(advection_field_k_tot), dt);
-
416
-
417
-
418 // Convergence test:
-
419 square_difference_feet = 0.;
-
420 ddc::for_each(grid, [&](IdxRTheta const irp) {
-
421 double sqr_diff_feet
-
422 = compute_square_polar_distance(feet_coords(irp), feet_coords_tmp(irp));
-
423 square_difference_feet = square_difference_feet > sqr_diff_feet
-
424 ? square_difference_feet
-
425 : sqr_diff_feet;
-
426 });
-
427
-
428 } while ((square_difference_feet > tau * tau) and (count < max_count));
-
429 }
-
430};
+
355
+
356
+
357private:
+
358 double compute_square_polar_distance(CoordRTheta const& coord1, CoordRTheta const& coord2) const
+
359 {
+
360 CoordXY coord_xy1(m_mapping(coord1));
+
361 CoordXY coord_xy2(m_mapping(coord2));
+
362
+
363 const double x1 = ddc::select<X>(coord_xy1);
+
364 const double y1 = ddc::select<Y>(coord_xy1);
+
365 const double x2 = ddc::select<X>(coord_xy2);
+
366 const double y2 = ddc::select<Y>(coord_xy2);
+
367
+
368 return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
+
369 }
+
370
+
371
+
372 void implicit_loop(
+
373 host_t<DVectorFieldRTheta<X, Y>> advection_field,
+
374 host_t<ConstVectorSplineCoeffs2D<X, Y>> advection_field_coefs_k,
+
375 host_t<FieldRTheta<CoordRTheta>> feet_coords,
+
376 double const dt,
+
377 double const tau) const
+
378 {
+
379 IdxRangeRTheta const grid = get_idx_range(advection_field);
+
380 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_k(grid);
+
381 host_t<DVectorFieldMemRTheta<X, Y>> advection_field_k_tot(grid);
+
382 host_t<FieldMemRTheta<CoordRTheta>> feet_coords_tmp(grid);
+
383
+
384 double square_difference_feet = 0.;
+
385 int count = 0;
+
386 const int max_count = 50;
+
387 do {
+
388 count++;
+
389
+
390 // Evaluate A at X^{k-1}:
+
391 m_evaluator(
+
392 get_field(ddcHelper::get<X>(advection_field_k)),
+
393 get_const_field(feet_coords),
+
394 ddcHelper::get<X>(advection_field_coefs_k));
+
395 m_evaluator(
+
396 get_field(ddcHelper::get<Y>(advection_field_k)),
+
397 get_const_field(feet_coords),
+
398 ddcHelper::get<Y>(advection_field_coefs_k));
+
399
+
400 // Compute the new advection field A(X^n) + A(X^{k-1}):
+
401 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
402 ddcHelper::get<X>(advection_field_k_tot)(irp)
+
403 = ddcHelper::get<X>(advection_field)(irp)
+
404 + ddcHelper::get<X>(advection_field_k)(irp);
+
405 ddcHelper::get<Y>(advection_field_k_tot)(irp)
+
406 = ddcHelper::get<Y>(advection_field)(irp)
+
407 + ddcHelper::get<Y>(advection_field_k)(irp);
+
408 });
+
409
+
410 // X^{k-1} = X^k:
+
411 ddc::parallel_deepcopy(feet_coords_tmp, feet_coords);
+
412
+
413 // X^k = X^n - dt* X^k:
+
414 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
415 feet_coords(irp) = CoordRTheta(ddc::coordinate(irp));
+
416 });
+
417 m_foot_finder(feet_coords, get_const_field(advection_field_k_tot), dt);
+
418
+
419
+
420 // Convergence test:
+
421 square_difference_feet = 0.;
+
422 ddc::for_each(grid, [&](IdxRTheta const irp) {
+
423 double sqr_diff_feet
+
424 = compute_square_polar_distance(feet_coords(irp), feet_coords_tmp(irp));
+
425 square_difference_feet = square_difference_feet > sqr_diff_feet
+
426 ? square_difference_feet
+
427 : sqr_diff_feet;
+
428 });
+
429
+
430 } while ((square_difference_feet > tau * tau) and (count < max_count));
+
431 }
+
432};
AdvectionDomain
Define a domain for the advection.
Definition advection_domain.hpp:40
AdvectionFieldFinder
Solve the Poisson-like equation and return the electric field for the coupled Vlasov equation.
Definition advection_field_rp.hpp:92
BslAdvectionRTheta
Define an advection operator on 2D index range.
Definition bsl_advection_rp.hpp:59
BslImplicitPredCorrRTheta
A second order implicit predictor-corrector for the Vlasov-Poisson equations.
Definition bsl_predcorr_second_order_implicit.hpp:67
+
BslImplicitPredCorrRTheta::BslImplicitPredCorrRTheta
BslImplicitPredCorrRTheta(AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > const &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)
Instantiate a BslImplicitPredCorrRTheta.
Definition bsl_predcorr_second_order_implicit.hpp:119
BslImplicitPredCorrRTheta::operator()
host_t< DFieldRTheta > operator()(host_t< DFieldRTheta > allfdistribu, double const dt, int const steps) const final
Solves on the equations system.
Definition bsl_predcorr_second_order_implicit.hpp:145
-
BslImplicitPredCorrRTheta::BslImplicitPredCorrRTheta
BslImplicitPredCorrRTheta(AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > const &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)
Instantiate a BslImplicitPredCorrRTheta.
Definition bsl_predcorr_second_order_implicit.hpp:119
Euler
A class which provides an implementation of an explicit Euler method.
Definition euler.hpp:33
ITimeSolverRTheta
Base class for the time solvers.
Definition itimesolver.hpp:11
ITimeSolverRTheta::display_time_difference
void display_time_difference(std::string const &title, std::chrono::time_point< std::chrono::system_clock > const &start_time, std::chrono::time_point< std::chrono::system_clock > const &end_time) const
Displays the time difference between two given times and a title.
Definition itimesolver.hpp:47
PoissonLikeRHSFunction
Type of right-hand side (rhs) function of the Poisson equation.
Definition poisson_like_rhs_function.hpp:17
-
PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
static int constexpr continuity
The continuity enforced by the bsplines at the singular point.
Definition polar_bsplines.hpp:61
+
PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
static int constexpr continuity
The continuity enforced by the bsplines at the singular point.
Definition polar_bsplines.hpp:62
PolarSplineEvaluator
Define an evaluator on polar B-splines.
Definition polar_spline_evaluator.hpp:13
-
PolarSplineFEMPoissonLikeSolver
Define a polar PDE solver for a Poisson-like equation.
Definition polarpoissonlikesolver.hpp:50
+
PolarSplineFEMPoissonLikeSolver
Define a polar PDE solver for a Poisson-like equation.
Definition polarpoissonlikesolver.hpp:51
SplineFootFinder
Define a base class for all the time integration methods used for the advection.
Definition spline_foot_finder.hpp:26
VectorField
A class which holds multiple (scalar) fields in order to represent a vector field.
Definition vector_field.hpp:64
GridR
Definition geometry.hpp:116
diff --git a/cartesian__to__circular_8hpp_source.html b/cartesian__to__circular_8hpp_source.html index 37b856ae7..f7930c620 100644 --- a/cartesian__to__circular_8hpp_source.html +++ b/cartesian__to__circular_8hpp_source.html @@ -248,8 +248,8 @@
CircularToCartesian
A class for describing the circular 2D mapping.
Definition circular_to_cartesian.hpp:43
R
Define non periodic real R dimension.
Definition geometry.hpp:31
Theta
Define periodic real Theta dimension.
Definition geometry.hpp:42
-
X
Define non periodic real X dimension.
Definition geometry.hpp:277
-
Y
Define non periodic real Y dimension.
Definition geometry.hpp:288
+
X
Define non periodic real X dimension.
Definition geometry.hpp:318
+
Y
Define non periodic real Y dimension.
Definition geometry.hpp:329
diff --git a/cartesian__to__czarny_8hpp_source.html b/cartesian__to__czarny_8hpp_source.html index 6e1002448..32ff51174 100644 --- a/cartesian__to__czarny_8hpp_source.html +++ b/cartesian__to__czarny_8hpp_source.html @@ -217,8 +217,8 @@
CzarnyToCartesian
A class for describing the Czarny 2D mapping.
Definition czarny_to_cartesian.hpp:50
R
Define non periodic real R dimension.
Definition geometry.hpp:31
Theta
Define periodic real Theta dimension.
Definition geometry.hpp:42
-
X
Define non periodic real X dimension.
Definition geometry.hpp:277
-
Y
Define non periodic real Y dimension.
Definition geometry.hpp:288
+
X
Define non periodic real X dimension.
Definition geometry.hpp:318
+
Y
Define non periodic real Y dimension.
Definition geometry.hpp:329
diff --git a/circular__to__cartesian_8hpp_source.html b/circular__to__cartesian_8hpp_source.html index 3a5a32c7e..c934f8c28 100644 --- a/circular__to__cartesian_8hpp_source.html +++ b/circular__to__cartesian_8hpp_source.html @@ -315,8 +315,8 @@
CircularToCartesian::CircularToCartesian
KOKKOS_FUNCTION CircularToCartesian(CircularToCartesian const &other)
Instantiate a CircularToCartesian from another CircularToCartesian (lvalue).
Definition circular_to_cartesian.hpp:68
R
Define non periodic real R dimension.
Definition geometry.hpp:31
Theta
Define periodic real Theta dimension.
Definition geometry.hpp:42
-
X
Define non periodic real X dimension.
Definition geometry.hpp:277
-
Y
Define non periodic real Y dimension.
Definition geometry.hpp:288
+
X
Define non periodic real X dimension.
Definition geometry.hpp:318
+
Y
Define non periodic real Y dimension.
Definition geometry.hpp:329
diff --git a/classBslExplicitPredCorrRTheta-members.html b/classBslExplicitPredCorrRTheta-members.html index baf4a814a..326c1f42e 100644 --- a/classBslExplicitPredCorrRTheta-members.html +++ b/classBslExplicitPredCorrRTheta-members.html @@ -109,7 +109,7 @@

This is the complete list of members for BslExplicitPredCorrRTheta< Mapping, AdvectionDomain >, including all inherited members.

- + diff --git a/classBslExplicitPredCorrRTheta.html b/classBslExplicitPredCorrRTheta.html index 2974e7be6..9821efd70 100644 --- a/classBslExplicitPredCorrRTheta.html +++ b/classBslExplicitPredCorrRTheta.html @@ -124,9 +124,9 @@
BslExplicitPredCorrRTheta(AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)BslExplicitPredCorrRTheta< Mapping, AdvectionDomain >inline
BslExplicitPredCorrRTheta(AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)BslExplicitPredCorrRTheta< Mapping, AdvectionDomain >inline
display_time_difference(std::string const &title, std::chrono::time_point< std::chrono::system_clock > const &start_time, std::chrono::time_point< std::chrono::system_clock > const &end_time) constITimeSolverRThetainlineprotected
operator()(host_t< DFieldRTheta > allfdistribu, double const dt, int const steps) const finalBslExplicitPredCorrRTheta< Mapping, AdvectionDomain >inlinevirtual
~ITimeSolverRTheta()=default (defined in ITimeSolverRTheta)ITimeSolverRThetavirtual
- - - + + + @@ -171,8 +171,8 @@

Constructor & Destructor Documentation

- -

◆ BslExplicitPredCorrRTheta()

+ +

◆ BslExplicitPredCorrRTheta()

@@ -221,7 +221,7 @@

- + diff --git a/classBslExplicitPredCorrRTheta.js b/classBslExplicitPredCorrRTheta.js index 48f6d99da..d227b1ed7 100644 --- a/classBslExplicitPredCorrRTheta.js +++ b/classBslExplicitPredCorrRTheta.js @@ -1,5 +1,5 @@ var classBslExplicitPredCorrRTheta = [ - [ "BslExplicitPredCorrRTheta", "classBslExplicitPredCorrRTheta.html#a06242b4dc42f0275ebd48935a822a41e", null ], + [ "BslExplicitPredCorrRTheta", "classBslExplicitPredCorrRTheta.html#af3274e5a2342ff8b6446622d48cd4ecf", null ], [ "operator()", "classBslExplicitPredCorrRTheta.html#aaeabe916423e28d00c1ab8e0d8a4db54", null ] ]; \ No newline at end of file diff --git a/classBslImplicitPredCorrRTheta-members.html b/classBslImplicitPredCorrRTheta-members.html index d5b96a7d7..53bc6d24c 100644 --- a/classBslImplicitPredCorrRTheta-members.html +++ b/classBslImplicitPredCorrRTheta-members.html @@ -109,7 +109,7 @@

This is the complete list of members for BslImplicitPredCorrRTheta< Mapping, AdvectionDomain >, including all inherited members.

Public Member Functions

 BslExplicitPredCorrRTheta (AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)
 Instantiate a BslExplicitPredCorrRTheta.
 
 BslExplicitPredCorrRTheta (AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)
 Instantiate a BslExplicitPredCorrRTheta.
 
host_t< DFieldRTheta > operator() (host_t< DFieldRTheta > allfdistribu, double const dt, int const steps) const final
 Solves on \( T = dt*N \) the equations system.
 
PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const & PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &  poisson_solver,
- + diff --git a/classBslImplicitPredCorrRTheta.html b/classBslImplicitPredCorrRTheta.html index c99e0ebae..cb528ce27 100644 --- a/classBslImplicitPredCorrRTheta.html +++ b/classBslImplicitPredCorrRTheta.html @@ -124,9 +124,9 @@
BslImplicitPredCorrRTheta(AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > const &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)BslImplicitPredCorrRTheta< Mapping, AdvectionDomain >inline
BslImplicitPredCorrRTheta(AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > const &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)BslImplicitPredCorrRTheta< Mapping, AdvectionDomain >inline
display_time_difference(std::string const &title, std::chrono::time_point< std::chrono::system_clock > const &start_time, std::chrono::time_point< std::chrono::system_clock > const &end_time) constITimeSolverRThetainlineprotected
operator()(host_t< DFieldRTheta > allfdistribu, double const dt, int const steps) const finalBslImplicitPredCorrRTheta< Mapping, AdvectionDomain >inlinevirtual
~ITimeSolverRTheta()=default (defined in ITimeSolverRTheta)ITimeSolverRThetavirtual
- - - + + + @@ -181,8 +181,8 @@

Constructor & Destructor Documentation

- -

◆ BslImplicitPredCorrRTheta()

+ +

◆ BslImplicitPredCorrRTheta()

@@ -231,7 +231,7 @@

- + diff --git a/classBslImplicitPredCorrRTheta.js b/classBslImplicitPredCorrRTheta.js index 07dcda5ce..646bc3a84 100644 --- a/classBslImplicitPredCorrRTheta.js +++ b/classBslImplicitPredCorrRTheta.js @@ -1,5 +1,5 @@ var classBslImplicitPredCorrRTheta = [ - [ "BslImplicitPredCorrRTheta", "classBslImplicitPredCorrRTheta.html#a6bd04e7ccba156c98c4516ae0a3a3cae", null ], + [ "BslImplicitPredCorrRTheta", "classBslImplicitPredCorrRTheta.html#a27731f9a9c3e076aca10206bb0bfd3ba", null ], [ "operator()", "classBslImplicitPredCorrRTheta.html#a35fb8dc2ae119da7ed06f1f8dc2d439e", null ] ]; \ No newline at end of file diff --git a/classBslPredCorrRTheta-members.html b/classBslPredCorrRTheta-members.html index fb8ce3c23..b1ec88e5f 100644 --- a/classBslPredCorrRTheta-members.html +++ b/classBslPredCorrRTheta-members.html @@ -109,7 +109,7 @@

This is the complete list of members for BslPredCorrRTheta< Mapping, FootFinder >, including all inherited members.

Public Member Functions

 BslImplicitPredCorrRTheta (AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > const &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)
 Instantiate a BslImplicitPredCorrRTheta.
 
 BslImplicitPredCorrRTheta (AdvectionDomain const &advection_domain, Mapping const &mapping, BslAdvectionRTheta< SplineFootFinderType, Mapping > const &advection_solver, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver, SplineRThetaEvaluatorConstBound_host const &advection_evaluator)
 Instantiate a BslImplicitPredCorrRTheta.
 
host_t< DFieldRTheta > operator() (host_t< DFieldRTheta > allfdistribu, double const dt, int const steps) const final
 Solves on \( T = dt*N \) the equations system.
 
PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const & PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &  poisson_solver,
- + diff --git a/classBslPredCorrRTheta.html b/classBslPredCorrRTheta.html index f6b6a9832..da71b4c12 100644 --- a/classBslPredCorrRTheta.html +++ b/classBslPredCorrRTheta.html @@ -124,9 +124,9 @@
BslPredCorrRTheta(Mapping const &mapping, BslAdvectionRTheta< FootFinder, Mapping > const &advection_solver, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver)BslPredCorrRTheta< Mapping, FootFinder >inline
BslPredCorrRTheta(Mapping const &mapping, BslAdvectionRTheta< FootFinder, Mapping > const &advection_solver, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver)BslPredCorrRTheta< Mapping, FootFinder >inline
display_time_difference(std::string const &title, std::chrono::time_point< std::chrono::system_clock > const &start_time, std::chrono::time_point< std::chrono::system_clock > const &end_time) constITimeSolverRThetainlineprotected
operator()(host_t< DFieldRTheta > allfdistribu, double const dt, int const steps) constBslPredCorrRTheta< Mapping, FootFinder >inlinevirtual
~ITimeSolverRTheta()=default (defined in ITimeSolverRTheta)ITimeSolverRThetavirtual
- - - + + + @@ -168,8 +168,8 @@

Constructor & Destructor Documentation

- -

◆ BslPredCorrRTheta()

+ +

◆ BslPredCorrRTheta()

@@ -206,7 +206,7 @@

- + diff --git a/classBslPredCorrRTheta.js b/classBslPredCorrRTheta.js index 4b4b52b73..de6a8f1b1 100644 --- a/classBslPredCorrRTheta.js +++ b/classBslPredCorrRTheta.js @@ -1,5 +1,5 @@ var classBslPredCorrRTheta = [ - [ "BslPredCorrRTheta", "classBslPredCorrRTheta.html#a82df60ba134e54e107c105544ef15763", null ], + [ "BslPredCorrRTheta", "classBslPredCorrRTheta.html#ac5a6457ec7d54f8fbb926aca93a55069", null ], [ "operator()", "classBslPredCorrRTheta.html#ad47f1c1d3fb1b113fee4bd955272a5b0", null ] ]; \ No newline at end of file diff --git a/classPolarSplineFEMPoissonLikeSolver-members.html b/classPolarSplineFEMPoissonLikeSolver-members.html index 3f22af710..d09d0cff1 100644 --- a/classPolarSplineFEMPoissonLikeSolver-members.html +++ b/classPolarSplineFEMPoissonLikeSolver-members.html @@ -103,18 +103,30 @@
-
PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull > Member List
+
PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull > Member List
-

This is the complete list of members for PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >, including all inherited members.

+

This is the complete list of members for PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >, including all inherited members.

Public Member Functions

 BslPredCorrRTheta (Mapping const &mapping, BslAdvectionRTheta< FootFinder, Mapping > const &advection_solver, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver)
 Instantiate a BslPredCorrRTheta.
 
 BslPredCorrRTheta (Mapping const &mapping, BslAdvectionRTheta< FootFinder, Mapping > const &advection_solver, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &rhs_evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver)
 Instantiate a BslPredCorrRTheta.
 
host_t< DFieldRTheta > operator() (host_t< DFieldRTheta > allfdistribu, double const dt, int const steps) const
 Solves on \( T = dt*N \) the equations system.
 
PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const & PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &  poisson_solver 
- - - - - - + + + + + + + + + + + + + + + + + +
init_nnz_per_line(Kokkos::View< int *, Kokkos::LayoutRight > nnz) constPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >inline
operator()(RHSFunction const &rhs, host_t< SplinePolar > &spline) constPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >inline
operator()(RHSFunction const &rhs, host_t< DFieldRTheta > phi) constPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >inline
PolarSplineFEMPoissonLikeSolver(host_t< ConstSpline2D > coeff_alpha, host_t< ConstSpline2D > coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound_host const &spline_evaluator)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >inline
R typedefPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >
Theta typedefPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >
compute_overlapping_singular_elements(ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator, Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inline
compute_singular_elements(ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator, Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inline
compute_stencil_elements(ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator, Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inline
fill_int_volume(Mapping const &mapping)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inline
get_matrix_stencil_element(IdxBSRTheta idx_test, IdxBSRTheta idx_trial, ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, SplineRThetaEvaluatorNullBound const &evaluator, Mapping const &mapping)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inline
get_quadrature_points_in_cell(int cell_idx_r, int cell_idx_theta)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inlinestatic
get_value_and_gradient(double &value, std::array< double, 2 > &gradient, EvalDeriv1DType const &r_basis, EvalDeriv1DType const &theta_basis)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inlinestatic
get_value_and_gradient(double &value, std::array< double, 2 > &gradient, EvalDeriv2DType const &basis, EvalDeriv2DType const &)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inlinestatic
IdxCell typedefPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >
init_nnz_per_line(Kokkos::View< int *, Kokkos::LayoutRight > nnz) constPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inline
operator()(RHSFunction const &rhs, host_t< SplinePolar > &spline) constPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inline
operator()(RHSFunction const &rhs, DFieldRTheta phi) constPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inline
PolarSplineFEMPoissonLikeSolver(ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inline
R typedefPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >
templated_weak_integral_element(IdxQuadratureR idx_r, IdxQuadratureTheta idx_theta, TestValDerivType const &test_bspline_val_and_deriv, TrialValDerivType const &trial_bspline_val_and_deriv, TestValDerivType const &test_bspline_val_and_deriv_theta, TrialValDerivType const &trial_bspline_val_and_deriv_theta, ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, SplineRThetaEvaluatorNullBound const &spline_evaluator, Mapping const &mapping, DField< IdxRangeQuadratureRTheta > int_volume)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inlinestatic
Theta typedefPolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >
theta_mod(int idx_theta)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inlinestatic
weak_integral_element(IdxQuadratureR idx_r, IdxQuadratureTheta idx_theta, EvalDeriv2DType const &test_bspline_val_and_deriv, EvalDeriv2DType const &trial_bspline_val_and_deriv, ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, SplineRThetaEvaluatorNullBound const &evaluator, Mapping const &mapping, DField< IdxRangeQuadratureRTheta > int_volume)PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >inlinestatic
diff --git a/classPolarSplineFEMPoissonLikeSolver.html b/classPolarSplineFEMPoissonLikeSolver.html index 96ab7090e..d1ae21ff4 100644 --- a/classPolarSplineFEMPoissonLikeSolver.html +++ b/classPolarSplineFEMPoissonLikeSolver.html @@ -5,7 +5,7 @@ -Gyselalib++: PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull > Class Template Reference +Gyselalib++: PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull > Class Template Reference @@ -107,8 +107,9 @@ Classes | Public Types | Public Member Functions | +Static Public Member Functions | List of all members -
PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull > Class Template Reference
+
PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull > Class Template Reference
@@ -117,6 +118,12 @@ + + + + + + @@ -134,36 +141,83 @@

Classes

struct  EvalDeriv1DType
 Object storing a value and a value of the derivative of a 1D function. More...
 
struct  EvalDeriv2DType
 Object storing a value and a value of the derivatives in each direction of a 2D function. More...
 
struct  QDimRMesh
 Tag the first dimension for the quadrature mesh. More...
 
- - - - + + - - + + + + +

Public Types

+
using R = typename GridR::continuous_dimension_type
 The radial dimension.
 
+
 The radial dimension.
 
using Theta = typename GridTheta::continuous_dimension_type
 The poloidal dimension.
 
 The poloidal dimension.
 
+using IdxCell = Idx< RCellDim, ThetaCellDim >
 Tag an index of cell.
 
- - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Public Member Functions

template<class Mapping >
 PolarSplineFEMPoissonLikeSolver (host_t< ConstSpline2D > coeff_alpha, host_t< ConstSpline2D > coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound_host const &spline_evaluator)
 Instantiate a polar Poisson-like solver using FEM with B-splines.
 
template<class RHSFunction >
void operator() (RHSFunction const &rhs, host_t< SplinePolar > &spline) const
 Solve the Poisson-like equation.
 
template<class RHSFunction >
void operator() (RHSFunction const &rhs, host_t< DFieldRTheta > phi) const
 Solve the Poisson-like equation.
 
void init_nnz_per_line (Kokkos::View< int *, Kokkos::LayoutRight > nnz) const
 Fills the nnz data structure by computing the number of non-zero per line.
 
template<class Mapping >
 PolarSplineFEMPoissonLikeSolver (ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator)
 Instantiate a polar Poisson-like solver using FEM with B-splines.
 
template<class Mapping >
void fill_int_volume (Mapping const &mapping)
 Compute the volume integrals and stores the values in a member variable.
 
template<class Mapping >
void compute_singular_elements (ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator, Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host)
 Computes the matrix element corresponding to the singular area.
 
template<class Mapping >
void compute_overlapping_singular_elements (ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator, Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host)
 Computes the matrix element corresponding to singular elements overlapping with regular grid.
 
template<class Mapping >
void compute_stencil_elements (ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator, Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host)
 Computes the matrix element corresponding to the regular stencil ie: out to singular or overlapping areas.
 
template<class RHSFunction >
void operator() (RHSFunction const &rhs, host_t< SplinePolar > &spline) const
 Solve the Poisson-like equation.
 
template<class RHSFunction >
void operator() (RHSFunction const &rhs, DFieldRTheta phi) const
 Solve the Poisson-like equation.
 
template<class Mapping >
double get_matrix_stencil_element (IdxBSRTheta idx_test, IdxBSRTheta idx_trial, ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, SplineRThetaEvaluatorNullBound const &evaluator, Mapping const &mapping)
 Computes the matrix element corresponding to two tensor product splines with index idx_test and idx_trial.
 
void init_nnz_per_line (Kokkos::View< int *, Kokkos::LayoutRight > nnz) const
 Fills the nnz data structure by computing the number of non-zero per line.
 
+ + + + + + + + + + + + + + + + + + + + +

+Static Public Member Functions

static KOKKOS_FUNCTION IdxRangeQuadratureRTheta get_quadrature_points_in_cell (int cell_idx_r, int cell_idx_theta)
 compute the quadrature range for a given pair of indices
 
template<class Mapping >
static KOKKOS_FUNCTION double weak_integral_element (IdxQuadratureR idx_r, IdxQuadratureTheta idx_theta, EvalDeriv2DType const &test_bspline_val_and_deriv, EvalDeriv2DType const &trial_bspline_val_and_deriv, ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, SplineRThetaEvaluatorNullBound const &evaluator, Mapping const &mapping, DField< IdxRangeQuadratureRTheta > int_volume)
 compute the weak integral value.
 
static KOKKOS_INLINE_FUNCTION void get_value_and_gradient (double &value, std::array< double, 2 > &gradient, EvalDeriv1DType const &r_basis, EvalDeriv1DType const &theta_basis)
 Computes the value and gradient from r_basis and theta_basis inputs.
 
static KOKKOS_INLINE_FUNCTION void get_value_and_gradient (double &value, std::array< double, 2 > &gradient, EvalDeriv2DType const &basis, EvalDeriv2DType const &)
 Computes the value and gradient from r_basis and theta_basis inputs.
 
template<class Mapping , class TestValDerivType , class TrialValDerivType >
static KOKKOS_FUNCTION double templated_weak_integral_element (IdxQuadratureR idx_r, IdxQuadratureTheta idx_theta, TestValDerivType const &test_bspline_val_and_deriv, TrialValDerivType const &trial_bspline_val_and_deriv, TestValDerivType const &test_bspline_val_and_deriv_theta, TrialValDerivType const &trial_bspline_val_and_deriv_theta, ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, SplineRThetaEvaluatorNullBound const &spline_evaluator, Mapping const &mapping, DField< IdxRangeQuadratureRTheta > int_volume)
 Computes a quadrature summand corresponding to the inner product.
 
static KOKKOS_FUNCTION int theta_mod (int idx_theta)
 Calculates the modulo idx_theta in relation to cells number along \( \theta \) direction .
 

Detailed Description

-
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound_host, class IdxRangeFull = IdxRange<GridR, GridTheta>>
-class PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >

Define a polar PDE solver for a Poisson-like equation.

+
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound, class IdxRangeFull = IdxRange<GridR, GridTheta>>
+class PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >

Define a polar PDE solver for a Poisson-like equation.

Solve the following Partial Differential Equation

(1) \( L\phi = - \nabla \cdot (\alpha \nabla \phi) + \beta \phi = \rho \), in \( \Omega\),

\( \phi = 0 \), on \( \partial \Omega\),

@@ -174,13 +228,81 @@ - - + +
GridRThe radial grid type.
GridRThe poloidal grid type.
PolarBSplinesRThetaThe type of the 2D polar bsplines (on the coordinate system (r,theta) including bsplines which traverse the O point).
SplineRThetaEvaluatorNullBound_hostThe type of the 2D (cross-product) spline evaluator.
PolarBSplinesRThetaThe type of the 2D polar bsplines (on the coordinate system \((r,\theta)\) including bsplines which traverse the O point).
SplineRThetaEvaluatorNullBoundThe type of the 2D (cross-product) spline evaluator.
IdxRangeFullThe full index range of \( \phi \) including any batch dimensions.

Class Documentation

+ +

◆ PolarSplineFEMPoissonLikeSolver::EvalDeriv1DType

+ +
+
+ + + + +
struct PolarSplineFEMPoissonLikeSolver::EvalDeriv1DType
+
+
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound, class IdxRangeFull = IdxRange<GridR, GridTheta>>
+struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::EvalDeriv1DType

Object storing a value and a value of the derivative of a 1D function.

+
+ + + + + + + +
Class Members
+double +value +
+double +derivative +
+ +
+
+ +

◆ PolarSplineFEMPoissonLikeSolver::EvalDeriv2DType

+ +
+
+ + + + +
struct PolarSplineFEMPoissonLikeSolver::EvalDeriv2DType
+
+
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound, class IdxRangeFull = IdxRange<GridR, GridTheta>>
+struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::EvalDeriv2DType

Object storing a value and a value of the derivatives in each direction of a 2D function.

+
+ + + + + + + + + + +
Class Members
+double +value +
+double +radial_derivative +
+double +poloidal_derivative +
+ +
+

◆ PolarSplineFEMPoissonLikeSolver::RBasisSubset

@@ -192,8 +314,8 @@

-
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound_host, class IdxRangeFull = IdxRange<GridR, GridTheta>>
-struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::RBasisSubset
+
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound, class IdxRangeFull = IdxRange<GridR, GridTheta>>
+struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::RBasisSubset

@@ -207,8 +329,8 @@

-
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound_host, class IdxRangeFull = IdxRange<GridR, GridTheta>>
-struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::RCellDim
+
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound, class IdxRangeFull = IdxRange<GridR, GridTheta>>
+struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::RCellDim
@@ -222,8 +344,8 @@

-
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound_host, class IdxRangeFull = IdxRange<GridR, GridTheta>>
-struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::ThetaBasisSubset
+
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound, class IdxRangeFull = IdxRange<GridR, GridTheta>>
+struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::ThetaBasisSubset
@@ -237,18 +359,18 @@

-
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound_host, class IdxRangeFull = IdxRange<GridR, GridTheta>>
-struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::ThetaCellDim
+
template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound, class IdxRangeFull = IdxRange<GridR, GridTheta>>
+struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::ThetaCellDim

Constructor & Destructor Documentation

- -

◆ PolarSplineFEMPoissonLikeSolver()

+ +

◆ PolarSplineFEMPoissonLikeSolver()

-template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound_host , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
template<class Mapping >
@@ -256,15 +378,15 @@

- + - + - + @@ -276,7 +398,7 @@

- + @@ -301,7 +423,7 @@

[in]

- +
PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::PolarSplineFEMPoissonLikeSolver PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::PolarSplineFEMPoissonLikeSolver (host_t< ConstSpline2D > ConstSpline2D  coeff_alpha,
host_t< ConstSpline2D > ConstSpline2D  coeff_beta,
SplineRThetaEvaluatorNullBound_host const & SplineRThetaEvaluatorNullBound const &  spline_evaluator 
coeff_alphaThe spline representation of the \( \alpha \) function in the definition of the Poisson-like equation.
[in]coeff_betaThe spline representation of the \( \beta \) function in the definition of the Poisson-like equation.
[in]mappingThe mapping from the logical index range to the physical index range where the equation is defined.
[in]spline_evaluatorAn evaluator for evaluating 2D splines on (r, theta)
[in]spline_evaluatorAn evaluator for evaluating 2D splines on \((r,\theta)\).
@@ -315,35 +437,109 @@

Member Function Documentation

- -

◆ operator()() [1/2]

+ +

◆ fill_int_volume()

-template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound_host , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
-template<class RHSFunction >
+template<class Mapping >
+ + +
- + - - + + + + +
void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::operator() void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::fill_int_volume (RHSFunction const & rhs, Mapping const & mapping)
+ 		+inline
+
+ +

Compute the volume integrals and stores the values in a member variable.

+
Parameters
+ + +
[in]mappingThe mapping from the logical index range to the physical index range where the equation is defined.
+
+
+
Template Parameters
+ + +
MappingA class describing a mapping from curvilinear coordinates to cartesian coordinates.
+
+
+ +
+ + +

◆ compute_singular_elements()

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+
+template<class Mapping >
+ + + @@ -353,25 +549,198 @@

-

Solve the Poisson-like equation.

-

This operator returns the coefficients associated with the B-Splines of the solution \(\phi\).

+

Computes the matrix element corresponding to the singular area.

+

ie: the region enclosing the O-point.

Parameters

+ + + + + + - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - +
void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::compute_singular_elements (ConstSpline2D coeff_alpha,
host_t< SplinePolar > & spline ConstSpline2D coeff_beta,
Mapping const & mapping,
SplineRThetaEvaluatorNullBound const & spline_evaluator,
Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host,
Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host,
Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host 
) const
- - + + + + + + + +
[in]rhsThe rhs \( \rho\) of the Poisson-like equation. The type is templated but we can use the PoissonLikeRHSFunction class.
[in,out]splineThe spline representation of the solution \(\phi\), also used as initial data for the iterative solver.
[in]coeff_alphaThe spline representation of the \( \alpha \) function in the definition of the Poisson-like equation.
[in]coeff_betaThe spline representation of the \( \beta \) function in the definition of the Poisson-like equation.
[in]mappingThe mapping from the logical index range to the physical index range where the equation is defined.
[in]spline_evaluatorAn evaluator for evaluating 2D splines on \((r,\theta)\).
[out]values_csr_hostA 2D Kokkos view which stores the values of non-zero elements for the whole batch.
[out]col_idx_csr_hostA 1D Kokkos view which stores the column indices for each non-zero component.(only for one matrix).
[in,out]nnz_per_row_csr_hostA 1D Kokkos view of length matrix_size+1 which stores the count of the non-zeros along the lines of the matrix.
+ + + +
+
+ +

◆ compute_overlapping_singular_elements()

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+
+template<class Mapping >
+ + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::compute_overlapping_singular_elements (ConstSpline2D coeff_alpha,
ConstSpline2D coeff_beta,
Mapping const & mapping,
SplineRThetaEvaluatorNullBound const & spline_evaluator,
Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host,
Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host,
Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host 
)
+ 		+inline
+
+ +

Computes the matrix element corresponding to singular elements overlapping with regular grid.

+
Parameters
+ + + + + + + + +
[in]coeff_alphaThe spline representation of the \( \alpha \) function in the definition of the Poisson-like equation.
[in]coeff_betaThe spline representation of the \( \beta \) function in the definition of the Poisson-like equation.
[in]mappingThe mapping from the logical index range to the physical index range where the equation is defined.
[in]spline_evaluatorAn evaluator for evaluating 2D splines on \((r,\theta)\).
[out]values_csr_hostA 2D Kokkos view which stores the values of non-zero elements for the whole batch.
[out]col_idx_csr_hostA 1D Kokkos view which stores the column indices for each non-zero component.(only for one matrix)
[in,out]nnz_per_row_csr_hostA 1D Kokkos view of length matrix_size+1 which stores the count of the non-zeros along the lines of the matrix.
+
+
+ +
+
+ +

◆ compute_stencil_elements()

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+
+template<class Mapping >
+ + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::compute_stencil_elements (ConstSpline2D coeff_alpha,
ConstSpline2D coeff_beta,
Mapping const & mapping,
SplineRThetaEvaluatorNullBound const & spline_evaluator,
Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host,
Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host,
Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host 
)
+ 		+inline
+
+ +

Computes the matrix element corresponding to the regular stencil ie: out to singular or overlapping areas.

+
Parameters
+ + + + + + + +
[in]coeff_alphaThe spline representation of the \( \alpha \) function in the definition of the Poisson-like equation.
[in]coeff_betaThe spline representation of the \( \beta \) function in the definition of the Poisson-like equation.
[in]mappingThe mapping from the logical index range to the physical index range where the equation is defined.
[in]spline_evaluatorAn evaluator for evaluating 2D splines on \((r,\theta)\).
[out]values_csr_hostA 2D Kokkos view which stores the values of non-zero elements for the whole batch.
[out]col_idx_csr_hostA 1D Kokkos view which stores the column indices for each non-zero component.(only for one matrix)
[in,out]nnz_per_row_csr_hostA 1D Kokkos view of length matrix_size+1 which stores the count of the non-zeros along the lines of the matrix.
- -

◆ operator()() [2/2]

+ +

◆ operator()() [1/2]

-template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound_host , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
template<class RHSFunction >
@@ -379,7 +748,7 @@

- + @@ -387,8 +756,8 @@

- - + + @@ -404,30 +773,576 @@

Solve the Poisson-like equation.

-

This operator uses the other operator () and returns the values on the grid of the solution \(\phi\).

+

This operator returns the coefficients associated with the B-Splines of the solution \(\phi\).

Parameters

void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::operator() void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::operator() ( RHSFunction const &  rhs, host_t< DFieldRTheta > phi host_t< SplinePolar > & spline 
- + +
[in]rhsThe rhs \( \rho\) of the Poisson-like equation. The type is templated but we can use the PoissonLikeRHSFunction class.
[in,out]phiThe values of the solution \(\phi\) on the given coords_eval, also used as initial data for the iterative solver.
[in,out]splineThe spline representation of the solution \(\phi\), also used as initial data for the iterative solver.
+ + + +
+ + +

◆ operator()() [2/2]

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+
+template<class RHSFunction >
+ + + + + +
+ + + + + + + + + + + + + + + + + + +
void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::operator() (RHSFunction const & rhs,
DFieldRTheta phi 
) const
+ 		+inline
+
+ +

Solve the Poisson-like equation.

+

This operator uses the other operator () and returns the values on the grid of the solution \(\phi\).

+
Parameters
+ + + +
[in]rhsThe rhs \( \rho\) of the Poisson-like equation. The type is templated but we can use the PoissonLikeRHSFunction class.
[in,out]phiThe values of the solution \(\phi\) on the given coords_eval, also used as initial data for the iterative solver.
+
+
+ +
+
+ +

◆ get_quadrature_points_in_cell()

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+ + + + + +
+ + + + + + + + + + + + + + + + + + +
static KOKKOS_FUNCTION IdxRangeQuadratureRTheta PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::get_quadrature_points_in_cell (int cell_idx_r,
int cell_idx_theta 
)
+ 		+inlinestatic
+
+ +

compute the quadrature range for a given pair of indices

+
Parameters
+ + + +
[in]cell_idx_rThe index for radial direction
[in]cell_idx_thetaThe index for poloidal direction
+
+
+
Returns
The quadrature range corresponding to the \((r,\theta)\) indices.
+ +
+
+ +

◆ weak_integral_element()

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+
+template<class Mapping >
+ + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
static KOKKOS_FUNCTION double PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::weak_integral_element (IdxQuadratureR idx_r,
IdxQuadratureTheta idx_theta,
EvalDeriv2DType const & test_bspline_val_and_deriv,
EvalDeriv2DType const & trial_bspline_val_and_deriv,
ConstSpline2D coeff_alpha,
ConstSpline2D coeff_beta,
SplineRThetaEvaluatorNullBound const & evaluator,
Mapping const & mapping,
DField< IdxRangeQuadratureRTheta > int_volume 
)
+ 		+inlinestatic
+
+ +

compute the weak integral value.

+
Parameters
+ + + + + + + + + + +
[in]idx_rThe index for radial direction.
[in]idx_thetaThe index for poloidal direction
[in]test_bspline_val_and_derivThe data structure containing the derivatives over radial and poloidal directions for test space.
[in]trial_bspline_val_and_derivThe data structure containing the derivatives over radial and poloidal directions for trial space.
[in]coeff_alphaThe spline representation of the \( \alpha \) function in the definition of the Poisson-like equation.
[in]coeff_betaThe spline representation of the \( \beta \) function in the definition of the Poisson-like equation.
[in]mappingThe mapping from the logical index range to the physical index range where the equation is defined.
[in]evaluatorAn evaluator for evaluating 2D splines on \((r,\theta)\).
[in]int_volumeThe integral volume associated with each point used in the quadrature scheme.
+
+
+
Returns
The value of the weak integral.
+ +
+
+ +

◆ get_value_and_gradient() [1/2]

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+ + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
static KOKKOS_INLINE_FUNCTION void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::get_value_and_gradient (double & value,
std::array< double, 2 > & gradient,
EvalDeriv1DType const & r_basis,
EvalDeriv1DType const & theta_basis 
)
+ 		+inlinestatic
+
+ +

Computes the value and gradient from r_basis and theta_basis inputs.

+
Parameters
+ + + + + +
[out]valueThe product of radial and poloidal values.
[out]gradientderivatives over \( (r, \theta) \) directions.
[in]r_basisA data structure containing values and derivative over radial direction.
[in]theta_basisA data structure containing values and derivative over poloidal direction.
+
+
+ +
+
+ +

◆ get_value_and_gradient() [2/2]

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+ + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
static KOKKOS_INLINE_FUNCTION void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::get_value_and_gradient (double & value,
std::array< double, 2 > & gradient,
EvalDeriv2DType const & basis,
EvalDeriv2DType const &  
)
+ 		+inlinestatic
+
+ +

Computes the value and gradient from r_basis and theta_basis inputs.

+
Parameters
+ + + + +
[out]valueThe product of radial and poloidal values.
[out]gradientderivatives over \( (r, \theta) \) directions.
[in]basisA data structure containing values and derivative over radial and poloidal directions.
+
+
+ +
+
+ +

◆ templated_weak_integral_element()

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+
+template<class Mapping , class TestValDerivType , class TrialValDerivType >
+ + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
static KOKKOS_FUNCTION double PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::templated_weak_integral_element (IdxQuadratureR idx_r,
IdxQuadratureTheta idx_theta,
TestValDerivType const & test_bspline_val_and_deriv,
TrialValDerivType const & trial_bspline_val_and_deriv,
TestValDerivType const & test_bspline_val_and_deriv_theta,
TrialValDerivType const & trial_bspline_val_and_deriv_theta,
ConstSpline2D coeff_alpha,
ConstSpline2D coeff_beta,
SplineRThetaEvaluatorNullBound const & spline_evaluator,
Mapping const & mapping,
DField< IdxRangeQuadratureRTheta > int_volume 
)
+ 		+inlinestatic
+
+ +

Computes a quadrature summand corresponding to the inner product.

+
Parameters
+ + + + + + + + + + + + +
[in]idx_rThe index for radial direction.
[in]idx_thetaThe index for poloidal direction
[in]test_bspline_val_and_derivThe data structure containing the derivatives over radial and poloidal directions for test space.
[in]trial_bspline_val_and_derivThe data structure containing the derivatives over radial and poloidal directions for trial space.
[in]test_bspline_val_and_deriv_thetaThe data structure containing the value and derivative along poloidal direction for test space.
[in]trial_bspline_val_and_deriv_thetaThe data structure containing the value and derivative along poloidal direction for trial space.
[in]coeff_alphaThe spline representation of the \( \alpha \) function in the definition of the Poisson-like equation.
[in]coeff_betaThe spline representation of the \( \beta \) function in the definition of the Poisson-like equation.
[in]spline_evaluatorAn evaluator for evaluating 2D splines on \((r,\theta)\).
[in]mappingThe mapping from the logical index range to the physical index range where the equation is defined.
[in]int_volumeThe integral volume associated with each point used in the quadrature scheme.
+
+
+
Returns
inner product of the test and trial spline is computed using a quadrature. This function returns one summand of the quadrature for the quadrature point given by the indices.
+ +
+
+ +

◆ get_matrix_stencil_element()

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+
+template<class Mapping >
+ + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
double PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::get_matrix_stencil_element (IdxBSRTheta idx_test,
IdxBSRTheta idx_trial,
ConstSpline2D coeff_alpha,
ConstSpline2D coeff_beta,
SplineRThetaEvaluatorNullBound const & evaluator,
Mapping const & mapping 
)
+ 		+inline
+
+ +

Computes the matrix element corresponding to two tensor product splines with index idx_test and idx_trial.

+
Parameters
+ + + + + + + +
[in]idx_testThe index for polar B-spline in the test space.
[in]idx_trialThe index for polar B-spline in the trial space.
[in]coeff_alphaThe spline representation of the \( \alpha \) function in the definition of the Poisson-like equation.
[in]coeff_betaThe spline representation of the \( \beta \) function in the definition of the Poisson-like equation.
[in]evaluatorAn evaluator for evaluating 2D splines on \( (r, \theta) \).
[in]mappingThe mapping from the logical index range to the physical index range where the equation is defined.
+
+
+
Returns
The value of the matrix element.
+ +
+
+ +

◆ theta_mod()

+ +
+
+
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+ + + + + +
+ + + + + + + + +
static KOKKOS_FUNCTION int PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::theta_mod (int idx_theta)
+ 		+inlinestatic
+
+ +

Calculates the modulo idx_theta in relation to cells number along \( \theta \) direction .

+
Parameters
+ +
[in]idx_theta\( \theta \) index.
+
Returns
The corresponding indice modulo \( \theta \) direction cells number
- -

◆ init_nnz_per_line()

+ +

◆ init_nnz_per_line()

-template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound_host , class IdxRangeFull = IdxRange<GridR, GridTheta>>
+template<class GridR , class GridTheta , class PolarBSplinesRTheta , class SplineRThetaEvaluatorNullBound , class IdxRangeFull = IdxRange<GridR, GridTheta>>
- + diff --git a/classPolarSplineFEMPoissonLikeSolver.js b/classPolarSplineFEMPoissonLikeSolver.js index 5ed5016ae..17fdaef7c 100644 --- a/classPolarSplineFEMPoissonLikeSolver.js +++ b/classPolarSplineFEMPoissonLikeSolver.js @@ -1,15 +1,23 @@ var classPolarSplineFEMPoissonLikeSolver = [ + [ "EvalDeriv1DType", "classPolarSplineFEMPoissonLikeSolver.html#structPolarSplineFEMPoissonLikeSolver_1_1EvalDeriv1DType", null ], + [ "EvalDeriv2DType", "classPolarSplineFEMPoissonLikeSolver.html#structPolarSplineFEMPoissonLikeSolver_1_1EvalDeriv2DType", null ], [ "QDimRMesh", "structPolarSplineFEMPoissonLikeSolver_1_1QDimRMesh.html", null ], [ "QDimThetaMesh", "structPolarSplineFEMPoissonLikeSolver_1_1QDimThetaMesh.html", null ], [ "RBasisSubset", "classPolarSplineFEMPoissonLikeSolver.html#structPolarSplineFEMPoissonLikeSolver_1_1RBasisSubset", null ], [ "RCellDim", "classPolarSplineFEMPoissonLikeSolver.html#structPolarSplineFEMPoissonLikeSolver_1_1RCellDim", null ], [ "ThetaBasisSubset", "classPolarSplineFEMPoissonLikeSolver.html#structPolarSplineFEMPoissonLikeSolver_1_1ThetaBasisSubset", null ], [ "ThetaCellDim", "classPolarSplineFEMPoissonLikeSolver.html#structPolarSplineFEMPoissonLikeSolver_1_1ThetaCellDim", null ], - [ "R", "classPolarSplineFEMPoissonLikeSolver.html#a4be4b0150bea8b8972bf3400e52d1bcb", null ], - [ "Theta", "classPolarSplineFEMPoissonLikeSolver.html#a68effe5bc79a8795c6513a38489d6813", null ], - [ "PolarSplineFEMPoissonLikeSolver", "classPolarSplineFEMPoissonLikeSolver.html#a5a09f433677b3358cdb5fe205a003bf8", null ], - [ "operator()", "classPolarSplineFEMPoissonLikeSolver.html#ab96025644e98f8d005f8df7f1c6506e4", null ], - [ "operator()", "classPolarSplineFEMPoissonLikeSolver.html#a400425e0ecc5088c1c6427ce8f1e881b", null ], - [ "init_nnz_per_line", "classPolarSplineFEMPoissonLikeSolver.html#ad6c2770cd84599b20bc3a9adc5a94c6b", null ] + [ "R", "classPolarSplineFEMPoissonLikeSolver.html#aea7575e5ec7f7e2a776c1677a79137d9", null ], + [ "Theta", "classPolarSplineFEMPoissonLikeSolver.html#a0c880f33d839cedfafdf2b3b32139417", null ], + [ "IdxCell", "classPolarSplineFEMPoissonLikeSolver.html#aea010ac6bec8090ec2686ad2110befd4", null ], + [ "PolarSplineFEMPoissonLikeSolver", "classPolarSplineFEMPoissonLikeSolver.html#a6e4d95b7b1ce10cf43579ff77b9ea88b", null ], + [ "fill_int_volume", "classPolarSplineFEMPoissonLikeSolver.html#a0d5abf61af4436e3bb7ee922b035447a", null ], + [ "compute_singular_elements", "classPolarSplineFEMPoissonLikeSolver.html#ae5645f014d26559165955e51746f3e70", null ], + [ "compute_overlapping_singular_elements", "classPolarSplineFEMPoissonLikeSolver.html#a36be84f08a082b52a73f5134b8f1a8e2", null ], + [ "compute_stencil_elements", "classPolarSplineFEMPoissonLikeSolver.html#a161e772a03b980ad5cb19bdeb6b02925", null ], + [ "operator()", "classPolarSplineFEMPoissonLikeSolver.html#a2ffbf750c185ff40c8a4697b3937bc63", null ], + [ "operator()", "classPolarSplineFEMPoissonLikeSolver.html#ac699f74359d1f9160bed57ffcf325861", null ], + [ "get_matrix_stencil_element", "classPolarSplineFEMPoissonLikeSolver.html#a90ab8ff1603bc0a3f36b5a0c5077de5b", null ], + [ "init_nnz_per_line", "classPolarSplineFEMPoissonLikeSolver.html#ad1b92b440d6e5c71e14b09d53beefd84", null ] ]; \ No newline at end of file diff --git a/classVortexMergerEquilibria-members.html b/classVortexMergerEquilibria-members.html index 4856fe2b2..5ee7104bf 100644 --- a/classVortexMergerEquilibria-members.html +++ b/classVortexMergerEquilibria-members.html @@ -111,7 +111,7 @@
void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::init_nnz_per_line void PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::init_nnz_per_line ( Kokkos::View< int *, Kokkos::LayoutRight >  nnz)
- +
find_equilibrium(host_t< DFieldRTheta > sigma, host_t< DFieldRTheta > phi_eq, host_t< DFieldRTheta > rho_eq, std::function< double(double const)> const &function, double const phi_max, double const tau, int count_max=25) constVortexMergerEquilibria< Mapping >inline
set_equilibrium(host_t< DFieldRTheta > rho_eq, std::function< double(double const)> function, double const phi_max, double const tau)VortexMergerEquilibria< Mapping >inline
VortexMergerEquilibria(Mapping const &mapping, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver)VortexMergerEquilibria< Mapping >inline
VortexMergerEquilibria(Mapping const &mapping, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver)VortexMergerEquilibria< Mapping >inline
diff --git a/classVortexMergerEquilibria.html b/classVortexMergerEquilibria.html index d5ae11b4e..dba4f3ace 100644 --- a/classVortexMergerEquilibria.html +++ b/classVortexMergerEquilibria.html @@ -115,9 +115,9 @@ - - - + + + @@ -135,8 +135,8 @@

Constructor & Destructor Documentation

- -

◆ VortexMergerEquilibria()

+ +

◆ VortexMergerEquilibria()

@@ -173,7 +173,7 @@

- + diff --git a/classVortexMergerEquilibria.js b/classVortexMergerEquilibria.js index 7e3610f0e..bf3c17639 100644 --- a/classVortexMergerEquilibria.js +++ b/classVortexMergerEquilibria.js @@ -1,6 +1,6 @@ var classVortexMergerEquilibria = [ - [ "VortexMergerEquilibria", "classVortexMergerEquilibria.html#a8e5ac553bd6628804db325b59ca8605d", null ], + [ "VortexMergerEquilibria", "classVortexMergerEquilibria.html#a3a8975ef28538c07c2a08ce9b0db3c9f", null ], [ "find_equilibrium", "classVortexMergerEquilibria.html#ad3b9139693f6f2aeabf9355d14c7c37b", null ], [ "set_equilibrium", "classVortexMergerEquilibria.html#afcf358db72fd433f4470facfecd25019", null ] ]; \ No newline at end of file diff --git a/czarny__to__cartesian_8hpp_source.html b/czarny__to__cartesian_8hpp_source.html index a5a1a05a5..b6ab7bc4d 100644 --- a/czarny__to__cartesian_8hpp_source.html +++ b/czarny__to__cartesian_8hpp_source.html @@ -431,8 +431,8 @@
CzarnyToCartesian::jacobian
KOKKOS_FUNCTION double jacobian(ddc::Coordinate< R, Theta > const &coord) const
Compute the Jacobian, the determinant of the Jacobian matrix of the mapping.
Definition czarny_to_cartesian.hpp:179
R
Define non periodic real R dimension.
Definition geometry.hpp:31
Theta
Define periodic real Theta dimension.
Definition geometry.hpp:42
-
X
Define non periodic real X dimension.
Definition geometry.hpp:277
-
Y
Define non periodic real Y dimension.
Definition geometry.hpp:288
+
X
Define non periodic real X dimension.
Definition geometry.hpp:318
+
Y
Define non periodic real Y dimension.
Definition geometry.hpp:329
diff --git a/discrete__mapping__builder_8hpp_source.html b/discrete__mapping__builder_8hpp_source.html index 1c34b6f81..8515fed64 100644 --- a/discrete__mapping__builder_8hpp_source.html +++ b/discrete__mapping__builder_8hpp_source.html @@ -535,8 +535,8 @@
RefinedDiscreteToCartesianBuilder::GridRRefined
The type of the grid of radial points on which the new mapping will be defined.
Definition discrete_mapping_builder.hpp:228
RefinedDiscreteToCartesianBuilder::GridThetaRefined
The type of the grid of poloidal points on which the new mapping will be defined.
Definition discrete_mapping_builder.hpp:233
Theta
Define periodic real Theta dimension.
Definition geometry.hpp:42
-
X
Define non periodic real X dimension.
Definition geometry.hpp:277
-
Y
Define non periodic real Y dimension.
Definition geometry.hpp:288
+
X
Define non periodic real X dimension.
Definition geometry.hpp:318
+
Y
Define non periodic real Y dimension.
Definition geometry.hpp:329
diff --git a/discrete__to__cartesian_8hpp_source.html b/discrete__to__cartesian_8hpp_source.html index 2fc21a297..0d80c7043 100644 --- a/discrete__to__cartesian_8hpp_source.html +++ b/discrete__to__cartesian_8hpp_source.html @@ -321,8 +321,8 @@
DiscreteToCartesian::BSplineTheta
typename SplineEvaluator::bsplines_type2 BSplineTheta
Indicate the bspline type of the second logical dimension.
Definition discrete_to_cartesian.hpp:43
R
Define non periodic real R dimension.
Definition geometry.hpp:31
Theta
Define periodic real Theta dimension.
Definition geometry.hpp:42
-
X
Define non periodic real X dimension.
Definition geometry.hpp:277
-
Y
Define non periodic real Y dimension.
Definition geometry.hpp:288
+
X
Define non periodic real X dimension.
Definition geometry.hpp:318
+
Y
Define non periodic real Y dimension.
Definition geometry.hpp:329
diff --git a/docs_DDC_in_gyselalibxx.html b/docs_DDC_in_gyselalibxx.html index 3d599c1b2..6a3929bc9 100644 --- a/docs_DDC_in_gyselalibxx.html +++ b/docs_DDC_in_gyselalibxx.html @@ -278,10 +278,10 @@

struct Vx {
static bool constexpr PERIODIC = false;
}
-
Vx
Define non periodic real X velocity dimension.
Definition geometry.hpp:300
-
Vx::PERIODIC
static bool constexpr PERIODIC
Define periodicity of the dimension.
Definition geometry.hpp:305
-
X
Define non periodic real X dimension.
Definition geometry.hpp:277
-
X::PERIODIC
static bool constexpr PERIODIC
Define periodicity of the dimension.
Definition geometry.hpp:282
+
Vx
Define non periodic real X velocity dimension.
Definition geometry.hpp:341
+
Vx::PERIODIC
static bool constexpr PERIODIC
Define periodicity of the dimension.
Definition geometry.hpp:346
+
X
Define non periodic real X dimension.
Definition geometry.hpp:318
+
X::PERIODIC
static bool constexpr PERIODIC
Define periodicity of the dimension.
Definition geometry.hpp:323

We also need types to define the grid on which the simulation will evolve. The domain is discretised on the following grid: \([i, e]\times[x_0,...,x_N]\times[v_0,...,v_{N_v}]\). Grid types are required to define the positions of the grid points in each of the three dimensions:

  • The object \([x_0,...,x_N]\) is defined with a grid and will be denoted \(GridX\).
  • The object \([v_0,...,v_{N_v}]\) is defined with a grid and will be denoted \(GridVx\).
    • diff --git a/geometryRTheta_2geometry_2geometry_8hpp_source.html b/geometryRTheta_2geometry_2geometry_8hpp_source.html index 410ba767d..dd2e741fb 100644 --- a/geometryRTheta_2geometry_2geometry_8hpp_source.html +++ b/geometryRTheta_2geometry_2geometry_8hpp_source.html @@ -261,139 +261,180 @@
    163 GridR,
    164 GridTheta>;
    165
    -
    166
    -
    167// --- Index definitions
    -
    168using IdxR = Idx<GridR>;
    -
    169using IdxTheta = Idx<GridTheta>;
    -
    170using IdxRTheta = Idx<GridR, GridTheta>;
    -
    171
    -
    172// --- Index Step definitions
    -
    173using IdxStepR = IdxStep<GridR>;
    -
    174using IdxStepTheta = IdxStep<GridTheta>;
    -
    175using IdxStepRTheta = IdxStep<GridR, GridTheta>;
    -
    176
    -
    177// --- Index Range definitions
    -
    178using IdxRangeR = IdxRange<GridR>;
    -
    179using IdxRangeTheta = IdxRange<GridTheta>;
    -
    180using IdxRangeRTheta = IdxRange<GridR, GridTheta>;
    -
    181
    -
    182using IdxRangeBSR = IdxRange<BSplinesR>;
    -
    183using IdxRangeBSTheta = IdxRange<BSplinesTheta>;
    -
    184using IdxRangeBSRTheta = IdxRange<BSplinesR, BSplinesTheta>;
    -
    185using IdxRangeBSPolar = IdxRange<PolarBSplinesRTheta>;
    -
    186
    -
    187
    -
    188// --- FieldMem definitions
    -
    189template <class ElementType>
    -
    190using FieldMemR = FieldMem<ElementType, IdxRangeR>;
    -
    191
    -
    192template <class ElementType>
    -
    193using FieldMemTheta = FieldMem<ElementType, IdxRangeTheta>;
    +
    166using SplineRThetaBuilder = ddc::SplineBuilder2D<
    +
    167 Kokkos::DefaultExecutionSpace,
    +
    168 typename Kokkos::DefaultExecutionSpace::memory_space,
    +
    169 BSplinesR,
    +
    170 BSplinesTheta,
    +
    171 GridR,
    +
    172 GridTheta,
    +
    173 SplineRBoundary, // boundary at r=0
    +
    174 SplineRBoundary, // boundary at rmax
    +
    175 SplinePBoundary,
    +
    176 SplinePBoundary,
    +
    177 ddc::SplineSolver::LAPACK,
    +
    178 GridR,
    +
    179 GridTheta>;
    +
    180
    +
    181using SplineRThetaEvaluatorConstBound = ddc::SplineEvaluator2D<
    +
    182 Kokkos::DefaultExecutionSpace,
    +
    183 typename Kokkos::DefaultExecutionSpace::memory_space,
    +
    184 BSplinesR,
    +
    185 BSplinesTheta,
    +
    186 GridR,
    +
    187 GridTheta,
    +
    188 ddc::ConstantExtrapolationRule<R, Theta>, // boundary at r=0
    +
    189 ddc::ConstantExtrapolationRule<R, Theta>, // boundary at rmax
    +
    190 ddc::PeriodicExtrapolationRule<Theta>,
    +
    191 ddc::PeriodicExtrapolationRule<Theta>,
    +
    192 GridR,
    +
    193 GridTheta>;
    194
    -
    195template <class ElementType>
    -
    196using FieldMemRTheta = FieldMem<ElementType, IdxRangeRTheta>;
    -
    197
    -
    198using DFieldMemR = FieldMemR<double>;
    -
    199using DFieldMemTheta = FieldMemTheta<double>;
    -
    200using DFieldMemRTheta = FieldMemRTheta<double>;
    -
    201
    -
    202// --- Field definitions
    -
    203template <class ElementType>
    -
    204using FieldR = Field<ElementType, IdxRangeR>;
    -
    205
    -
    206template <class ElementType>
    -
    207using FieldTheta = Field<ElementType, IdxRangeTheta>;
    -
    208
    -
    209template <class ElementType>
    -
    210using FieldRTheta = Field<ElementType, IdxRangeRTheta>;
    -
    211
    -
    212using DFieldR = FieldR<double>;
    -
    213using DFieldTheta = FieldTheta<double>;
    -
    214using DFieldRTheta = FieldRTheta<double>;
    -
    215
    -
    216// --- Const Field definitions
    -
    217template <class ElementType>
    -
    218using ConstFieldR = ConstField<ElementType, IdxRangeR>;
    -
    219
    -
    220template <class ElementType>
    -
    221using ConstFieldTheta = ConstField<ElementType, IdxRangeTheta>;
    +
    195using SplineRThetaEvaluatorNullBound = ddc::SplineEvaluator2D<
    +
    196 Kokkos::DefaultExecutionSpace,
    +
    197 typename Kokkos::DefaultExecutionSpace::memory_space,
    +
    198 BSplinesR,
    +
    199 BSplinesTheta,
    +
    200 GridR,
    +
    201 GridTheta,
    +
    202 ddc::NullExtrapolationRule, // boundary at r=0
    +
    203 ddc::NullExtrapolationRule, // boundary at rmax
    +
    204 ddc::PeriodicExtrapolationRule<Theta>,
    +
    205 ddc::PeriodicExtrapolationRule<Theta>,
    +
    206 GridR,
    +
    207 GridTheta>;
    +
    208// --- Index definitions
    +
    209using IdxR = Idx<GridR>;
    +
    210using IdxTheta = Idx<GridTheta>;
    +
    211using IdxRTheta = Idx<GridR, GridTheta>;
    +
    212
    +
    213// --- Index Step definitions
    +
    214using IdxStepR = IdxStep<GridR>;
    +
    215using IdxStepTheta = IdxStep<GridTheta>;
    +
    216using IdxStepRTheta = IdxStep<GridR, GridTheta>;
    +
    217
    +
    218// --- Index Range definitions
    +
    219using IdxRangeR = IdxRange<GridR>;
    +
    220using IdxRangeTheta = IdxRange<GridTheta>;
    +
    221using IdxRangeRTheta = IdxRange<GridR, GridTheta>;
    222
    -
    223template <class ElementType>
    -
    224using ConstFieldRTheta = ConstField<ElementType, IdxRangeRTheta>;
    -
    225
    -
    226using DConstFieldR = ConstFieldR<double>;
    -
    227using DConstFieldTheta = ConstFieldTheta<double>;
    -
    228using DConstFieldRTheta = ConstFieldRTheta<double>;
    -
    229
    -
    230// --- Spline representation definitions
    -
    231using Spline2DMem = DFieldMem<IdxRangeBSRTheta>;
    -
    232using Spline2D = DField<IdxRangeBSRTheta>;
    -
    233using ConstSpline2D = DConstField<IdxRangeBSRTheta>;
    -
    234
    -
    240using SplinePolar = PolarSpline<PolarBSplinesRTheta>;
    -
    241
    -
    245using IdxPolarBspl = Idx<PolarBSplinesRTheta>;
    +
    223using IdxRangeBSR = IdxRange<BSplinesR>;
    +
    224using IdxRangeBSTheta = IdxRange<BSplinesTheta>;
    +
    225using IdxRangeBSRTheta = IdxRange<BSplinesR, BSplinesTheta>;
    +
    226using IdxRangeBSPolar = IdxRange<PolarBSplinesRTheta>;
    +
    227
    +
    228
    +
    229// --- FieldMem definitions
    +
    230template <class ElementType>
    +
    231using FieldMemR = FieldMem<ElementType, IdxRangeR>;
    +
    232
    +
    233template <class ElementType>
    +
    234using FieldMemTheta = FieldMem<ElementType, IdxRangeTheta>;
    +
    235
    +
    236template <class ElementType>
    +
    237using FieldMemRTheta = FieldMem<ElementType, IdxRangeRTheta>;
    +
    238
    +
    239using DFieldMemR = FieldMemR<double>;
    +
    240using DFieldMemTheta = FieldMemTheta<double>;
    +
    241using DFieldMemRTheta = FieldMemRTheta<double>;
    +
    242
    +
    243// --- Field definitions
    +
    244template <class ElementType>
    +
    245using FieldR = Field<ElementType, IdxRangeR>;
    246
    -
    247
    -
    248// --- VectorFieldMem definitions
    -
    249template <class Dim1, class Dim2>
    -
    250using DVectorFieldMemRTheta = VectorFieldMem<double, IdxRangeRTheta, NDTag<Dim1, Dim2>>;
    -
    251
    -
    252template <class Dim1, class Dim2>
    -
    253using DVectorFieldRTheta = VectorField<double, IdxRangeRTheta, NDTag<Dim1, Dim2>>;
    -
    254
    -
    255template <class Dim1, class Dim2>
    -
    256using DConstVectorFieldRTheta = VectorConstField<double, IdxRangeRTheta, NDTag<Dim1, Dim2>>;
    -
    257
    -
    258
    -
    259
    -
    260template <class Dim1, class Dim2>
    -
    261using VectorSplineCoeffsMem2D = VectorFieldMem<double, IdxRangeBSRTheta, NDTag<Dim1, Dim2>>;
    -
    262
    -
    263template <class Dim1, class Dim2>
    -
    264using VectorSplineCoeffs2D = VectorField<double, IdxRangeBSRTheta, NDTag<Dim1, Dim2>>;
    -
    265
    -
    266template <class Dim1, class Dim2>
    -
    267using ConstVectorSplineCoeffs2D = VectorConstField<double, IdxRangeBSRTheta, NDTag<Dim1, Dim2>>;
    -
    268
    -
    269
    +
    247template <class ElementType>
    +
    248using FieldTheta = Field<ElementType, IdxRangeTheta>;
    +
    249
    +
    250template <class ElementType>
    +
    251using FieldRTheta = Field<ElementType, IdxRangeRTheta>;
    +
    252
    +
    253using DFieldR = FieldR<double>;
    +
    254using DFieldTheta = FieldTheta<double>;
    +
    255using DFieldRTheta = FieldRTheta<double>;
    +
    256
    +
    257// --- Const Field definitions
    +
    258template <class ElementType>
    +
    259using ConstFieldR = ConstField<ElementType, IdxRangeR>;
    +
    260
    +
    261template <class ElementType>
    +
    262using ConstFieldTheta = ConstField<ElementType, IdxRangeTheta>;
    +
    263
    +
    264template <class ElementType>
    +
    265using ConstFieldRTheta = ConstField<ElementType, IdxRangeRTheta>;
    +
    266
    +
    267using DConstFieldR = ConstFieldR<double>;
    +
    268using DConstFieldTheta = ConstFieldTheta<double>;
    +
    269using DConstFieldRTheta = ConstFieldRTheta<double>;
    270
    -
    271// CARTESIAN SPACE AND VELOCITY ------------------------------------------------------------------
    -
    272// --- Continuous dimensions
    -
    -
    276struct X
    -
    277{
    -
    282 static bool constexpr PERIODIC = false;
    -
    283};
    +
    271// --- Spline representation definitions
    +
    272using Spline2DMem = DFieldMem<IdxRangeBSRTheta>;
    +
    273using Spline2D = DField<IdxRangeBSRTheta>;
    +
    274using ConstSpline2D = DConstField<IdxRangeBSRTheta>;
    +
    275
    +
    281using SplinePolar = PolarSpline<PolarBSplinesRTheta>;
    +
    282
    +
    286using IdxPolarBspl = Idx<PolarBSplinesRTheta>;
    +
    287
    +
    288
    +
    289// --- VectorFieldMem definitions
    +
    290template <class Dim1, class Dim2>
    +
    291using DVectorFieldMemRTheta = VectorFieldMem<double, IdxRangeRTheta, NDTag<Dim1, Dim2>>;
    +
    292
    +
    293template <class Dim1, class Dim2>
    +
    294using DVectorFieldRTheta = VectorField<double, IdxRangeRTheta, NDTag<Dim1, Dim2>>;
    +
    295
    +
    296template <class Dim1, class Dim2>
    +
    297using DConstVectorFieldRTheta = VectorConstField<double, IdxRangeRTheta, NDTag<Dim1, Dim2>>;
    +
    298
    +
    299
    +
    300
    +
    301template <class Dim1, class Dim2>
    +
    302using VectorSplineCoeffsMem2D = VectorFieldMem<double, IdxRangeBSRTheta, NDTag<Dim1, Dim2>>;
    +
    303
    +
    304template <class Dim1, class Dim2>
    +
    305using VectorSplineCoeffs2D = VectorField<double, IdxRangeBSRTheta, NDTag<Dim1, Dim2>>;
    +
    306
    +
    307template <class Dim1, class Dim2>
    +
    308using ConstVectorSplineCoeffs2D = VectorConstField<double, IdxRangeBSRTheta, NDTag<Dim1, Dim2>>;
    +
    309
    +
    310
    +
    311
    +
    312// CARTESIAN SPACE AND VELOCITY ------------------------------------------------------------------
    +
    313// --- Continuous dimensions
    +
    +
    317struct X
    +
    318{
    +
    323 static bool constexpr PERIODIC = false;
    +
    324};
    -
    -
    287struct Y
    -
    288{
    -
    293 static bool constexpr PERIODIC = false;
    -
    294};
    +
    +
    328struct Y
    +
    329{
    +
    334 static bool constexpr PERIODIC = false;
    +
    335};
    -
    295
    -
    -
    299struct Vx
    -
    300{
    -
    305 static bool constexpr PERIODIC = false;
    -
    306};
    +
    336
    +
    +
    340struct Vx
    +
    341{
    +
    346 static bool constexpr PERIODIC = false;
    +
    347};
    -
    -
    310struct Vy
    -
    311{
    -
    316 static bool constexpr PERIODIC = false;
    -
    317};
    +
    +
    351struct Vy
    +
    352{
    +
    357 static bool constexpr PERIODIC = false;
    +
    358};
    -
    318
    -
    319
    -
    320using CoordX = Coord<X>;
    -
    321using CoordY = Coord<Y>;
    -
    322using CoordXY = Coord<X, Y>;
    -
    323
    -
    324using CoordVx = Coord<Vx>;
    -
    325using CoordVy = Coord<Vy>;
    -
    PolarBSplines
    A class containing all information describing polar bsplines.
    Definition polar_bsplines.hpp:28
    +
    359
    +
    360
    +
    361using CoordX = Coord<X>;
    +
    362using CoordY = Coord<Y>;
    +
    363using CoordXY = Coord<X, Y>;
    +
    364
    +
    365using CoordVx = Coord<Vx>;
    +
    366using CoordVy = Coord<Vy>;
    +
    PolarBSplines
    A class containing all information describing polar bsplines.
    Definition polar_bsplines.hpp:29
    VectorFieldMem
    Pre-declaration of VectorFieldMem.
    Definition vector_field_mem.hpp:54
    VectorField
    A class which holds multiple (scalar) fields in order to represent a vector field.
    Definition vector_field.hpp:64
    BSplinesR
    Definition geometry.hpp:93
    @@ -410,14 +451,14 @@
    Vr::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:59
    Vtheta
    Define periodic real Theta velocity dimension.
    Definition geometry.hpp:65
    Vtheta::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:70
    -
    Vx
    Define non periodic real X velocity dimension.
    Definition geometry.hpp:300
    -
    Vx::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:305
    -
    Vy
    Define non periodic real Y velocity dimension.
    Definition geometry.hpp:311
    -
    Vy::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:316
    -
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:277
    -
    X::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:282
    -
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:288
    -
    Y::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:293
    +
    Vx
    Define non periodic real X velocity dimension.
    Definition geometry.hpp:341
    +
    Vx::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:346
    +
    Vy
    Define non periodic real Y velocity dimension.
    Definition geometry.hpp:352
    +
    Vy::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:357
    +
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:318
    +
    X::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:323
    +
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:329
    +
    Y::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:334
    diff --git a/geometryXVx_2geometry_2geometry_8hpp_source.html b/geometryXVx_2geometry_2geometry_8hpp_source.html index 926fa4b3e..380017185 100644 --- a/geometryXVx_2geometry_2geometry_8hpp_source.html +++ b/geometryXVx_2geometry_2geometry_8hpp_source.html @@ -524,10 +524,10 @@
    GridX
    Definition geometry.hpp:94
    T
    A class which describes the real space in the temporal direction.
    Definition geometry.hpp:44
    T::PERIODIC
    static bool constexpr PERIODIC
    A boolean indicating if the dimension is periodic.
    Definition geometry.hpp:48
    -
    Vx
    Define non periodic real X velocity dimension.
    Definition geometry.hpp:300
    -
    Vx::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:305
    -
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:277
    -
    X::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:282
    +
    Vx
    Define non periodic real X velocity dimension.
    Definition geometry.hpp:341
    +
    Vx::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:346
    +
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:318
    +
    X::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:323
    diff --git a/geometryXYVxVy_2geometry_2geometry_8hpp_source.html b/geometryXYVxVy_2geometry_2geometry_8hpp_source.html index 76174abc0..24e847250 100644 --- a/geometryXYVxVy_2geometry_2geometry_8hpp_source.html +++ b/geometryXYVxVy_2geometry_2geometry_8hpp_source.html @@ -480,14 +480,14 @@
    GridVy
    Definition geometry.hpp:131
    GridX
    Definition geometry.hpp:94
    GridY
    Definition geometry.hpp:78
    -
    Vx
    Define non periodic real X velocity dimension.
    Definition geometry.hpp:300
    -
    Vx::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:305
    -
    Vy
    Define non periodic real Y velocity dimension.
    Definition geometry.hpp:311
    -
    Vy::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:316
    -
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:277
    -
    X::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:282
    -
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:288
    -
    Y::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:293
    +
    Vx
    Define non periodic real X velocity dimension.
    Definition geometry.hpp:341
    +
    Vx::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:346
    +
    Vy
    Define non periodic real Y velocity dimension.
    Definition geometry.hpp:352
    +
    Vy::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:357
    +
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:318
    +
    X::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:323
    +
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:329
    +
    Y::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:334
    diff --git a/geometryXY_2geometry_2geometry_8hpp_source.html b/geometryXY_2geometry_2geometry_8hpp_source.html index 31fb62641..7abca520b 100644 --- a/geometryXY_2geometry_2geometry_8hpp_source.html +++ b/geometryXY_2geometry_2geometry_8hpp_source.html @@ -301,10 +301,10 @@
    BSplinesY
    Definition geometry.hpp:61
    GridX
    Definition geometry.hpp:94
    GridY
    Definition geometry.hpp:78
    -
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:277
    -
    X::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:282
    -
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:288
    -
    Y::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:293
    +
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:318
    +
    X::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:323
    +
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:329
    +
    Y::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:334
    diff --git a/inv__jacobian__o__point_8hpp_source.html b/inv__jacobian__o__point_8hpp_source.html index bf34fe51a..d3c614341 100644 --- a/inv__jacobian__o__point_8hpp_source.html +++ b/inv__jacobian__o__point_8hpp_source.html @@ -291,8 +291,8 @@
    InvJacobianOPoint
    An operator for calculating the inverse of the Jacobian at an O-point.
    Definition inv_jacobian_o_point.hpp:27
    R
    Define non periodic real R dimension.
    Definition geometry.hpp:31
    Theta
    Define periodic real Theta dimension.
    Definition geometry.hpp:42
    -
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:277
    -
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:288
    +
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:318
    +
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:329
    diff --git a/math__tools_8hpp_source.html b/math__tools_8hpp_source.html index 729c60fea..867f1065a 100644 --- a/math__tools_8hpp_source.html +++ b/math__tools_8hpp_source.html @@ -197,7 +197,7 @@
    89}
    90
    91template <class T, std::size_t D>
    -
    92inline T dot_product(std::array<T, D> const& a, std::array<T, D> const& b)
    +
    92KOKKOS_INLINE_FUNCTION T dot_product(std::array<T, D> const& a, std::array<T, D> const& b)
    93{
    94 T result = 0;
    95 for (std::size_t i(0); i < D; ++i) {
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    R
    Define non periodic real R dimension.
    Definition geometry.hpp:31
    Theta
    Define periodic real Theta dimension.
    Definition geometry.hpp:42
    Theta::PERIODIC
    static bool constexpr PERIODIC
    Define periodicity of the dimension.
    Definition geometry.hpp:47
    -
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:277
    -
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:288
    +
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:318
    +
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:329
    diff --git a/polar__bsplines_8hpp_source.html b/polar__bsplines_8hpp_source.html index 2a9f99489..7a38ba1bd 100644 --- a/polar__bsplines_8hpp_source.html +++ b/polar__bsplines_8hpp_source.html @@ -115,604 +115,606 @@
    7#include <sll/bernstein.hpp>
    8#include <sll/mapping/cartesian_to_barycentric.hpp>
    9#include <sll/mapping/discrete_to_cartesian.hpp>
    -
    10#include <sll/polar_spline.hpp>
    -
    11#include <sll/view.hpp>
    -
    12
    -
    26template <class BSplinesR, class BSplinesTheta, int C>
    -
    -
    27class PolarBSplines
    -
    28{
    -
    29 static_assert(C >= -1, "Parameter `C` cannot be less than -1");
    -
    30 static_assert(C < 2, "Values larger than 1 are not implemented for parameter `C`");
    -
    31 static_assert(!BSplinesR::is_periodic(), "Radial bsplines must not be periodic.");
    -
    32 static_assert(!BSplinesR::is_uniform(), "Radial bsplines must have knots at the boundary.");
    -
    33 static_assert(BSplinesTheta::is_periodic(), "Poloidal bsplines should be periodic.");
    -
    34
    -
    35private:
    -
    36 // Tags to determine what to evaluate
    -
    37 struct eval_type
    -
    38 {
    -
    39 };
    -
    40
    -
    41 struct eval_deriv_type
    -
    42 {
    -
    43 };
    -
    44
    -
    45public:
    -
    47 using BSplinesR_tag = BSplinesR;
    -
    48
    -
    50 using BSplinesTheta_tag = BSplinesTheta;
    -
    51
    +
    10#include <sll/mapping/mapping_tools.hpp>
    +
    11#include <sll/polar_spline.hpp>
    +
    12#include <sll/view.hpp>
    +
    13
    +
    27template <class BSplinesR, class BSplinesTheta, int C>
    +
    +
    28class PolarBSplines
    +
    29{
    +
    30 static_assert(C >= -1, "Parameter `C` cannot be less than -1");
    +
    31 static_assert(C < 2, "Values larger than 1 are not implemented for parameter `C`");
    +
    32 static_assert(!BSplinesR::is_periodic(), "Radial bsplines must not be periodic.");
    +
    33 static_assert(!BSplinesR::is_uniform(), "Radial bsplines must have knots at the boundary.");
    +
    34 static_assert(BSplinesTheta::is_periodic(), "Poloidal bsplines should be periodic.");
    +
    35
    +
    36private:
    +
    37 // Tags to determine what to evaluate
    +
    38 struct eval_type
    +
    39 {
    +
    40 };
    +
    41
    +
    42 struct eval_deriv_type
    +
    43 {
    +
    44 };
    +
    45
    +
    46public:
    +
    48 using BSplinesR_tag = BSplinesR;
    +
    49
    +
    51 using BSplinesTheta_tag = BSplinesTheta;
    52
    -
    54 using DimR = typename BSplinesR::continuous_dimension_type;
    -
    55
    -
    57 using DimTheta = typename BSplinesTheta::continuous_dimension_type;
    -
    58
    -
    59public:
    -
    61 static int constexpr continuity = C;
    -
    62
    -
    63public:
    -
    71 using discrete_dimension_type = PolarBSplines;
    -
    72
    -
    77 using tensor_product_index_type = ddc::DiscreteElement<BSplinesR, BSplinesTheta>;
    -
    78
    -
    83 using tensor_product_idx_range_type = ddc::DiscreteDomain<BSplinesR, BSplinesTheta>;
    -
    84
    -
    89 using tensor_product_idx_step_type = ddc::DiscreteVector<BSplinesR, BSplinesTheta>;
    -
    90
    -
    91private:
    -
    92 using IdxR = ddc::DiscreteElement<BSplinesR>;
    -
    93 using IdxTheta = ddc::DiscreteElement<BSplinesTheta>;
    -
    94 using IdxStepR = ddc::DiscreteVector<BSplinesR>;
    -
    95 using IdxStepTheta = ddc::DiscreteVector<BSplinesTheta>;
    -
    96
    -
    97public:
    -
    -
    103 static constexpr std::size_t n_singular_basis()
    -
    104 {
    -
    105 return (C + 1) * (C + 2) / 2;
    -
    106 }
    -
    -
    107
    +
    53
    +
    55 using DimR = typename BSplinesR::continuous_dimension_type;
    +
    56
    +
    58 using DimTheta = typename BSplinesTheta::continuous_dimension_type;
    +
    59
    +
    60public:
    +
    62 static int constexpr continuity = C;
    +
    63
    +
    64public:
    +
    72 using discrete_dimension_type = PolarBSplines;
    +
    73
    +
    78 using tensor_product_index_type = ddc::DiscreteElement<BSplinesR, BSplinesTheta>;
    +
    79
    +
    84 using tensor_product_idx_range_type = ddc::DiscreteDomain<BSplinesR, BSplinesTheta>;
    +
    85
    +
    90 using tensor_product_idx_step_type = ddc::DiscreteVector<BSplinesR, BSplinesTheta>;
    +
    91
    +
    92private:
    +
    93 using IdxR = ddc::DiscreteElement<BSplinesR>;
    +
    94 using IdxTheta = ddc::DiscreteElement<BSplinesTheta>;
    +
    95 using IdxStepR = ddc::DiscreteVector<BSplinesR>;
    +
    96 using IdxStepTheta = ddc::DiscreteVector<BSplinesTheta>;
    +
    97
    +
    98public:
    +
    +
    104 static constexpr std::size_t n_singular_basis()
    +
    105 {
    +
    106 return (C + 1) * (C + 2) / 2;
    +
    107 }
    +
    108
    -
    116 template <class DDim>
    -
    -
    117 static constexpr ddc::DiscreteDomain<DDim> singular_idx_range()
    -
    118 {
    -
    119 return ddc::DiscreteDomain<DDim>(
    -
    120 ddc::DiscreteElement<DDim> {0},
    -
    121 ddc::DiscreteVector<DDim> {n_singular_basis()});
    -
    122 }
    -
    -
    123
    -
    132 template <class DDim>
    -
    -
    133 static KOKKOS_FUNCTION ddc::DiscreteElement<DDim> get_polar_index(
    -
    134 tensor_product_index_type const& idx)
    -
    135 {
    -
    136 int const r_idx = ddc::select<BSplinesR>(idx).uid();
    -
    137 int const theta_idx = ddc::select<BSplinesTheta>(idx).uid();
    -
    138 assert(r_idx >= C + 1);
    -
    139 int local_idx((r_idx - C - 1) * ddc::discrete_space<BSplinesTheta>().nbasis() + theta_idx);
    -
    140 return ddc::DiscreteElement<DDim>(n_singular_basis() + local_idx);
    -
    141 }
    -
    -
    142
    -
    151 template <class DDim>
    -
    152 static KOKKOS_FUNCTION tensor_product_index_type
    -
    -
    153 get_2d_index(ddc::DiscreteElement<DDim> const& idx)
    -
    154 {
    -
    155 assert(idx.uid() >= n_singular_basis());
    -
    156 int const idx_2d = idx.uid() - n_singular_basis();
    -
    157 int const r_idx = idx_2d / ddc::discrete_space<BSplinesTheta>().nbasis();
    -
    158 int const theta_idx = idx_2d - r_idx * ddc::discrete_space<BSplinesTheta>().nbasis();
    -
    159 ddc::DiscreteElement<BSplinesR> r_idx_elem(r_idx + C + 1);
    -
    160 ddc::DiscreteElement<BSplinesTheta> theta_idx_elem(theta_idx);
    -
    161 return ddc::DiscreteElement<BSplinesR, BSplinesTheta>(r_idx_elem, theta_idx_elem);
    -
    162 }
    -
    -
    163
    -
    164public:
    -
    171 template <class DDim, class MemorySpace>
    -
    -
    172 class Impl
    -
    173 {
    -
    174 template <class ODDim, class OMemorySpace>
    -
    175 friend class Impl;
    -
    176
    -
    177 template <class ExecSpace, class PBSpl, class OMemorySpace>
    -
    178 friend PolarSplineSpan<PBSpl, OMemorySpace> integrals(
    -
    179 ExecSpace const& execution_space,
    -
    180 PolarSplineSpan<PBSpl, OMemorySpace> int_vals);
    -
    181
    -
    182 private:
    -
    191 using singular_basis_linear_combination_idx_range_type
    -
    192 = ddc::DiscreteDomain<DDim, BSplinesR, BSplinesTheta>;
    -
    193
    -
    194 ddc::Chunk<
    -
    195 double,
    -
    196 singular_basis_linear_combination_idx_range_type,
    -
    197 ddc::KokkosAllocator<double, MemorySpace>>
    -
    198 m_singular_basis_elements_alloc;
    -
    199
    -
    200 ddc::ChunkSpan<
    -
    201 double,
    -
    202 singular_basis_linear_combination_idx_range_type,
    -
    203 Kokkos::layout_right,
    -
    204 MemorySpace>
    -
    205 m_singular_basis_elements;
    -
    206
    -
    207 public:
    -
    -
    209 struct Corner1Tag
    -
    210 {
    -
    211 };
    -
    -
    -
    213 struct Corner2Tag
    -
    214 {
    -
    215 };
    -
    -
    -
    217 struct Corner3Tag
    -
    218 {
    -
    219 };
    -
    -
    220
    -
    221 template <class DiscreteMapping>
    -
    -
    222 struct IntermediateBernsteinBasis
    -
    223 : TriangularBernsteinPolynomialBasis<
    -
    224 typename DiscreteMapping::cartesian_tag_x,
    -
    225 typename DiscreteMapping::cartesian_tag_y,
    -
    226 Corner1Tag,
    -
    227 Corner2Tag,
    -
    228 Corner3Tag,
    -
    229 C>
    -
    230 {
    -
    231 };
    -
    -
    232
    -
    234 using discrete_dimension_type = PolarBSplines;
    -
    235
    -
    237 using discrete_element_type = ddc::DiscreteElement<DDim>;
    -
    238
    -
    240 using discrete_domain_type = ddc::DiscreteDomain<DDim>;
    -
    241
    -
    243 using discrete_vector_type = ddc::DiscreteVector<DDim>;
    -
    244
    -
    252 template <class DiscreteMapping>
    -
    -
    253 Impl(const DiscreteMapping& curvilinear_to_cartesian)
    -
    254 {
    -
    255 static_assert(std::is_same_v<MemorySpace, Kokkos::HostSpace>);
    -
    256 using DimX = typename DiscreteMapping::cartesian_tag_x;
    -
    257 using DimY = typename DiscreteMapping::cartesian_tag_y;
    -
    258 using mapping_tensor_product_index_type = ddc::DiscreteElement<
    -
    259 typename DiscreteMapping::BSplineR,
    -
    260 typename DiscreteMapping::BSplineTheta>;
    -
    261 if constexpr (C > -1) {
    -
    262 const ddc::Coordinate<DimX, DimY> pole
    -
    263 = curvilinear_to_cartesian(ddc::Coordinate<DimR, DimTheta>(0.0, 0.0));
    -
    264 const double x0 = ddc::get<DimX>(pole);
    -
    265 const double y0 = ddc::get<DimY>(pole);
    -
    266 double tau = 0.0;
    -
    267 for (std::size_t i(0); i < ddc::discrete_space<BSplinesTheta>().size(); ++i) {
    -
    268 const ddc::Coordinate<DimX, DimY> point
    -
    269 = curvilinear_to_cartesian.control_point(
    -
    270 mapping_tensor_product_index_type(1, i));
    -
    271
    -
    272 const double c_x = ddc::get<DimX>(point);
    -
    273 const double c_y = ddc::get<DimY>(point);
    -
    274
    -
    275 double tau1 = -2.0 * (c_x - x0);
    -
    276 double tau2 = c_x - x0 - sqrt(3.0) * (c_y - y0);
    -
    277 double tau3 = c_x - x0 + sqrt(3.0) * (c_y - y0);
    -
    278 tau = tau > tau1 ? tau : tau1;
    -
    279 tau = tau > tau2 ? tau : tau2;
    -
    280 tau = tau > tau3 ? tau : tau3;
    -
    281 }
    -
    282 // Determine the corners for the barycentric coordinates
    -
    283 const ddc::Coordinate<DimX, DimY> corner1(x0 + tau, y0);
    -
    284 const ddc::Coordinate<DimX, DimY>
    -
    285 corner2(x0 - 0.5 * tau, y0 + 0.5 * tau * sqrt(3.0));
    +
    109
    +
    117 template <class DDim>
    +
    +
    118 static constexpr ddc::DiscreteDomain<DDim> singular_idx_range()
    +
    119 {
    +
    120 return ddc::DiscreteDomain<DDim>(
    +
    121 ddc::DiscreteElement<DDim> {0},
    +
    122 ddc::DiscreteVector<DDim> {n_singular_basis()});
    +
    123 }
    +
    +
    124
    +
    133 template <class DDim>
    +
    +
    134 static KOKKOS_FUNCTION ddc::DiscreteElement<DDim> get_polar_index(
    +
    135 tensor_product_index_type const& idx)
    +
    136 {
    +
    137 int const r_idx = ddc::select<BSplinesR>(idx).uid();
    +
    138 int const theta_idx = ddc::select<BSplinesTheta>(idx).uid();
    +
    139 assert(r_idx >= C + 1);
    +
    140 int local_idx((r_idx - C - 1) * ddc::discrete_space<BSplinesTheta>().nbasis() + theta_idx);
    +
    141 return ddc::DiscreteElement<DDim>(n_singular_basis() + local_idx);
    +
    142 }
    +
    +
    143
    +
    152 template <class DDim>
    +
    153 static KOKKOS_FUNCTION tensor_product_index_type
    +
    +
    154 get_2d_index(ddc::DiscreteElement<DDim> const& idx)
    +
    155 {
    +
    156 assert(idx.uid() >= n_singular_basis());
    +
    157 int const idx_2d = idx.uid() - n_singular_basis();
    +
    158 int const r_idx = idx_2d / ddc::discrete_space<BSplinesTheta>().nbasis();
    +
    159 int const theta_idx = idx_2d - r_idx * ddc::discrete_space<BSplinesTheta>().nbasis();
    +
    160 ddc::DiscreteElement<BSplinesR> r_idx_elem(r_idx + C + 1);
    +
    161 ddc::DiscreteElement<BSplinesTheta> theta_idx_elem(theta_idx);
    +
    162 return ddc::DiscreteElement<BSplinesR, BSplinesTheta>(r_idx_elem, theta_idx_elem);
    +
    163 }
    +
    +
    164
    +
    165public:
    +
    172 template <class DDim, class MemorySpace>
    +
    +
    173 class Impl
    +
    174 {
    +
    175 template <class ODDim, class OMemorySpace>
    +
    176 friend class Impl;
    +
    177
    +
    178 template <class ExecSpace, class PBSpl, class OMemorySpace>
    +
    179 friend PolarSplineSpan<PBSpl, OMemorySpace> integrals(
    +
    180 ExecSpace const& execution_space,
    +
    181 PolarSplineSpan<PBSpl, OMemorySpace> int_vals);
    +
    182
    +
    183 private:
    +
    192 using singular_basis_linear_combination_idx_range_type
    +
    193 = ddc::DiscreteDomain<DDim, BSplinesR, BSplinesTheta>;
    +
    194
    +
    195 ddc::Chunk<
    +
    196 double,
    +
    197 singular_basis_linear_combination_idx_range_type,
    +
    198 ddc::KokkosAllocator<double, MemorySpace>>
    +
    199 m_singular_basis_elements_alloc;
    +
    200
    +
    201 ddc::ChunkSpan<
    +
    202 double,
    +
    203 singular_basis_linear_combination_idx_range_type,
    +
    204 Kokkos::layout_right,
    +
    205 MemorySpace>
    +
    206 m_singular_basis_elements;
    +
    207
    +
    208 public:
    +
    +
    210 struct Corner1Tag
    +
    211 {
    +
    212 };
    +
    +
    +
    214 struct Corner2Tag
    +
    215 {
    +
    216 };
    +
    +
    +
    218 struct Corner3Tag
    +
    219 {
    +
    220 };
    +
    +
    221
    +
    222 template <class DiscreteMapping>
    +
    +
    223 struct IntermediateBernsteinBasis
    +
    224 : TriangularBernsteinPolynomialBasis<
    +
    225 typename DiscreteMapping::cartesian_tag_x,
    +
    226 typename DiscreteMapping::cartesian_tag_y,
    +
    227 Corner1Tag,
    +
    228 Corner2Tag,
    +
    229 Corner3Tag,
    +
    230 C>
    +
    231 {
    +
    232 };
    +
    +
    233
    +
    235 using discrete_dimension_type = PolarBSplines;
    +
    236
    +
    238 using discrete_element_type = ddc::DiscreteElement<DDim>;
    +
    239
    +
    241 using discrete_domain_type = ddc::DiscreteDomain<DDim>;
    +
    242
    +
    244 using discrete_vector_type = ddc::DiscreteVector<DDim>;
    +
    245
    +
    253 template <class DiscreteMapping>
    +
    +
    254 Impl(const DiscreteMapping& curvilinear_to_cartesian)
    +
    255 {
    +
    256 static_assert(is_accessible_v<Kokkos::DefaultHostExecutionSpace, DiscreteMapping>);
    +
    257 static_assert(std::is_same_v<MemorySpace, Kokkos::HostSpace>);
    +
    258 using DimX = typename DiscreteMapping::cartesian_tag_x;
    +
    259 using DimY = typename DiscreteMapping::cartesian_tag_y;
    +
    260 using mapping_tensor_product_index_type = ddc::DiscreteElement<
    +
    261 typename DiscreteMapping::BSplineR,
    +
    262 typename DiscreteMapping::BSplineTheta>;
    +
    263 if constexpr (C > -1) {
    +
    264 const ddc::Coordinate<DimX, DimY> pole
    +
    265 = curvilinear_to_cartesian(ddc::Coordinate<DimR, DimTheta>(0.0, 0.0));
    +
    266 const double x0 = ddc::get<DimX>(pole);
    +
    267 const double y0 = ddc::get<DimY>(pole);
    +
    268 double tau = 0.0;
    +
    269 for (std::size_t i(0); i < ddc::discrete_space<BSplinesTheta>().size(); ++i) {
    +
    270 const ddc::Coordinate<DimX, DimY> point
    +
    271 = curvilinear_to_cartesian.control_point(
    +
    272 mapping_tensor_product_index_type(1, i));
    +
    273
    +
    274 const double c_x = ddc::get<DimX>(point);
    +
    275 const double c_y = ddc::get<DimY>(point);
    +
    276
    +
    277 double tau1 = -2.0 * (c_x - x0);
    +
    278 double tau2 = c_x - x0 - sqrt(3.0) * (c_y - y0);
    +
    279 double tau3 = c_x - x0 + sqrt(3.0) * (c_y - y0);
    +
    280 tau = tau > tau1 ? tau : tau1;
    +
    281 tau = tau > tau2 ? tau : tau2;
    +
    282 tau = tau > tau3 ? tau : tau3;
    +
    283 }
    +
    284 // Determine the corners for the barycentric coordinates
    +
    285 const ddc::Coordinate<DimX, DimY> corner1(x0 + tau, y0);
    286 const ddc::Coordinate<DimX, DimY>
    -
    287 corner3(x0 - 0.5 * tau, y0 - 0.5 * tau * sqrt(3.0));
    -
    288
    -
    289 const CartesianToBarycentric<DimX, DimY, Corner1Tag, Corner2Tag, Corner3Tag>
    -
    290 barycentric_coordinate_converter(corner1, corner2, corner3);
    -
    291
    -
    292 using BernsteinBasis = IntermediateBernsteinBasis<DiscreteMapping>;
    +
    287 corner2(x0 - 0.5 * tau, y0 + 0.5 * tau * sqrt(3.0));
    +
    288 const ddc::Coordinate<DimX, DimY>
    +
    289 corner3(x0 - 0.5 * tau, y0 - 0.5 * tau * sqrt(3.0));
    +
    290
    +
    291 const CartesianToBarycentric<DimX, DimY, Corner1Tag, Corner2Tag, Corner3Tag>
    +
    292 barycentric_coordinate_converter(corner1, corner2, corner3);
    293
    -
    294 ddc::init_discrete_space<BernsteinBasis>(barycentric_coordinate_converter);
    +
    294 using BernsteinBasis = IntermediateBernsteinBasis<DiscreteMapping>;
    295
    -
    296 // The number of radial bases used to construct the bsplines traversing the singular point.
    -
    297 constexpr IdxStepR nr_in_singular(C + 1);
    -
    298 assert(nr_in_singular.value() < int(ddc::discrete_space<BSplinesR>().size()));
    -
    299
    -
    300 // The number of poloidal bases used to construct the bsplines traversing the singular point.
    -
    301 const IdxStepTheta np_in_singular(ddc::discrete_space<BSplinesTheta>().nbasis());
    -
    302
    -
    303 // The number of elements of the poloidal basis which will have an associated coefficient
    -
    304 // (This will be larger than np_in_singular as it includes the periodicity)
    -
    305 const IdxStepTheta np_tot(ddc::discrete_space<BSplinesTheta>().size());
    -
    306
    -
    307 // The index range of the 2D bsplines in the innermost circles from which the polar bsplines
    -
    308 // traversing the singular point will be constructed.
    -
    309 tensor_product_idx_range_type const dom_bsplines_inner(
    -
    310 tensor_product_index_type(0, 0),
    -
    311 tensor_product_idx_step_type(nr_in_singular, np_tot));
    -
    312
    -
    313 // Initialise memory
    -
    314 m_singular_basis_elements_alloc
    -
    315 = ddc::Chunk<double, singular_basis_linear_combination_idx_range_type>(
    -
    316 singular_basis_linear_combination_idx_range_type(
    -
    317 singular_idx_range<DDim>(),
    -
    318 dom_bsplines_inner));
    -
    319 m_singular_basis_elements = m_singular_basis_elements_alloc.span_view();
    -
    320
    -
    321 ddc::DiscreteDomain<BernsteinBasis> bernstein_idx_range(
    -
    322 ddc::DiscreteElement<BernsteinBasis> {0},
    -
    323 ddc::DiscreteVector<BernsteinBasis> {n_singular_basis()});
    -
    324
    -
    325 ddc::DiscreteDomain<BSplinesTheta> poloidal_spline_idx_range
    -
    326 = ddc::discrete_space<BSplinesTheta>().full_domain();
    -
    327
    -
    328 for (IdxR const ir : ddc::DiscreteDomain<BSplinesR>(IdxR(0), IdxStepR(C + 1))) {
    -
    329 for (IdxTheta const ip : poloidal_spline_idx_range.take_first(np_in_singular)) {
    -
    330 const ddc::Coordinate<DimX, DimY> point
    -
    331 = curvilinear_to_cartesian.control_point(
    -
    332 mapping_tensor_product_index_type(ir, ip));
    -
    333 ddc::Chunk<double, ddc::DiscreteDomain<BernsteinBasis>> bernstein_vals(
    -
    334 bernstein_idx_range);
    -
    335 ddc::discrete_space<BernsteinBasis>()
    -
    336 .eval_basis(bernstein_vals.span_view(), point);
    -
    337 // Fill spline coefficients
    -
    338 for (auto k : bernstein_idx_range) {
    -
    339 m_singular_basis_elements(discrete_element_type {k.uid()}, ir, ip)
    -
    340 = bernstein_vals(k);
    -
    341 }
    -
    342 }
    -
    343 for (discrete_element_type k : singular_idx_range<DDim>()) {
    -
    344 for (IdxTheta const ip : poloidal_spline_idx_range.take_first(
    -
    345 IdxStepTheta {BSplinesTheta::degree()})) {
    -
    346 m_singular_basis_elements(k, ir, ip + np_in_singular)
    -
    347 = m_singular_basis_elements(k, ir, ip);
    -
    348 }
    -
    349 }
    -
    350 }
    -
    351 } else {
    -
    352 // Initialise m_singular_basis_elements to avoid any problems in the copy constructor
    -
    353 tensor_product_idx_range_type const empty_dom_bsplines(
    -
    354 tensor_product_index_type(0, 0),
    -
    355 tensor_product_idx_step_type(0, 0));
    -
    356 m_singular_basis_elements_alloc
    -
    357 = ddc::Chunk<double, singular_basis_linear_combination_idx_range_type>(
    -
    358 singular_basis_linear_combination_idx_range_type(
    -
    359 singular_idx_range<DDim>(),
    -
    360 empty_dom_bsplines));
    -
    361 m_singular_basis_elements = m_singular_basis_elements_alloc.span_view();
    -
    362 }
    -
    363 }
    -
    -
    364
    -
    370 template <class OriginMemorySpace>
    -
    -
    371 explicit Impl(Impl<DDim, OriginMemorySpace> const& impl)
    -
    372 : m_singular_basis_elements_alloc(impl.m_singular_basis_elements.domain())
    -
    373 {
    -
    374 m_singular_basis_elements = m_singular_basis_elements_alloc.span_view();
    -
    375 ddc::parallel_deepcopy(m_singular_basis_elements, impl.m_singular_basis_elements);
    -
    376 }
    -
    -
    377
    -
    383 Impl(Impl const& x) = default;
    -
    384
    -
    390 Impl(Impl&& x) = default;
    -
    391
    -
    395 ~Impl() = default;
    -
    396
    -
    404 Impl& operator=(Impl const& x) = default;
    -
    405
    -
    413 Impl& operator=(Impl&& x) = default;
    -
    414
    -
    -
    431 tensor_product_index_type eval_basis(
    -
    432 DSpan1D singular_values,
    -
    433 DSpan2D values,
    -
    434 ddc::Coordinate<DimR, DimTheta> p) const;
    -
    435
    -
    -
    452 tensor_product_index_type eval_deriv_r(
    -
    453 DSpan1D singular_derivs,
    -
    454 DSpan2D derivs,
    -
    455 ddc::Coordinate<DimR, DimTheta> p) const;
    -
    456
    -
    -
    473 tensor_product_index_type eval_deriv_theta(
    -
    474 DSpan1D singular_derivs,
    -
    475 DSpan2D derivs,
    -
    476 ddc::Coordinate<DimR, DimTheta> p) const;
    -
    477
    -
    -
    495 tensor_product_index_type eval_deriv_r_and_theta(
    -
    496 DSpan1D singular_derivs,
    -
    497 DSpan2D derivs,
    -
    498 ddc::Coordinate<DimR, DimTheta> p) const;
    -
    499
    -
    505 template <class MemorySpace2>
    -
    -
    506 [[deprecated("Use `integrals` instead")]] void integrals(
    -
    507 PolarSplineSpan<DDim, MemorySpace2> int_vals) const;
    -
    508
    -
    -
    514 std::size_t nbasis() const noexcept
    -
    515 {
    -
    516 std::size_t nr = ddc::discrete_space<BSplinesR>().nbasis() - C - 1;
    -
    517 std::size_t ntheta = ddc::discrete_space<BSplinesTheta>().nbasis();
    -
    518 return n_singular_basis() + nr * ntheta;
    -
    519 }
    -
    -
    520
    - -
    530
    -
    -
    538 discrete_domain_type tensor_bspline_idx_range() const noexcept
    -
    539 {
    -
    540 return full_domain().remove_first(discrete_vector_type {n_singular_basis()});
    -
    541 }
    -
    -
    542
    -
    543 private:
    -
    544 template <class EvalTypeR, class EvalTypeTheta>
    -
    545 ddc::DiscreteElement<BSplinesR, BSplinesTheta> eval(
    -
    546 DSpan1D singular_values,
    -
    547 DSpan2D values,
    -
    548 ddc::Coordinate<DimR, DimTheta> coord_eval,
    -
    549 EvalTypeR const,
    -
    550 EvalTypeTheta const) const;
    -
    551 };
    -
    552};
    -
    553
    -
    554template <class BSplinesR, class BSplinesTheta, int C>
    -
    555template <class DDim, class MemorySpace>
    -
    556ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    -
    -
    557 Impl<DDim, MemorySpace>::eval_basis(
    -
    558 DSpan1D singular_values,
    -
    559 DSpan2D values,
    -
    560 ddc::Coordinate<DimR, DimTheta> p) const
    -
    561{
    -
    562 return eval(singular_values, values, p, eval_type(), eval_type());
    -
    563}
    -
    -
    564
    -
    565template <class BSplinesR, class BSplinesTheta, int C>
    -
    566template <class DDim, class MemorySpace>
    -
    567ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    -
    -
    568 Impl<DDim, MemorySpace>::eval_deriv_r(
    -
    569 DSpan1D singular_derivs,
    -
    570 DSpan2D derivs,
    -
    571 ddc::Coordinate<DimR, DimTheta> p) const
    -
    572{
    -
    573 return eval(singular_derivs, derivs, p, eval_deriv_type(), eval_type());
    -
    574}
    -
    -
    575
    -
    576template <class BSplinesR, class BSplinesTheta, int C>
    -
    577template <class DDim, class MemorySpace>
    -
    578ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    -
    -
    579 Impl<DDim, MemorySpace>::eval_deriv_theta(
    -
    580 DSpan1D singular_derivs,
    -
    581 DSpan2D derivs,
    -
    582 ddc::Coordinate<DimR, DimTheta> p) const
    -
    583{
    -
    584 return eval(singular_derivs, derivs, p, eval_type(), eval_deriv_type());
    -
    585}
    -
    -
    586
    -
    587template <class BSplinesR, class BSplinesTheta, int C>
    -
    588template <class DDim, class MemorySpace>
    -
    589ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    -
    -
    590 Impl<DDim, MemorySpace>::eval_deriv_r_and_theta(
    -
    591 DSpan1D singular_derivs,
    -
    592 DSpan2D derivs,
    -
    593 ddc::Coordinate<DimR, DimTheta> p) const
    -
    594{
    -
    595 return eval(singular_derivs, derivs, p, eval_deriv_type(), eval_deriv_type());
    -
    596}
    -
    -
    597
    -
    598template <class BSplinesR, class BSplinesTheta, int C>
    -
    599template <class DDim, class MemorySpace>
    -
    600template <class EvalTypeR, class EvalTypeTheta>
    -
    601ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    -
    602 Impl<DDim, MemorySpace>::eval(
    -
    603 DSpan1D singular_values,
    -
    604 DSpan2D values,
    -
    605 ddc::Coordinate<DimR, DimTheta> coord_eval,
    -
    606 EvalTypeR const,
    -
    607 EvalTypeTheta const) const
    -
    608{
    -
    609 assert(singular_values.extent(0) == n_singular_basis());
    -
    610 assert(values.extent(0) == BSplinesR::degree() + 1);
    -
    611 assert(values.extent(1) == BSplinesTheta::degree() + 1);
    -
    612 static_assert(
    -
    613 std::is_same_v<EvalTypeR, eval_type> || std::is_same_v<EvalTypeR, eval_deriv_type>);
    +
    296 ddc::init_discrete_space<BernsteinBasis>(barycentric_coordinate_converter);
    +
    297
    +
    298 // The number of radial bases used to construct the bsplines traversing the singular point.
    +
    299 constexpr IdxStepR nr_in_singular(C + 1);
    +
    300 assert(nr_in_singular.value() < int(ddc::discrete_space<BSplinesR>().size()));
    +
    301
    +
    302 // The number of poloidal bases used to construct the bsplines traversing the singular point.
    +
    303 const IdxStepTheta np_in_singular(ddc::discrete_space<BSplinesTheta>().nbasis());
    +
    304
    +
    305 // The number of elements of the poloidal basis which will have an associated coefficient
    +
    306 // (This will be larger than np_in_singular as it includes the periodicity)
    +
    307 const IdxStepTheta np_tot(ddc::discrete_space<BSplinesTheta>().size());
    +
    308
    +
    309 // The index range of the 2D bsplines in the innermost circles from which the polar bsplines
    +
    310 // traversing the singular point will be constructed.
    +
    311 tensor_product_idx_range_type const dom_bsplines_inner(
    +
    312 tensor_product_index_type(0, 0),
    +
    313 tensor_product_idx_step_type(nr_in_singular, np_tot));
    +
    314
    +
    315 // Initialise memory
    +
    316 m_singular_basis_elements_alloc
    +
    317 = ddc::Chunk<double, singular_basis_linear_combination_idx_range_type>(
    +
    318 singular_basis_linear_combination_idx_range_type(
    +
    319 singular_idx_range<DDim>(),
    +
    320 dom_bsplines_inner));
    +
    321 m_singular_basis_elements = m_singular_basis_elements_alloc.span_view();
    +
    322
    +
    323 ddc::DiscreteDomain<BernsteinBasis> bernstein_idx_range(
    +
    324 ddc::DiscreteElement<BernsteinBasis> {0},
    +
    325 ddc::DiscreteVector<BernsteinBasis> {n_singular_basis()});
    +
    326
    +
    327 ddc::DiscreteDomain<BSplinesTheta> poloidal_spline_idx_range
    +
    328 = ddc::discrete_space<BSplinesTheta>().full_domain();
    +
    329
    +
    330 for (IdxR const ir : ddc::DiscreteDomain<BSplinesR>(IdxR(0), IdxStepR(C + 1))) {
    +
    331 for (IdxTheta const ip : poloidal_spline_idx_range.take_first(np_in_singular)) {
    +
    332 const ddc::Coordinate<DimX, DimY> point
    +
    333 = curvilinear_to_cartesian.control_point(
    +
    334 mapping_tensor_product_index_type(ir, ip));
    +
    335 ddc::Chunk<double, ddc::DiscreteDomain<BernsteinBasis>> bernstein_vals(
    +
    336 bernstein_idx_range);
    +
    337 ddc::discrete_space<BernsteinBasis>()
    +
    338 .eval_basis(bernstein_vals.span_view(), point);
    +
    339 // Fill spline coefficients
    +
    340 for (auto k : bernstein_idx_range) {
    +
    341 m_singular_basis_elements(discrete_element_type {k.uid()}, ir, ip)
    +
    342 = bernstein_vals(k);
    +
    343 }
    +
    344 }
    +
    345 for (discrete_element_type k : singular_idx_range<DDim>()) {
    +
    346 for (IdxTheta const ip : poloidal_spline_idx_range.take_first(
    +
    347 IdxStepTheta {BSplinesTheta::degree()})) {
    +
    348 m_singular_basis_elements(k, ir, ip + np_in_singular)
    +
    349 = m_singular_basis_elements(k, ir, ip);
    +
    350 }
    +
    351 }
    +
    352 }
    +
    353 } else {
    +
    354 // Initialise m_singular_basis_elements to avoid any problems in the copy constructor
    +
    355 tensor_product_idx_range_type const empty_dom_bsplines(
    +
    356 tensor_product_index_type(0, 0),
    +
    357 tensor_product_idx_step_type(0, 0));
    +
    358 m_singular_basis_elements_alloc
    +
    359 = ddc::Chunk<double, singular_basis_linear_combination_idx_range_type>(
    +
    360 singular_basis_linear_combination_idx_range_type(
    +
    361 singular_idx_range<DDim>(),
    +
    362 empty_dom_bsplines));
    +
    363 m_singular_basis_elements = m_singular_basis_elements_alloc.span_view();
    +
    364 }
    +
    365 }
    +
    +
    366
    +
    372 template <class OriginMemorySpace>
    +
    +
    373 explicit Impl(Impl<DDim, OriginMemorySpace> const& impl)
    +
    374 : m_singular_basis_elements_alloc(impl.m_singular_basis_elements.domain())
    +
    375 {
    +
    376 m_singular_basis_elements = m_singular_basis_elements_alloc.span_view();
    +
    377 ddc::parallel_deepcopy(m_singular_basis_elements, impl.m_singular_basis_elements);
    +
    378 }
    +
    +
    379
    +
    385 Impl(Impl const& x) = default;
    +
    386
    +
    392 Impl(Impl&& x) = default;
    +
    393
    +
    397 ~Impl() = default;
    +
    398
    +
    406 Impl& operator=(Impl const& x) = default;
    +
    407
    +
    415 Impl& operator=(Impl&& x) = default;
    +
    416
    +
    +
    433 tensor_product_index_type eval_basis(
    +
    434 DSpan1D singular_values,
    +
    435 DSpan2D values,
    +
    436 ddc::Coordinate<DimR, DimTheta> p) const;
    +
    437
    +
    +
    454 tensor_product_index_type eval_deriv_r(
    +
    455 DSpan1D singular_derivs,
    +
    456 DSpan2D derivs,
    +
    457 ddc::Coordinate<DimR, DimTheta> p) const;
    +
    458
    +
    +
    475 tensor_product_index_type eval_deriv_theta(
    +
    476 DSpan1D singular_derivs,
    +
    477 DSpan2D derivs,
    +
    478 ddc::Coordinate<DimR, DimTheta> p) const;
    +
    479
    +
    +
    497 tensor_product_index_type eval_deriv_r_and_theta(
    +
    498 DSpan1D singular_derivs,
    +
    499 DSpan2D derivs,
    +
    500 ddc::Coordinate<DimR, DimTheta> p) const;
    +
    501
    +
    507 template <class MemorySpace2>
    +
    +
    508 [[deprecated("Use `integrals` instead")]] void integrals(
    +
    509 PolarSplineSpan<DDim, MemorySpace2> int_vals) const;
    +
    510
    +
    +
    516 std::size_t nbasis() const noexcept
    +
    517 {
    +
    518 std::size_t nr = ddc::discrete_space<BSplinesR>().nbasis() - C - 1;
    +
    519 std::size_t ntheta = ddc::discrete_space<BSplinesTheta>().nbasis();
    +
    520 return n_singular_basis() + nr * ntheta;
    +
    521 }
    +
    +
    522
    + +
    532
    +
    +
    540 discrete_domain_type tensor_bspline_idx_range() const noexcept
    +
    541 {
    +
    542 return full_domain().remove_first(discrete_vector_type {n_singular_basis()});
    +
    543 }
    +
    +
    544
    +
    545 private:
    +
    546 template <class EvalTypeR, class EvalTypeTheta>
    +
    547 ddc::DiscreteElement<BSplinesR, BSplinesTheta> eval(
    +
    548 DSpan1D singular_values,
    +
    549 DSpan2D values,
    +
    550 ddc::Coordinate<DimR, DimTheta> coord_eval,
    +
    551 EvalTypeR const,
    +
    552 EvalTypeTheta const) const;
    +
    553 };
    +
    554};
    +
    555
    +
    556template <class BSplinesR, class BSplinesTheta, int C>
    +
    557template <class DDim, class MemorySpace>
    +
    558ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    +
    +
    559 Impl<DDim, MemorySpace>::eval_basis(
    +
    560 DSpan1D singular_values,
    +
    561 DSpan2D values,
    +
    562 ddc::Coordinate<DimR, DimTheta> p) const
    +
    563{
    +
    564 return eval(singular_values, values, p, eval_type(), eval_type());
    +
    565}
    +
    +
    566
    +
    567template <class BSplinesR, class BSplinesTheta, int C>
    +
    568template <class DDim, class MemorySpace>
    +
    569ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    +
    +
    570 Impl<DDim, MemorySpace>::eval_deriv_r(
    +
    571 DSpan1D singular_derivs,
    +
    572 DSpan2D derivs,
    +
    573 ddc::Coordinate<DimR, DimTheta> p) const
    +
    574{
    +
    575 return eval(singular_derivs, derivs, p, eval_deriv_type(), eval_type());
    +
    576}
    +
    +
    577
    +
    578template <class BSplinesR, class BSplinesTheta, int C>
    +
    579template <class DDim, class MemorySpace>
    +
    580ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    +
    +
    581 Impl<DDim, MemorySpace>::eval_deriv_theta(
    +
    582 DSpan1D singular_derivs,
    +
    583 DSpan2D derivs,
    +
    584 ddc::Coordinate<DimR, DimTheta> p) const
    +
    585{
    +
    586 return eval(singular_derivs, derivs, p, eval_type(), eval_deriv_type());
    +
    587}
    +
    +
    588
    +
    589template <class BSplinesR, class BSplinesTheta, int C>
    +
    590template <class DDim, class MemorySpace>
    +
    591ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    +
    +
    592 Impl<DDim, MemorySpace>::eval_deriv_r_and_theta(
    +
    593 DSpan1D singular_derivs,
    +
    594 DSpan2D derivs,
    +
    595 ddc::Coordinate<DimR, DimTheta> p) const
    +
    596{
    +
    597 return eval(singular_derivs, derivs, p, eval_deriv_type(), eval_deriv_type());
    +
    598}
    +
    +
    599
    +
    600template <class BSplinesR, class BSplinesTheta, int C>
    +
    601template <class DDim, class MemorySpace>
    +
    602template <class EvalTypeR, class EvalTypeTheta>
    +
    603ddc::DiscreteElement<BSplinesR, BSplinesTheta> PolarBSplines<BSplinesR, BSplinesTheta, C>::
    +
    604 Impl<DDim, MemorySpace>::eval(
    +
    605 DSpan1D singular_values,
    +
    606 DSpan2D values,
    +
    607 ddc::Coordinate<DimR, DimTheta> coord_eval,
    +
    608 EvalTypeR const,
    +
    609 EvalTypeTheta const) const
    +
    610{
    +
    611 assert(singular_values.extent(0) == n_singular_basis());
    +
    612 assert(values.extent(0) == BSplinesR::degree() + 1);
    +
    613 assert(values.extent(1) == BSplinesTheta::degree() + 1);
    614 static_assert(
    -
    615 std::is_same_v<
    -
    616 EvalTypeTheta,
    -
    617 eval_type> || std::is_same_v<EvalTypeTheta, eval_deriv_type>);
    -
    618
    -
    619 ddc::DiscreteElement<BSplinesR> jmin_r;
    -
    620 ddc::DiscreteElement<BSplinesTheta> jmin_theta;
    -
    621
    -
    622 std::size_t constexpr nr = BSplinesR::degree() + 1;
    -
    623 std::size_t constexpr ntheta = BSplinesTheta::degree() + 1;
    -
    624
    -
    625 std::array<double, nr> vals_r_ptr;
    -
    626 std::array<double, ntheta> vals_theta_ptr;
    -
    627 DSpan1D const vals_r(vals_r_ptr.data(), nr);
    -
    628 DSpan1D const vals_theta(vals_theta_ptr.data(), ntheta);
    -
    629
    -
    630 if constexpr (std::is_same_v<EvalTypeR, eval_type>) {
    -
    631 jmin_r = ddc::discrete_space<BSplinesR>().eval_basis(vals_r, ddc::select<DimR>(coord_eval));
    -
    632 } else if constexpr (std::is_same_v<EvalTypeR, eval_deriv_type>) {
    -
    633 jmin_r = ddc::discrete_space<BSplinesR>().eval_deriv(vals_r, ddc::select<DimR>(coord_eval));
    -
    634 }
    -
    635 if constexpr (std::is_same_v<EvalTypeTheta, eval_type>) {
    -
    636 jmin_theta = ddc::discrete_space<BSplinesTheta>()
    -
    637 .eval_basis(vals_theta, ddc::select<DimTheta>(coord_eval));
    -
    638 } else if constexpr (std::is_same_v<EvalTypeTheta, eval_deriv_type>) {
    -
    639 jmin_theta = ddc::discrete_space<BSplinesTheta>()
    -
    640 .eval_deriv(vals_theta, ddc::select<DimTheta>(coord_eval));
    -
    641 }
    -
    642
    -
    643 std::size_t nr_done = 0;
    +
    615 std::is_same_v<EvalTypeR, eval_type> || std::is_same_v<EvalTypeR, eval_deriv_type>);
    +
    616 static_assert(
    +
    617 std::is_same_v<
    +
    618 EvalTypeTheta,
    +
    619 eval_type> || std::is_same_v<EvalTypeTheta, eval_deriv_type>);
    +
    620
    +
    621 ddc::DiscreteElement<BSplinesR> jmin_r;
    +
    622 ddc::DiscreteElement<BSplinesTheta> jmin_theta;
    +
    623
    +
    624 std::size_t constexpr nr = BSplinesR::degree() + 1;
    +
    625 std::size_t constexpr ntheta = BSplinesTheta::degree() + 1;
    +
    626
    +
    627 std::array<double, nr> vals_r_ptr;
    +
    628 std::array<double, ntheta> vals_theta_ptr;
    +
    629 DSpan1D const vals_r(vals_r_ptr.data(), nr);
    +
    630 DSpan1D const vals_theta(vals_theta_ptr.data(), ntheta);
    +
    631
    +
    632 if constexpr (std::is_same_v<EvalTypeR, eval_type>) {
    +
    633 jmin_r = ddc::discrete_space<BSplinesR>().eval_basis(vals_r, ddc::select<DimR>(coord_eval));
    +
    634 } else if constexpr (std::is_same_v<EvalTypeR, eval_deriv_type>) {
    +
    635 jmin_r = ddc::discrete_space<BSplinesR>().eval_deriv(vals_r, ddc::select<DimR>(coord_eval));
    +
    636 }
    +
    637 if constexpr (std::is_same_v<EvalTypeTheta, eval_type>) {
    +
    638 jmin_theta = ddc::discrete_space<BSplinesTheta>()
    +
    639 .eval_basis(vals_theta, ddc::select<DimTheta>(coord_eval));
    +
    640 } else if constexpr (std::is_same_v<EvalTypeTheta, eval_deriv_type>) {
    +
    641 jmin_theta = ddc::discrete_space<BSplinesTheta>()
    +
    642 .eval_deriv(vals_theta, ddc::select<DimTheta>(coord_eval));
    +
    643 }
    644
    -
    645 if (jmin_r.uid() < C + 1) {
    -
    646 nr_done = C + 1 - jmin_r.uid();
    -
    647 for (discrete_element_type k : singular_idx_range<DDim>()) {
    -
    648 singular_values(k.uid()) = 0.0;
    -
    649 for (std::size_t i(0); i < nr_done; ++i) {
    -
    650 for (std::size_t j(0); j < ntheta; ++j) {
    -
    651 singular_values(k.uid())
    -
    652 += m_singular_basis_elements(k, jmin_r + i, jmin_theta + j) * vals_r[i]
    -
    653 * vals_theta[j];
    -
    654 }
    -
    655 }
    -
    656 }
    -
    657 } else {
    -
    658 for (std::size_t k(0); k < n_singular_basis(); ++k) {
    -
    659 singular_values(k) = 0.0;
    -
    660 }
    -
    661 }
    -
    662
    -
    663 for (std::size_t i(0); i < nr - nr_done; ++i) {
    -
    664 for (std::size_t j(0); j < ntheta; ++j) {
    -
    665 values(i, j) = vals_r[i + nr_done] * vals_theta[j];
    -
    666 }
    -
    667 }
    -
    668 for (std::size_t i(nr - nr_done); i < nr; ++i) {
    -
    669 for (std::size_t j(0); j < ntheta; ++j) {
    -
    670 values(i, j) = 0.0;
    -
    671 }
    -
    672 }
    -
    673 return ddc::DiscreteElement<BSplinesR, BSplinesTheta>(jmin_r, jmin_theta);
    -
    674}
    -
    675
    -
    676template <class ExecSpace, class DDim, class MemorySpace>
    -
    677PolarSplineSpan<DDim, MemorySpace> integrals(
    -
    678 ExecSpace const& execution_space,
    -
    679 PolarSplineSpan<DDim, MemorySpace> int_vals)
    -
    680{
    -
    681 static_assert(
    -
    682 Kokkos::SpaceAccessibility<ExecSpace, MemorySpace>::accessible,
    -
    683 "MemorySpace has to be accessible for ExecutionSpace.");
    -
    684 using BSplinesR = typename DDim::BSplinesR_tag;
    -
    685 using BSplinesTheta = typename DDim::BSplinesTheta_tag;
    -
    686 using tensor_product_idx_range_type = ddc::DiscreteDomain<BSplinesR, BSplinesTheta>;
    -
    687 using tensor_product_idx_type = ddc::DiscreteElement<BSplinesR, BSplinesTheta>;
    -
    688 using IdxR = ddc::DiscreteElement<BSplinesR>;
    -
    689 using IdxTheta = ddc::DiscreteElement<BSplinesTheta>;
    -
    690
    -
    691 auto r_bspl_space = ddc::discrete_space<BSplinesR>();
    -
    692 auto theta_bspl_space = ddc::discrete_space<BSplinesTheta>();
    -
    693
    -
    694 assert(int_vals.singular_spline_coef.domain().extents() == DDim::n_singular_basis());
    -
    695 assert(int_vals.spline_coef.domain().front().template uid<BSplinesR>() == DDim::continuity + 1);
    -
    696 assert(int_vals.spline_coef.domain().back().template uid<BSplinesR>()
    -
    697 == r_bspl_space.nbasis() - 1);
    -
    698 assert(int_vals.spline_coef.domain().template extent<BSplinesTheta>()
    -
    699 == theta_bspl_space.nbasis()
    -
    700 || int_vals.spline_coef.domain().template extent<BSplinesTheta>()
    -
    701 == theta_bspl_space.size());
    -
    702
    -
    703 ddc::Chunk<double, ddc::DiscreteDomain<BSplinesR>, ddc::KokkosAllocator<double, MemorySpace>>
    -
    704 r_integrals_alloc(r_bspl_space.full_domain().take_first(
    -
    705 ddc::DiscreteVector<BSplinesR> {r_bspl_space.nbasis()}));
    -
    706 ddc::Chunk<
    -
    707 double,
    -
    708 ddc::DiscreteDomain<BSplinesTheta>,
    -
    709 ddc::KokkosAllocator<double, MemorySpace>>
    -
    710 theta_integrals_alloc(theta_bspl_space.full_domain().take_first(
    -
    711 ddc::DiscreteVector<BSplinesTheta> {theta_bspl_space.size()}));
    -
    712 ddc::ChunkSpan r_integrals = r_integrals_alloc.span_view();
    -
    713 ddc::ChunkSpan theta_integrals = theta_integrals_alloc.span_view();
    -
    714
    -
    715 ddc::integrals(execution_space, r_integrals);
    -
    716 ddc::integrals(execution_space, theta_integrals);
    -
    717
    -
    718 ddc::DiscreteDomain<BSplinesR, BSplinesTheta> singular_2d_idx_range(
    -
    719 ddc::discrete_space<DDim>().m_singular_basis_elements.domain());
    -
    720 ddc::ChunkSpan singular_spline_integrals = int_vals.singular_spline_coef.span_view();
    -
    721
    -
    722 ddc::DiscreteDomain<DDim> singular_idx_range = DDim::template singular_idx_range<DDim>();
    -
    723 Kokkos::parallel_for(
    -
    724 Kokkos::TeamPolicy<>(execution_space, singular_idx_range.size(), Kokkos::AUTO),
    -
    725 KOKKOS_LAMBDA(const Kokkos::TeamPolicy<>::member_type& team) {
    -
    726 const int idx = team.league_rank();
    -
    727 ddc::DiscreteElement<DDim> k(idx);
    -
    728
    -
    729 // Sum over quadrature dimensions
    -
    730 double teamSum = 0;
    -
    731 Kokkos::parallel_reduce(
    -
    732 Kokkos::TeamThreadMDRange(
    -
    733 team,
    -
    734 singular_2d_idx_range.template extent<BSplinesR>().value(),
    -
    735 singular_2d_idx_range.template extent<BSplinesTheta>().value()),
    -
    736 [&](int r_thread_index, int theta_thread_index, double& sum) {
    -
    737 IdxR i(r_thread_index);
    -
    738 IdxTheta j(theta_thread_index);
    -
    739 sum += ddc::discrete_space<DDim>().m_singular_basis_elements(k, i, j)
    -
    740 * r_integrals(i) * theta_integrals(j);
    -
    741 },
    -
    742 teamSum);
    -
    743 singular_spline_integrals(k) = teamSum;
    -
    744 });
    -
    745
    -
    746
    -
    747 ddc::DiscreteDomain<BSplinesR> r_tensor_product_dom(
    -
    748 ddc::select<BSplinesR>(int_vals.spline_coef.domain()));
    -
    749 tensor_product_idx_range_type
    -
    750 tensor_bspline_idx_range(r_tensor_product_dom, theta_integrals.domain());
    -
    751 ddc::ChunkSpan spline_integrals = int_vals.spline_coef.span_view();
    -
    752
    -
    753 ddc::parallel_for_each(
    -
    754 execution_space,
    -
    755 tensor_bspline_idx_range,
    -
    756 KOKKOS_LAMBDA(tensor_product_idx_type idx) {
    -
    757 int_vals.spline_coef(idx) = r_integrals(ddc::select<BSplinesR>(idx))
    -
    758 * theta_integrals(ddc::select<BSplinesTheta>(idx));
    -
    759 });
    -
    760
    -
    761 if (int_vals.spline_coef.domain().template extent<BSplinesTheta>() == theta_bspl_space.size()) {
    -
    762 ddc::DiscreteDomain<BSplinesTheta> periodic_points(theta_integrals.domain().take_last(
    -
    763 ddc::DiscreteVector<BSplinesTheta> {BSplinesTheta::degree()}));
    -
    764 tensor_product_idx_range_type repeat_idx_range(r_tensor_product_dom, periodic_points);
    -
    765 ddc::parallel_fill(execution_space, int_vals.spline_coef, 0.0);
    -
    766 }
    -
    767 return int_vals;
    -
    768}
    -
    769
    -
    770template <class BSplinesR, class BSplinesTheta, int C>
    -
    771template <class DDim, class MemorySpace>
    -
    772template <class MemorySpace2>
    -
    -
    773void PolarBSplines<BSplinesR, BSplinesTheta, C>::Impl<DDim, MemorySpace>::integrals(
    -
    774 PolarSplineSpan<DDim, MemorySpace2> int_vals) const
    -
    775{
    -
    776 integrals(Kokkos::DefaultHostExecutionSpace(), int_vals);
    -
    777}
    +
    645 std::size_t nr_done = 0;
    +
    646
    +
    647 if (jmin_r.uid() < C + 1) {
    +
    648 nr_done = C + 1 - jmin_r.uid();
    +
    649 for (discrete_element_type k : singular_idx_range<DDim>()) {
    +
    650 singular_values(k.uid()) = 0.0;
    +
    651 for (std::size_t i(0); i < nr_done; ++i) {
    +
    652 for (std::size_t j(0); j < ntheta; ++j) {
    +
    653 singular_values(k.uid())
    +
    654 += m_singular_basis_elements(k, jmin_r + i, jmin_theta + j) * vals_r[i]
    +
    655 * vals_theta[j];
    +
    656 }
    +
    657 }
    +
    658 }
    +
    659 } else {
    +
    660 for (std::size_t k(0); k < n_singular_basis(); ++k) {
    +
    661 singular_values(k) = 0.0;
    +
    662 }
    +
    663 }
    +
    664
    +
    665 for (std::size_t i(0); i < nr - nr_done; ++i) {
    +
    666 for (std::size_t j(0); j < ntheta; ++j) {
    +
    667 values(i, j) = vals_r[i + nr_done] * vals_theta[j];
    +
    668 }
    +
    669 }
    +
    670 for (std::size_t i(nr - nr_done); i < nr; ++i) {
    +
    671 for (std::size_t j(0); j < ntheta; ++j) {
    +
    672 values(i, j) = 0.0;
    +
    673 }
    +
    674 }
    +
    675 return ddc::DiscreteElement<BSplinesR, BSplinesTheta>(jmin_r, jmin_theta);
    +
    676}
    +
    677
    +
    678template <class ExecSpace, class DDim, class MemorySpace>
    +
    679PolarSplineSpan<DDim, MemorySpace> integrals(
    +
    680 ExecSpace const& execution_space,
    +
    681 PolarSplineSpan<DDim, MemorySpace> int_vals)
    +
    682{
    +
    683 static_assert(
    +
    684 Kokkos::SpaceAccessibility<ExecSpace, MemorySpace>::accessible,
    +
    685 "MemorySpace has to be accessible for ExecutionSpace.");
    +
    686 using BSplinesR = typename DDim::BSplinesR_tag;
    +
    687 using BSplinesTheta = typename DDim::BSplinesTheta_tag;
    +
    688 using tensor_product_idx_range_type = ddc::DiscreteDomain<BSplinesR, BSplinesTheta>;
    +
    689 using tensor_product_idx_type = ddc::DiscreteElement<BSplinesR, BSplinesTheta>;
    +
    690 using IdxR = ddc::DiscreteElement<BSplinesR>;
    +
    691 using IdxTheta = ddc::DiscreteElement<BSplinesTheta>;
    +
    692
    +
    693 auto r_bspl_space = ddc::discrete_space<BSplinesR>();
    +
    694 auto theta_bspl_space = ddc::discrete_space<BSplinesTheta>();
    +
    695
    +
    696 assert(int_vals.singular_spline_coef.domain().extents() == DDim::n_singular_basis());
    +
    697 assert(int_vals.spline_coef.domain().front().template uid<BSplinesR>() == DDim::continuity + 1);
    +
    698 assert(int_vals.spline_coef.domain().back().template uid<BSplinesR>()
    +
    699 == r_bspl_space.nbasis() - 1);
    +
    700 assert(int_vals.spline_coef.domain().template extent<BSplinesTheta>()
    +
    701 == theta_bspl_space.nbasis()
    +
    702 || int_vals.spline_coef.domain().template extent<BSplinesTheta>()
    +
    703 == theta_bspl_space.size());
    +
    704
    +
    705 ddc::Chunk<double, ddc::DiscreteDomain<BSplinesR>, ddc::KokkosAllocator<double, MemorySpace>>
    +
    706 r_integrals_alloc(r_bspl_space.full_domain().take_first(
    +
    707 ddc::DiscreteVector<BSplinesR> {r_bspl_space.nbasis()}));
    +
    708 ddc::Chunk<
    +
    709 double,
    +
    710 ddc::DiscreteDomain<BSplinesTheta>,
    +
    711 ddc::KokkosAllocator<double, MemorySpace>>
    +
    712 theta_integrals_alloc(theta_bspl_space.full_domain().take_first(
    +
    713 ddc::DiscreteVector<BSplinesTheta> {theta_bspl_space.size()}));
    +
    714 ddc::ChunkSpan r_integrals = r_integrals_alloc.span_view();
    +
    715 ddc::ChunkSpan theta_integrals = theta_integrals_alloc.span_view();
    +
    716
    +
    717 ddc::integrals(execution_space, r_integrals);
    +
    718 ddc::integrals(execution_space, theta_integrals);
    +
    719
    +
    720 ddc::DiscreteDomain<BSplinesR, BSplinesTheta> singular_2d_idx_range(
    +
    721 ddc::discrete_space<DDim>().m_singular_basis_elements.domain());
    +
    722 ddc::ChunkSpan singular_spline_integrals = int_vals.singular_spline_coef.span_view();
    +
    723
    +
    724 ddc::DiscreteDomain<DDim> singular_idx_range = DDim::template singular_idx_range<DDim>();
    +
    725 Kokkos::parallel_for(
    +
    726 Kokkos::TeamPolicy<>(execution_space, singular_idx_range.size(), Kokkos::AUTO),
    +
    727 KOKKOS_LAMBDA(const Kokkos::TeamPolicy<>::member_type& team) {
    +
    728 const int idx = team.league_rank();
    +
    729 ddc::DiscreteElement<DDim> k(idx);
    +
    730
    +
    731 // Sum over quadrature dimensions
    +
    732 double teamSum = 0;
    +
    733 Kokkos::parallel_reduce(
    +
    734 Kokkos::TeamThreadMDRange(
    +
    735 team,
    +
    736 singular_2d_idx_range.template extent<BSplinesR>().value(),
    +
    737 singular_2d_idx_range.template extent<BSplinesTheta>().value()),
    +
    738 [&](int r_thread_index, int theta_thread_index, double& sum) {
    +
    739 IdxR i(r_thread_index);
    +
    740 IdxTheta j(theta_thread_index);
    +
    741 sum += ddc::discrete_space<DDim>().m_singular_basis_elements(k, i, j)
    +
    742 * r_integrals(i) * theta_integrals(j);
    +
    743 },
    +
    744 teamSum);
    +
    745 singular_spline_integrals(k) = teamSum;
    +
    746 });
    +
    747
    +
    748
    +
    749 ddc::DiscreteDomain<BSplinesR> r_tensor_product_dom(
    +
    750 ddc::select<BSplinesR>(int_vals.spline_coef.domain()));
    +
    751 tensor_product_idx_range_type
    +
    752 tensor_bspline_idx_range(r_tensor_product_dom, theta_integrals.domain());
    +
    753 ddc::ChunkSpan spline_integrals = int_vals.spline_coef.span_view();
    +
    754
    +
    755 ddc::parallel_for_each(
    +
    756 execution_space,
    +
    757 tensor_bspline_idx_range,
    +
    758 KOKKOS_LAMBDA(tensor_product_idx_type idx) {
    +
    759 int_vals.spline_coef(idx) = r_integrals(ddc::select<BSplinesR>(idx))
    +
    760 * theta_integrals(ddc::select<BSplinesTheta>(idx));
    +
    761 });
    +
    762
    +
    763 if (int_vals.spline_coef.domain().template extent<BSplinesTheta>() == theta_bspl_space.size()) {
    +
    764 ddc::DiscreteDomain<BSplinesTheta> periodic_points(theta_integrals.domain().take_last(
    +
    765 ddc::DiscreteVector<BSplinesTheta> {BSplinesTheta::degree()}));
    +
    766 tensor_product_idx_range_type repeat_idx_range(r_tensor_product_dom, periodic_points);
    +
    767 ddc::parallel_fill(execution_space, int_vals.spline_coef, 0.0);
    +
    768 }
    +
    769 return int_vals;
    +
    770}
    +
    771
    +
    772template <class BSplinesR, class BSplinesTheta, int C>
    +
    773template <class DDim, class MemorySpace>
    +
    774template <class MemorySpace2>
    +
    +
    775void PolarBSplines<BSplinesR, BSplinesTheta, C>::Impl<DDim, MemorySpace>::integrals(
    +
    776 PolarSplineSpan<DDim, MemorySpace2> int_vals) const
    +
    777{
    +
    778 integrals(Kokkos::DefaultHostExecutionSpace(), int_vals);
    +
    779}
    @@ -722,42 +724,42 @@
    CartesianToBarycentric
    A class to convert cartesian coordinates to barycentric coordinates on a triangle.
    Definition cartesian_to_barycentric.hpp:22
    -
    PolarBSplines::Impl
    The Impl class holds the implementation of the PolarBSplines.
    Definition polar_bsplines.hpp:173
    -
    PolarBSplines::Impl::nbasis
    std::size_t nbasis() const noexcept
    Get the total number of basis functions.
    Definition polar_bsplines.hpp:514
    -
    PolarBSplines::Impl::full_domain
    discrete_domain_type full_domain() const noexcept
    Returns the index range containing the indices of all the polar b-splines.
    Definition polar_bsplines.hpp:526
    +
    PolarBSplines::Impl
    The Impl class holds the implementation of the PolarBSplines.
    Definition polar_bsplines.hpp:174
    +
    PolarBSplines::Impl::nbasis
    std::size_t nbasis() const noexcept
    Get the total number of basis functions.
    Definition polar_bsplines.hpp:516
    +
    PolarBSplines::Impl::full_domain
    discrete_domain_type full_domain() const noexcept
    Returns the index range containing the indices of all the polar b-splines.
    Definition polar_bsplines.hpp:528
    PolarBSplines::Impl::Impl
    Impl(Impl &&x)=default
    A copy constructor for the PolarBSplines taking a temporary r-value.
    PolarBSplines::Impl::operator=
    Impl & operator=(Impl &&x)=default
    A copy operator for the PolarBSplines taking a temporary r-value.
    -
    PolarBSplines::Impl::eval_deriv_r_and_theta
    tensor_product_index_type eval_deriv_r_and_theta(DSpan1D singular_derivs, DSpan2D derivs, ddc::Coordinate< DimR, DimTheta > p) const
    Evaluate the second order derivative of the polar basis splines in the radial and poloidal directions...
    Definition polar_bsplines.hpp:590
    -
    PolarBSplines::Impl::Impl
    Impl(const DiscreteMapping &curvilinear_to_cartesian)
    A constructor for the PolarBSplines.
    Definition polar_bsplines.hpp:253
    -
    PolarBSplines::Impl::discrete_domain_type
    ddc::DiscreteDomain< DDim > discrete_domain_type
    The type of a index range of PolarBSplines.
    Definition polar_bsplines.hpp:240
    +
    PolarBSplines::Impl::eval_deriv_r_and_theta
    tensor_product_index_type eval_deriv_r_and_theta(DSpan1D singular_derivs, DSpan2D derivs, ddc::Coordinate< DimR, DimTheta > p) const
    Evaluate the second order derivative of the polar basis splines in the radial and poloidal directions...
    Definition polar_bsplines.hpp:592
    +
    PolarBSplines::Impl::Impl
    Impl(const DiscreteMapping &curvilinear_to_cartesian)
    A constructor for the PolarBSplines.
    Definition polar_bsplines.hpp:254
    +
    PolarBSplines::Impl::discrete_domain_type
    ddc::DiscreteDomain< DDim > discrete_domain_type
    The type of a index range of PolarBSplines.
    Definition polar_bsplines.hpp:241
    PolarBSplines::Impl::operator=
    Impl & operator=(Impl const &x)=default
    A copy operator for the PolarBSplines.
    PolarBSplines::Impl::~Impl
    ~Impl()=default
    The destructor for the PolarBSplines.
    -
    PolarBSplines::Impl::Impl
    Impl(Impl< DDim, OriginMemorySpace > const &impl)
    A copy constructor for the PolarBSplines.
    Definition polar_bsplines.hpp:371
    -
    PolarBSplines::Impl::discrete_vector_type
    ddc::DiscreteVector< DDim > discrete_vector_type
    The type of a vector associated with a PolarBSpline.
    Definition polar_bsplines.hpp:243
    -
    PolarBSplines::Impl::eval_basis
    tensor_product_index_type eval_basis(DSpan1D singular_values, DSpan2D values, ddc::Coordinate< DimR, DimTheta > p) const
    Evaluate the polar basis splines at the coordinate p.
    Definition polar_bsplines.hpp:557
    -
    PolarBSplines::Impl::discrete_element_type
    ddc::DiscreteElement< DDim > discrete_element_type
    The type of an index associated with a PolarBSpline.
    Definition polar_bsplines.hpp:237
    -
    PolarBSplines::Impl::eval_deriv_theta
    tensor_product_index_type eval_deriv_theta(DSpan1D singular_derivs, DSpan2D derivs, ddc::Coordinate< DimR, DimTheta > p) const
    Evaluate the poloidal derivative of the polar basis splines at the coordinate p.
    Definition polar_bsplines.hpp:579
    -
    PolarBSplines::Impl::eval_deriv_r
    tensor_product_index_type eval_deriv_r(DSpan1D singular_derivs, DSpan2D derivs, ddc::Coordinate< DimR, DimTheta > p) const
    Evaluate the radial derivative of the polar basis splines at the coordinate p.
    Definition polar_bsplines.hpp:568
    -
    PolarBSplines::Impl::tensor_bspline_idx_range
    discrete_domain_type tensor_bspline_idx_range() const noexcept
    Returns the ddc::DiscreteDomain containing the indices of the b-splines which don't traverse the sing...
    Definition polar_bsplines.hpp:538
    +
    PolarBSplines::Impl::Impl
    Impl(Impl< DDim, OriginMemorySpace > const &impl)
    A copy constructor for the PolarBSplines.
    Definition polar_bsplines.hpp:373
    +
    PolarBSplines::Impl::discrete_vector_type
    ddc::DiscreteVector< DDim > discrete_vector_type
    The type of a vector associated with a PolarBSpline.
    Definition polar_bsplines.hpp:244
    +
    PolarBSplines::Impl::eval_basis
    tensor_product_index_type eval_basis(DSpan1D singular_values, DSpan2D values, ddc::Coordinate< DimR, DimTheta > p) const
    Evaluate the polar basis splines at the coordinate p.
    Definition polar_bsplines.hpp:559
    +
    PolarBSplines::Impl::discrete_element_type
    ddc::DiscreteElement< DDim > discrete_element_type
    The type of an index associated with a PolarBSpline.
    Definition polar_bsplines.hpp:238
    +
    PolarBSplines::Impl::eval_deriv_theta
    tensor_product_index_type eval_deriv_theta(DSpan1D singular_derivs, DSpan2D derivs, ddc::Coordinate< DimR, DimTheta > p) const
    Evaluate the poloidal derivative of the polar basis splines at the coordinate p.
    Definition polar_bsplines.hpp:581
    +
    PolarBSplines::Impl::eval_deriv_r
    tensor_product_index_type eval_deriv_r(DSpan1D singular_derivs, DSpan2D derivs, ddc::Coordinate< DimR, DimTheta > p) const
    Evaluate the radial derivative of the polar basis splines at the coordinate p.
    Definition polar_bsplines.hpp:570
    +
    PolarBSplines::Impl::tensor_bspline_idx_range
    discrete_domain_type tensor_bspline_idx_range() const noexcept
    Returns the ddc::DiscreteDomain containing the indices of the b-splines which don't traverse the sing...
    Definition polar_bsplines.hpp:540
    PolarBSplines::Impl::Impl
    Impl(Impl const &x)=default
    A copy constructor for the PolarBSplines.
    -
    PolarBSplines::Impl::Corner1Tag
    The tag for the first corner of the Barycentric coordinates.
    Definition polar_bsplines.hpp:210
    -
    PolarBSplines::Impl::Corner2Tag
    The tag for the second corner of the Barycentric coordinates.
    Definition polar_bsplines.hpp:214
    -
    PolarBSplines::Impl::Corner3Tag
    The tag for the third corner of the Barycentric coordinates.
    Definition polar_bsplines.hpp:218
    -
    PolarBSplines
    A class containing all information describing polar bsplines.
    Definition polar_bsplines.hpp:28
    -
    PolarBSplines::get_polar_index
    static KOKKOS_FUNCTION ddc::DiscreteElement< DDim > get_polar_index(tensor_product_index_type const &idx)
    Get the index of the polar bspline which, when evaluated at the same point, returns the same values a...
    Definition polar_bsplines.hpp:133
    -
    PolarBSplines::get_2d_index
    static KOKKOS_FUNCTION tensor_product_index_type get_2d_index(ddc::DiscreteElement< DDim > const &idx)
    Get the 2D index of the tensor product bspline which, when evaluated at the same point,...
    Definition polar_bsplines.hpp:153
    -
    PolarBSplines::tensor_product_idx_step_type
    ddc::DiscreteVector< BSplinesR, BSplinesTheta > tensor_product_idx_step_type
    The type of a 2D vector for the subset of the polar bsplines which can be expressed as a tensor produ...
    Definition polar_bsplines.hpp:89
    -
    PolarBSplines::n_singular_basis
    static constexpr std::size_t n_singular_basis()
    Get the number of singular bsplines i.e.
    Definition polar_bsplines.hpp:103
    -
    PolarBSplines::DimTheta
    typename BSplinesTheta::continuous_dimension_type DimTheta
    The tag for the poloidal direction of the bsplines.
    Definition polar_bsplines.hpp:57
    -
    PolarBSplines::tensor_product_idx_range_type
    ddc::DiscreteDomain< BSplinesR, BSplinesTheta > tensor_product_idx_range_type
    The type of the 2D idx_range for the subset of the polar bsplines which can be expressed as a tensor ...
    Definition polar_bsplines.hpp:83
    -
    PolarBSplines::singular_idx_range
    static constexpr ddc::DiscreteDomain< DDim > singular_idx_range()
    Get the ddc::DiscreteDomain containing the indices of the b-splines which traverse the singular point...
    Definition polar_bsplines.hpp:117
    -
    PolarBSplines::tensor_product_index_type
    ddc::DiscreteElement< BSplinesR, BSplinesTheta > tensor_product_index_type
    The type of a 2D index for the subset of the polar bsplines which can be expressed as a tensor produc...
    Definition polar_bsplines.hpp:77
    -
    PolarBSplines::DimR
    typename BSplinesR::continuous_dimension_type DimR
    The tag for the radial direction of the bsplines.
    Definition polar_bsplines.hpp:54
    -
    PolarBSplines::continuity
    static int constexpr continuity
    The continuity enforced by the bsplines at the singular point.
    Definition polar_bsplines.hpp:61
    +
    PolarBSplines::Impl::Corner1Tag
    The tag for the first corner of the Barycentric coordinates.
    Definition polar_bsplines.hpp:211
    +
    PolarBSplines::Impl::Corner2Tag
    The tag for the second corner of the Barycentric coordinates.
    Definition polar_bsplines.hpp:215
    +
    PolarBSplines::Impl::Corner3Tag
    The tag for the third corner of the Barycentric coordinates.
    Definition polar_bsplines.hpp:219
    +
    PolarBSplines
    A class containing all information describing polar bsplines.
    Definition polar_bsplines.hpp:29
    +
    PolarBSplines::get_polar_index
    static KOKKOS_FUNCTION ddc::DiscreteElement< DDim > get_polar_index(tensor_product_index_type const &idx)
    Get the index of the polar bspline which, when evaluated at the same point, returns the same values a...
    Definition polar_bsplines.hpp:134
    +
    PolarBSplines::get_2d_index
    static KOKKOS_FUNCTION tensor_product_index_type get_2d_index(ddc::DiscreteElement< DDim > const &idx)
    Get the 2D index of the tensor product bspline which, when evaluated at the same point,...
    Definition polar_bsplines.hpp:154
    +
    PolarBSplines::tensor_product_idx_step_type
    ddc::DiscreteVector< BSplinesR, BSplinesTheta > tensor_product_idx_step_type
    The type of a 2D vector for the subset of the polar bsplines which can be expressed as a tensor produ...
    Definition polar_bsplines.hpp:90
    +
    PolarBSplines::n_singular_basis
    static constexpr std::size_t n_singular_basis()
    Get the number of singular bsplines i.e.
    Definition polar_bsplines.hpp:104
    +
    PolarBSplines::DimTheta
    typename BSplinesTheta::continuous_dimension_type DimTheta
    The tag for the poloidal direction of the bsplines.
    Definition polar_bsplines.hpp:58
    +
    PolarBSplines::tensor_product_idx_range_type
    ddc::DiscreteDomain< BSplinesR, BSplinesTheta > tensor_product_idx_range_type
    The type of the 2D idx_range for the subset of the polar bsplines which can be expressed as a tensor ...
    Definition polar_bsplines.hpp:84
    +
    PolarBSplines::singular_idx_range
    static constexpr ddc::DiscreteDomain< DDim > singular_idx_range()
    Get the ddc::DiscreteDomain containing the indices of the b-splines which traverse the singular point...
    Definition polar_bsplines.hpp:118
    +
    PolarBSplines::tensor_product_index_type
    ddc::DiscreteElement< BSplinesR, BSplinesTheta > tensor_product_index_type
    The type of a 2D index for the subset of the polar bsplines which can be expressed as a tensor produc...
    Definition polar_bsplines.hpp:78
    +
    PolarBSplines::DimR
    typename BSplinesR::continuous_dimension_type DimR
    The tag for the radial direction of the bsplines.
    Definition polar_bsplines.hpp:55
    +
    PolarBSplines::continuity
    static int constexpr continuity
    The continuity enforced by the bsplines at the singular point.
    Definition polar_bsplines.hpp:62
    TriangularBernsteinPolynomialBasis
    A class which evaluates the triangular Bernstein polynomials.
    Definition bernstein.hpp:29
    BSplinesR
    Definition geometry.hpp:93
    BSplinesTheta
    Definition geometry.hpp:100
    -
    PolarBSplines::Impl::IntermediateBernsteinBasis
    Definition polar_bsplines.hpp:230
    +
    PolarBSplines::Impl::IntermediateBernsteinBasis
    Definition polar_bsplines.hpp:231
    PolarSplineSpan
    A structure containing the two ChunkSpans necessary to define a reference to a spline on a set of pol...
    Definition polar_spline.hpp:116
    PolarSplineSpan::spline_coef
    ddc::ChunkSpan< double, ddc::DiscreteDomain< BSplinesR, BSplinesTheta >, Kokkos::layout_right, MemSpace > spline_coef
    A ChunkSpan containing the coefficients in front of the b-spline elements which can be expressed as a...
    Definition polar_spline.hpp:133
    PolarSplineSpan::singular_spline_coef
    ddc::ChunkSpan< double, ddc::DiscreteDomain< PolarBSplinesType >, Kokkos::layout_right, MemSpace > singular_spline_coef
    A ChunkSpan containing the coefficients in front of the b-spline elements near the singular point whi...
    Definition polar_spline.hpp:140
    diff --git a/polar__poisson_2test__cases_8hpp_source.html b/polar__poisson_2test__cases_8hpp_source.html index e3df00ca9..84441d4a4 100644 --- a/polar__poisson_2test__cases_8hpp_source.html +++ b/polar__poisson_2test__cases_8hpp_source.html @@ -295,8 +295,8 @@
    PoissonSolution::PoissonSolution
    PoissonSolution(CurvilinearToCartesian const &coordinate_converter)
    Instantiate a PoissonSolution.
    Definition test_cases.hpp:55
    R
    Define non periodic real R dimension.
    Definition geometry.hpp:31
    Theta
    Define periodic real Theta dimension.
    Definition geometry.hpp:42
    -
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:277
    -
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:288
    +
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:318
    +
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:329
    diff --git a/polarpoissonlikesolver_8hpp_source.html b/polarpoissonlikesolver_8hpp_source.html index 60763d6c6..806e1c885 100644 --- a/polarpoissonlikesolver_8hpp_source.html +++ b/polarpoissonlikesolver_8hpp_source.html @@ -123,62 +123,62 @@
    15#include "ddc_aliases.hpp"
    16#include "matrix_batch_csr.hpp"
    17
    -
    43template <
    -
    44 class GridR,
    -
    45 class GridTheta,
    -
    46 class PolarBSplinesRTheta,
    -
    47 class SplineRThetaEvaluatorNullBound_host,
    -
    48 class IdxRangeFull = IdxRange<GridR, GridTheta>>
    -
    -
    49class PolarSplineFEMPoissonLikeSolver
    -
    50{
    -
    51 // TODO: Add a batch loop to operator()
    -
    52 static_assert(
    -
    53 std::is_same_v<IdxRangeFull, IdxRange<GridR, GridTheta>>,
    -
    54 "PolarSplineFEMPoissonLikeSolver is not yet batched");
    -
    55
    -
    56public:
    -
    58 using R = typename GridR::continuous_dimension_type;
    -
    60 using Theta = typename GridTheta::continuous_dimension_type;
    -
    61
    -
    62public:
    -
    -
    63 struct RBasisSubset
    -
    64 {
    -
    65 };
    +
    18
    +
    44template <
    +
    45 class GridR,
    +
    46 class GridTheta,
    +
    47 class PolarBSplinesRTheta,
    +
    48 class SplineRThetaEvaluatorNullBound,
    +
    49 class IdxRangeFull = IdxRange<GridR, GridTheta>>
    +
    +
    50class PolarSplineFEMPoissonLikeSolver
    +
    51{
    +
    52 // TODO: Add a batch loop to operator()
    +
    53 static_assert(
    +
    54 std::is_same_v<IdxRangeFull, IdxRange<GridR, GridTheta>>,
    +
    55 "PolarSplineFEMPoissonLikeSolver is not yet batched");
    +
    56
    +
    57public:
    +
    59 using R = typename GridR::continuous_dimension_type;
    +
    61 using Theta = typename GridTheta::continuous_dimension_type;
    +
    62
    +
    63public:
    +
    +
    64 struct RBasisSubset
    +
    65 {
    +
    66 };
    -
    -
    66 struct ThetaBasisSubset
    -
    67 {
    -
    68 };
    +
    +
    67 struct ThetaBasisSubset
    +
    68 {
    +
    69 };
    -
    -
    69 struct RCellDim
    -
    70 {
    -
    71 };
    +
    +
    70 struct RCellDim
    +
    71 {
    +
    72 };
    -
    -
    72 struct ThetaCellDim
    -
    73 {
    -
    74 };
    +
    +
    73 struct ThetaCellDim
    +
    74 {
    +
    75 };
    -
    75
    76
    -
    77public:
    -
    -
    81 struct QDimRMesh : NonUniformGridBase<R>
    -
    82 {
    -
    83 };
    +
    77
    +
    78public:
    +
    +
    82 struct QDimRMesh : NonUniformGridBase<R>
    +
    83 {
    +
    84 };
    -
    -
    87 struct QDimThetaMesh : NonUniformGridBase<Theta>
    -
    88 {
    -
    89 };
    +
    +
    88 struct QDimThetaMesh : NonUniformGridBase<Theta>
    +
    89 {
    +
    90 };
    -
    90
    -
    91private:
    -
    92 using CoordRTheta = Coord<R, Theta>;
    -
    93
    +
    91
    +
    92private:
    +
    93 using CoordRTheta = Coord<R, Theta>;
    95 using BSplinesR = typename PolarBSplinesRTheta::BSplinesR_tag;
    97 using BSplinesTheta = typename PolarBSplinesRTheta::BSplinesTheta_tag;
    98
    @@ -220,1083 +220,1266 @@
    159 using CoordFieldRTheta = Field<CoordRTheta, IdxRangeRTheta>;
    160 using DFieldRTheta = DField<IdxRangeRTheta>;
    161
    -
    166 struct EvalDeriv1DType
    -
    167 {
    -
    168 double value;
    -
    169 double derivative;
    -
    170 };
    -
    175 struct EvalDeriv2DType
    -
    176 {
    -
    177 double value;
    -
    178 double radial_derivative;
    -
    179 double poloidal_derivative;
    -
    180 };
    -
    181
    -
    185 using IdxCell = Idx<RCellDim, ThetaCellDim>;
    -
    186
    -
    187private:
    -
    188 static constexpr int m_n_gauss_legendre_r = BSplinesR::degree() + 1;
    -
    189 static constexpr int m_n_gauss_legendre_theta = BSplinesTheta::degree() + 1;
    -
    190 // The number of cells (in the radial direction) in which both types of basis splines can be found
    -
    191 static constexpr int m_n_overlap_cells = PolarBSplinesRTheta::continuity + 1;
    -
    192
    -
    193 // Number of cells over which a radial B-splines has its support
    -
    194 // This is the case for b-splines which are not affected by the higher knot multiplicity at the boundary.
    -
    195 static constexpr IdxStep<RBasisSubset> m_n_non_zero_bases_r
    -
    196 = IdxStep<RBasisSubset>(BSplinesR::degree() + 1);
    -
    197
    -
    198 // Number of cells over which a poloidal B-splines has its support
    -
    199 static constexpr IdxStep<ThetaBasisSubset> m_n_non_zero_bases_theta
    -
    200 = IdxStep<ThetaBasisSubset>(BSplinesTheta::degree() + 1);
    -
    201
    -
    202 static constexpr IdxRange<RBasisSubset> m_non_zero_bases_r
    -
    203 = IdxRange<RBasisSubset>(Idx<RBasisSubset> {0}, m_n_non_zero_bases_r);
    -
    204 static constexpr IdxRange<ThetaBasisSubset> m_non_zero_bases_theta
    -
    205 = IdxRange<ThetaBasisSubset>(Idx<ThetaBasisSubset> {0}, m_n_non_zero_bases_theta);
    -
    206
    -
    207 const int m_nbasis_r;
    -
    208 const int m_nbasis_theta;
    -
    209
    -
    210 // Domains
    -
    211 IdxRangeBSPolar m_idxrange_fem_non_singular;
    -
    212 IdxRangeBSR m_idxrange_bsplines_r;
    -
    213 IdxRangeBSTheta m_idxrange_bsplines_theta;
    +
    162public:
    +
    +
    167 struct EvalDeriv1DType
    +
    168 {
    +
    169 double value;
    +
    170 double derivative;
    +
    171 };
    +
    +
    172
    +
    +
    177 struct EvalDeriv2DType
    +
    178 {
    +
    179 double value;
    +
    180 double radial_derivative;
    +
    181 double poloidal_derivative;
    +
    182 };
    +
    +
    183
    +
    187 using IdxCell = Idx<RCellDim, ThetaCellDim>;
    +
    188
    +
    189private:
    +
    190 static constexpr int m_n_gauss_legendre_r = BSplinesR::degree() + 1;
    +
    191 static constexpr int m_n_gauss_legendre_theta = BSplinesTheta::degree() + 1;
    +
    192 // The number of cells (in the radial direction) in which both types of basis splines can be found
    +
    193 static constexpr int m_n_overlap_cells = PolarBSplinesRTheta::continuity + 1;
    +
    194
    +
    195 // Number of cells over which a radial B-splines has its support
    +
    196 // This is the case for b-splines which are not affected by the higher knot multiplicity at the boundary.
    +
    197 static constexpr IdxStep<RBasisSubset> m_n_non_zero_bases_r
    +
    198 = IdxStep<RBasisSubset>(BSplinesR::degree() + 1);
    +
    199
    +
    200 // Number of cells over which a poloidal B-splines has its support
    +
    201 static constexpr IdxStep<ThetaBasisSubset> m_n_non_zero_bases_theta
    +
    202 = IdxStep<ThetaBasisSubset>(BSplinesTheta::degree() + 1);
    +
    203
    +
    204 static constexpr IdxRange<RBasisSubset> m_non_zero_bases_r
    +
    205 = IdxRange<RBasisSubset>(Idx<RBasisSubset> {0}, m_n_non_zero_bases_r);
    +
    206 static constexpr IdxRange<ThetaBasisSubset> m_non_zero_bases_theta
    +
    207 = IdxRange<ThetaBasisSubset>(Idx<ThetaBasisSubset> {0}, m_n_non_zero_bases_theta);
    +
    208
    +
    209 const int m_nbasis_r;
    +
    210 const int m_nbasis_theta;
    +
    211
    +
    212 // Matrix size is equal to the number of Polar bspline
    +
    213 const int m_matrix_size;
    214
    -
    215 IdxRangeQuadratureR m_idxrange_quadrature_r;
    -
    216 IdxRangeQuadratureTheta m_idxrange_quadrature_theta;
    -
    217 IdxRangeQuadratureRTheta m_idxrange_quadrature_singular;
    -
    218
    -
    219 // Gauss-Legendre points and weights
    -
    220 host_t<FieldMem<Coord<R>, IdxRangeQuadratureR>> m_points_r;
    -
    221 host_t<FieldMem<Coord<Theta>, IdxRangeQuadratureTheta>> m_points_theta;
    -
    222 host_t<FieldMem<double, IdxRangeQuadratureR>> m_weights_r;
    -
    223 host_t<FieldMem<double, IdxRangeQuadratureTheta>> m_weights_theta;
    -
    224
    -
    225 // Basis Spline values and derivatives at Gauss-Legendre points
    -
    226 host_t<FieldMem<EvalDeriv2DType, IdxRange<PolarBSplinesRTheta, QDimRMesh, QDimThetaMesh>>>
    -
    227 m_singular_basis_vals_and_derivs;
    -
    228 host_t<FieldMem<EvalDeriv1DType, IdxRange<RBasisSubset, QDimRMesh>>> r_basis_vals_and_derivs;
    -
    229 host_t<FieldMem<EvalDeriv1DType, IdxRange<ThetaBasisSubset, QDimThetaMesh>>>
    -
    230 m_theta_basis_vals_and_derivs;
    -
    231
    -
    232 host_t<FieldMem<double, IdxRangeQuadratureRTheta>> m_int_volume;
    -
    233
    -
    234 PolarSplineEvaluator<PolarBSplinesRTheta, ddc::NullExtrapolationRule, Kokkos::HostSpace>
    -
    235 m_polar_spline_evaluator;
    -
    236 std::unique_ptr<MatrixBatchCsr<Kokkos::DefaultExecutionSpace, MatrixBatchCsrSolver::CG>>
    -
    237 m_gko_matrix;
    -
    238 mutable host_t<SplinePolar> m_phi_spline_coef;
    -
    239 Kokkos::View<double**, Kokkos::LayoutRight> m_x_init;
    -
    240
    -
    241 const int m_batch_idx {0}; // TODO: Remove when batching is supported
    -
    242
    -
    243public:
    -
    267 template <class Mapping>
    -
    -
    268 PolarSplineFEMPoissonLikeSolver(
    -
    269 host_t<ConstSpline2D> coeff_alpha,
    -
    270 host_t<ConstSpline2D> coeff_beta,
    -
    271 Mapping const& mapping,
    -
    272 SplineRThetaEvaluatorNullBound_host const& spline_evaluator)
    -
    273 : m_nbasis_r(ddc::discrete_space<BSplinesR>().nbasis() - m_n_overlap_cells - 1)
    -
    274 , m_nbasis_theta(ddc::discrete_space<BSplinesTheta>().nbasis())
    -
    275 , m_idxrange_fem_non_singular(
    -
    276 ddc::discrete_space<PolarBSplinesRTheta>().tensor_bspline_idx_range().remove_last(
    -
    277 IdxStep<PolarBSplinesRTheta> {m_nbasis_theta}))
    -
    278 , m_idxrange_bsplines_r(ddc::discrete_space<BSplinesR>().full_domain().remove_first(
    -
    279 IdxStep<BSplinesR> {m_n_overlap_cells}))
    -
    280 , m_idxrange_bsplines_theta(ddc::discrete_space<BSplinesTheta>().full_domain().take_first(
    -
    281 IdxStep<BSplinesTheta> {m_nbasis_theta}))
    -
    282 , m_idxrange_quadrature_r(
    -
    283 Idx<QDimRMesh>(0),
    -
    284 IdxStep<QDimRMesh>(
    -
    285 m_n_gauss_legendre_r * ddc::discrete_space<BSplinesR>().ncells()))
    -
    286 , m_idxrange_quadrature_theta(
    -
    287 Idx<QDimThetaMesh>(0),
    -
    288 IdxStep<QDimThetaMesh>(
    -
    289 m_n_gauss_legendre_theta * ddc::discrete_space<BSplinesTheta>().ncells()))
    -
    290 , m_idxrange_quadrature_singular(
    -
    291 m_idxrange_quadrature_r.take_first(
    -
    292 IdxStep<QDimRMesh> {m_n_overlap_cells * m_n_gauss_legendre_r}),
    -
    293 m_idxrange_quadrature_theta)
    -
    294 , m_points_r(m_idxrange_quadrature_r)
    -
    295 , m_points_theta(m_idxrange_quadrature_theta)
    -
    296 , m_weights_r(m_idxrange_quadrature_r)
    -
    297 , m_weights_theta(m_idxrange_quadrature_theta)
    -
    298 , m_singular_basis_vals_and_derivs(IdxRange<PolarBSplinesRTheta, QDimRMesh, QDimThetaMesh>(
    -
    299 PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>(),
    -
    300 ddc::select<QDimRMesh>(m_idxrange_quadrature_singular),
    -
    301 ddc::select<QDimThetaMesh>(m_idxrange_quadrature_singular)))
    -
    302 , r_basis_vals_and_derivs(
    -
    303 IdxRange<RBasisSubset, QDimRMesh>(m_non_zero_bases_r, m_idxrange_quadrature_r))
    -
    304 , m_theta_basis_vals_and_derivs(
    -
    305 IdxRange<
    -
    306 ThetaBasisSubset,
    -
    307 QDimThetaMesh>(m_non_zero_bases_theta, m_idxrange_quadrature_theta))
    -
    308 , m_int_volume(
    -
    309 IdxRangeQuadratureRTheta(m_idxrange_quadrature_r, m_idxrange_quadrature_theta))
    -
    310 , m_polar_spline_evaluator(ddc::NullExtrapolationRule())
    -
    311 , m_phi_spline_coef(
    -
    312 PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>(),
    -
    313 IdxRangeBSRTheta(
    -
    314 m_idxrange_bsplines_r,
    -
    315 ddc::discrete_space<BSplinesTheta>().full_domain()))
    -
    316 , m_x_init(
    -
    317 "x_init",
    -
    318 1,
    -
    319 ddc::discrete_space<PolarBSplinesRTheta>().nbasis()
    -
    320 - ddc::discrete_space<BSplinesTheta>().nbasis())
    -
    321 {
    -
    322 static_assert(has_2d_jacobian_v<Mapping, CoordRTheta>);
    -
    323 //initialize x_init
    -
    324 Kokkos::deep_copy(m_x_init, 0);
    -
    325 // Get break points
    -
    326 IdxRange<KnotsR> idxrange_r_edges = ddc::discrete_space<BSplinesR>().break_point_domain();
    -
    327 IdxRange<KnotsTheta> idxrange_theta_edges
    -
    328 = ddc::discrete_space<BSplinesTheta>().break_point_domain();
    -
    329 host_t<FieldMem<Coord<R>, IdxRange<KnotsR>>> breaks_r(idxrange_r_edges);
    -
    330 host_t<FieldMem<Coord<Theta>, IdxRange<KnotsTheta>>> breaks_theta(idxrange_theta_edges);
    -
    331
    -
    332 ddc::for_each(idxrange_r_edges, [&](Idx<KnotsR> i) { breaks_r(i) = ddc::coordinate(i); });
    -
    333 ddc::for_each(idxrange_theta_edges, [&](Idx<KnotsTheta> i) {
    -
    334 breaks_theta(i) = ddc::coordinate(i);
    -
    335 });
    +
    215 // Domains
    +
    216 IdxRangeBSPolar m_idxrange_fem_non_singular;
    +
    217 IdxRangeBSR m_idxrange_bsplines_r;
    +
    218 IdxRangeBSTheta m_idxrange_bsplines_theta;
    +
    219
    +
    220 IdxRangeQuadratureR m_idxrange_quadrature_r;
    +
    221 IdxRangeQuadratureTheta m_idxrange_quadrature_theta;
    +
    222 IdxRangeQuadratureRTheta m_idxrange_quadrature_singular;
    +
    223
    +
    224 // Gauss-Legendre points and weights
    +
    225 host_t<FieldMem<Coord<R>, IdxRangeQuadratureR>> m_points_r;
    +
    226 host_t<FieldMem<Coord<Theta>, IdxRangeQuadratureTheta>> m_points_theta;
    +
    227 host_t<FieldMem<double, IdxRangeQuadratureR>> m_weights_r;
    +
    228 host_t<FieldMem<double, IdxRangeQuadratureTheta>> m_weights_theta;
    +
    229
    +
    230 // Basis Spline values and derivatives at Gauss-Legendre points
    +
    231 host_t<FieldMem<EvalDeriv2DType, IdxRange<PolarBSplinesRTheta, QDimRMesh, QDimThetaMesh>>>
    +
    232 m_singular_basis_vals_and_derivs;
    +
    233 host_t<FieldMem<EvalDeriv1DType, IdxRange<RBasisSubset, QDimRMesh>>> m_r_basis_vals_and_derivs;
    +
    234 host_t<FieldMem<EvalDeriv1DType, IdxRange<ThetaBasisSubset, QDimThetaMesh>>>
    +
    235 m_theta_basis_vals_and_derivs;
    +
    236
    +
    237 FieldMem<double, IdxRangeQuadratureRTheta> m_int_volume;
    +
    238
    +
    239 PolarSplineEvaluator<PolarBSplinesRTheta, ddc::NullExtrapolationRule, Kokkos::HostSpace>
    +
    240 m_polar_spline_evaluator;
    +
    241 std::unique_ptr<MatrixBatchCsr<Kokkos::DefaultExecutionSpace, MatrixBatchCsrSolver::CG>>
    +
    242 m_gko_matrix;
    +
    243 mutable host_t<SplinePolar> m_phi_spline_coef;
    +
    244 Kokkos::View<double**, Kokkos::LayoutRight> m_x_init;
    +
    245
    +
    246 const int m_batch_idx {0}; // TODO: Remove when batching is supported
    +
    247public:
    +
    271 template <class Mapping>
    +
    +
    272 PolarSplineFEMPoissonLikeSolver(
    +
    273 ConstSpline2D coeff_alpha,
    +
    274 ConstSpline2D coeff_beta,
    +
    275 Mapping const& mapping,
    +
    276 SplineRThetaEvaluatorNullBound const& spline_evaluator)
    +
    277 : m_nbasis_r(ddc::discrete_space<BSplinesR>().nbasis() - m_n_overlap_cells - 1)
    +
    278 , m_nbasis_theta(ddc::discrete_space<BSplinesTheta>().nbasis())
    +
    279 , m_matrix_size(ddc::discrete_space<PolarBSplinesRTheta>().nbasis() - m_nbasis_theta)
    +
    280 , m_idxrange_fem_non_singular(
    +
    281 ddc::discrete_space<PolarBSplinesRTheta>().tensor_bspline_idx_range().remove_last(
    +
    282 IdxStep<PolarBSplinesRTheta> {m_nbasis_theta}))
    +
    283 , m_idxrange_bsplines_r(ddc::discrete_space<BSplinesR>().full_domain().remove_first(
    +
    284 IdxStep<BSplinesR> {m_n_overlap_cells}))
    +
    285 , m_idxrange_bsplines_theta(ddc::discrete_space<BSplinesTheta>().full_domain().take_first(
    +
    286 IdxStep<BSplinesTheta> {m_nbasis_theta}))
    +
    287 , m_idxrange_quadrature_r(
    +
    288 Idx<QDimRMesh>(0),
    +
    289 IdxStep<QDimRMesh>(
    +
    290 m_n_gauss_legendre_r * ddc::discrete_space<BSplinesR>().ncells()))
    +
    291 , m_idxrange_quadrature_theta(
    +
    292 Idx<QDimThetaMesh>(0),
    +
    293 IdxStep<QDimThetaMesh>(
    +
    294 m_n_gauss_legendre_theta * ddc::discrete_space<BSplinesTheta>().ncells()))
    +
    295 , m_idxrange_quadrature_singular(
    +
    296 m_idxrange_quadrature_r.take_first(
    +
    297 IdxStep<QDimRMesh> {m_n_overlap_cells * m_n_gauss_legendre_r}),
    +
    298 m_idxrange_quadrature_theta)
    +
    299 , m_points_r(m_idxrange_quadrature_r)
    +
    300 , m_points_theta(m_idxrange_quadrature_theta)
    +
    301 , m_weights_r(m_idxrange_quadrature_r)
    +
    302 , m_weights_theta(m_idxrange_quadrature_theta)
    +
    303 , m_singular_basis_vals_and_derivs(IdxRange<PolarBSplinesRTheta, QDimRMesh, QDimThetaMesh>(
    +
    304 PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>(),
    +
    305 ddc::select<QDimRMesh>(m_idxrange_quadrature_singular),
    +
    306 ddc::select<QDimThetaMesh>(m_idxrange_quadrature_singular)))
    +
    307 , m_r_basis_vals_and_derivs(
    +
    308 IdxRange<RBasisSubset, QDimRMesh>(m_non_zero_bases_r, m_idxrange_quadrature_r))
    +
    309 , m_theta_basis_vals_and_derivs(
    +
    310 IdxRange<
    +
    311 ThetaBasisSubset,
    +
    312 QDimThetaMesh>(m_non_zero_bases_theta, m_idxrange_quadrature_theta))
    +
    313 , m_int_volume(
    +
    314 IdxRangeQuadratureRTheta(m_idxrange_quadrature_r, m_idxrange_quadrature_theta))
    +
    315 , m_polar_spline_evaluator(ddc::NullExtrapolationRule())
    +
    316 , m_phi_spline_coef(
    +
    317 PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>(),
    +
    318 IdxRangeBSRTheta(
    +
    319 m_idxrange_bsplines_r,
    +
    320 ddc::discrete_space<BSplinesTheta>().full_domain()))
    +
    321 , m_x_init(
    +
    322 "x_init",
    +
    323 1,
    +
    324 ddc::discrete_space<PolarBSplinesRTheta>().nbasis()
    +
    325 - ddc::discrete_space<BSplinesTheta>().nbasis())
    +
    326 {
    +
    327 static_assert(has_2d_jacobian_v<Mapping, CoordRTheta>);
    +
    328 //initialize x_init
    +
    329 Kokkos::deep_copy(m_x_init, 0);
    +
    330 // Get break points
    +
    331 IdxRange<KnotsR> idxrange_r_edges = ddc::discrete_space<BSplinesR>().break_point_domain();
    +
    332 IdxRange<KnotsTheta> idxrange_theta_edges
    +
    333 = ddc::discrete_space<BSplinesTheta>().break_point_domain();
    +
    334 host_t<FieldMem<Coord<R>, IdxRange<KnotsR>>> breaks_r(idxrange_r_edges);
    +
    335 host_t<FieldMem<Coord<Theta>, IdxRange<KnotsTheta>>> breaks_theta(idxrange_theta_edges);
    336
    -
    337 // Define quadrature points and weights
    -
    338 GaussLegendre<R> gl_coeffs_r(m_n_gauss_legendre_r);
    -
    339 GaussLegendre<Theta> gl_coeffs_theta(m_n_gauss_legendre_theta);
    -
    340 gl_coeffs_r.compute_points_and_weights_on_mesh(
    -
    341 get_field(m_points_r),
    -
    342 get_field(m_weights_r),
    -
    343 get_const_field(breaks_r));
    -
    344 gl_coeffs_theta.compute_points_and_weights_on_mesh(
    -
    345 get_field(m_points_theta),
    -
    346 get_field(m_weights_theta),
    -
    347 get_const_field(breaks_theta));
    -
    348
    -
    349 std::vector<double> vect_points_r(m_points_r.size());
    -
    350 for (IdxQuadratureR i : m_idxrange_quadrature_r) {
    -
    351 vect_points_r[i - m_idxrange_quadrature_r.front()] = m_points_r(i);
    -
    352 }
    -
    353 std::vector<double> vect_points_theta(m_points_theta.size());
    -
    354 for (IdxQuadratureTheta i : m_idxrange_quadrature_theta) {
    -
    355 vect_points_theta[i - m_idxrange_quadrature_theta.front()] = m_points_theta(i);
    -
    356 }
    -
    357
    -
    358 // Create quadrature index range
    -
    359 ddc::init_discrete_space<QDimRMesh>(vect_points_r);
    -
    360 ddc::init_discrete_space<QDimThetaMesh>(vect_points_theta);
    -
    361
    -
    362 // Find value and derivative of 1D bsplines in radial direction
    -
    363 ddc::for_each(m_idxrange_quadrature_r, [&](IdxQuadratureR const idx_r) {
    -
    364 std::array<double, 2 * m_n_non_zero_bases_r> data;
    -
    365 DSpan2D vals(data.data(), m_n_non_zero_bases_r, 2);
    -
    366 ddc::discrete_space<BSplinesR>()
    -
    367 .eval_basis_and_n_derivs(vals, ddc::coordinate(idx_r), 1);
    -
    368 for (auto ib : m_non_zero_bases_r) {
    -
    369 const int ib_idx = ib - m_non_zero_bases_r.front();
    -
    370 r_basis_vals_and_derivs(ib, idx_r).value = vals(ib_idx, 0);
    -
    371 r_basis_vals_and_derivs(ib, idx_r).derivative = vals(ib_idx, 1);
    -
    372 }
    -
    373 });
    -
    374
    -
    375 // Find value and derivative of 1D bsplines in poloidal direction
    -
    376 ddc::for_each(m_idxrange_quadrature_theta, [&](IdxQuadratureTheta const idx_theta) {
    -
    377 std::array<double, 2 * m_n_non_zero_bases_theta> data;
    -
    378 DSpan2D vals(data.data(), m_n_non_zero_bases_theta, 2);
    -
    379 ddc::discrete_space<BSplinesTheta>()
    -
    380 .eval_basis_and_n_derivs(vals, ddc::coordinate(idx_theta), 1);
    -
    381 for (auto ib : m_non_zero_bases_theta) {
    -
    382 const int ib_idx = ib - m_non_zero_bases_theta.front();
    -
    383 m_theta_basis_vals_and_derivs(ib, idx_theta).value = vals(ib_idx, 0);
    -
    384 m_theta_basis_vals_and_derivs(ib, idx_theta).derivative = vals(ib_idx, 1);
    -
    385 }
    -
    386 });
    -
    387
    -
    388 IdxRangeBSPolar idxrange_singular
    -
    389 = PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>();
    -
    390
    -
    391 // Find value and derivative of 2D bsplines covering the singular point
    -
    392 ddc::for_each(m_idxrange_quadrature_singular, [&](IdxQuadratureRTheta const irp) {
    -
    393 std::array<double, PolarBSplinesRTheta::n_singular_basis()> singular_data;
    -
    394 std::array<double, m_n_non_zero_bases_r * m_n_non_zero_bases_theta> data;
    -
    395 // Values of the polar basis splines around the singular point
    -
    396 // at a given coordinate
    -
    397 DSpan1D singular_vals(singular_data.data(), PolarBSplinesRTheta::n_singular_basis());
    -
    398 // Values of the polar basis splines, that do not cover the singular point,
    -
    399 // at a given coordinate
    -
    400 DSpan2D vals(data.data(), m_n_non_zero_bases_r, m_n_non_zero_bases_theta);
    -
    401 IdxQuadratureR idx_r = ddc::select<QDimRMesh>(irp);
    -
    402 IdxQuadratureTheta idx_theta = ddc::select<QDimThetaMesh>(irp);
    -
    403
    -
    404 const CoordRTheta coord(ddc::coordinate(irp));
    -
    405
    -
    406 // Calculate the value
    -
    407 ddc::discrete_space<PolarBSplinesRTheta>().eval_basis(singular_vals, vals, coord);
    -
    408 for (IdxBSPolar ib : idxrange_singular) {
    -
    409 m_singular_basis_vals_and_derivs(ib, idx_r, idx_theta).value
    -
    410 = singular_vals[ib - idxrange_singular.front()];
    -
    411 }
    -
    412
    -
    413 // Calculate the radial derivative
    -
    414 ddc::discrete_space<PolarBSplinesRTheta>().eval_deriv_r(singular_vals, vals, coord);
    -
    415 for (IdxBSPolar ib : idxrange_singular) {
    -
    416 m_singular_basis_vals_and_derivs(ib, idx_r, idx_theta).radial_derivative
    -
    417 = singular_vals[ib - idxrange_singular.front()];
    -
    418 }
    -
    419
    -
    420 // Calculate the poloidal derivative
    -
    421 ddc::discrete_space<PolarBSplinesRTheta>().eval_deriv_theta(singular_vals, vals, coord);
    -
    422 for (IdxBSPolar ib : idxrange_singular) {
    -
    423 m_singular_basis_vals_and_derivs(ib, idx_r, idx_theta).poloidal_derivative
    -
    424 = singular_vals[ib - idxrange_singular.front()];
    -
    425 }
    -
    426 });
    -
    427
    -
    428 // Find the integral volume associated with each point used in the quadrature scheme
    -
    429 IdxRangeQuadratureRTheta
    -
    430 all_quad_points(m_idxrange_quadrature_r, m_idxrange_quadrature_theta);
    -
    431 ddc::for_each(all_quad_points, [&](IdxQuadratureRTheta const irp) {
    -
    432 IdxQuadratureR const idx_r = ddc::select<QDimRMesh>(irp);
    -
    433 IdxQuadratureTheta const idx_theta = ddc::select<QDimThetaMesh>(irp);
    -
    434 CoordRTheta coord(ddc::coordinate(irp));
    -
    435 m_int_volume(idx_r, idx_theta) = abs(mapping.jacobian(coord)) * m_weights_r(idx_r)
    -
    436 * m_weights_theta(idx_theta);
    -
    437 });
    -
    438
    -
    439 // Number of elements in the matrix that correspond to the splines
    -
    440 // that cover the singular point
    -
    441 constexpr int n_elements_singular
    -
    442 = PolarBSplinesRTheta::n_singular_basis() * PolarBSplinesRTheta::n_singular_basis();
    -
    443 // Number of non-zero elements in the matrix corresponding to the inner product of
    -
    444 // polar splines at the singular point and the other splines
    -
    445 const int n_elements_overlap = 2
    -
    446 * (PolarBSplinesRTheta::n_singular_basis()
    -
    447 * BSplinesR::degree() * m_nbasis_theta);
    -
    448 const int n_stencil_theta
    -
    449 = m_nbasis_theta * min(int(1 + 2 * BSplinesTheta::degree()), m_nbasis_theta);
    -
    450 const int n_stencil_r = m_nbasis_r * (1 + 2 * BSplinesR::degree())
    -
    451 - (1 + BSplinesR::degree()) * BSplinesR::degree();
    -
    452 // Number of non-zero elements in the matrix corresponding to the inner product of
    -
    453 // non-central splines. These have a tensor product structure
    -
    454 const int n_elements_stencil = n_stencil_r * n_stencil_theta;
    -
    455
    -
    456 const int batch_size = 1;
    -
    457 // Matrix size is equal to the number Polar bspline
    -
    458 const int matrix_size
    -
    459 = ddc::discrete_space<PolarBSplinesRTheta>().nbasis() - m_nbasis_theta;
    -
    460 const int n_matrix_elements = n_elements_singular + n_elements_overlap + n_elements_stencil;
    -
    461
    -
    462 //CSR data storage
    -
    463 Kokkos::View<double**, Kokkos::LayoutRight, Kokkos::HostSpace>
    -
    464 values_csr_host("values_csr", batch_size, n_matrix_elements);
    -
    465 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace>
    -
    466 col_idx_csr_host("idx_csr", n_matrix_elements);
    -
    467 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::DefaultExecutionSpace>
    -
    468 nnz_per_row_csr("nnz_per_row_csr", matrix_size + 1);
    -
    469 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace>
    -
    470 nnz_per_row_csr_host("nnz_per_row_csr", matrix_size + 1);
    -
    471
    -
    472 init_nnz_per_line(nnz_per_row_csr);
    -
    473 Kokkos::deep_copy(nnz_per_row_csr_host, nnz_per_row_csr);
    -
    474
    -
    475 Kokkos::Profiling::pushRegion("PolarPoissonFillFemMatrix");
    -
    476 // Calculate the matrix elements corresponding to the bsplines which cover the singular point
    -
    477 ddc::for_each(idxrange_singular, [&](IdxBSPolar const idx_test) {
    -
    478 ddc::for_each(idxrange_singular, [&](IdxBSPolar const idx_trial) {
    -
    479 // Calculate the weak integral
    -
    480 double const element = ddc::transform_reduce(
    -
    481 m_idxrange_quadrature_singular,
    -
    482 0.0,
    -
    483 ddc::reducer::sum<double>(),
    -
    484 [&](IdxQuadratureRTheta const idx_quad) {
    -
    485 IdxQuadratureR const idx_r = ddc::select<QDimRMesh>(idx_quad);
    -
    486 IdxQuadratureTheta const idx_theta
    -
    487 = ddc::select<QDimThetaMesh>(idx_quad);
    -
    488 return weak_integral_element(
    -
    489 idx_r,
    -
    490 idx_theta,
    -
    491 m_singular_basis_vals_and_derivs(idx_test, idx_r, idx_theta),
    -
    492 m_singular_basis_vals_and_derivs(idx_trial, idx_r, idx_theta),
    -
    493 coeff_alpha,
    -
    494 coeff_beta,
    -
    495 spline_evaluator,
    -
    496 mapping);
    -
    497 });
    -
    498 const int row_idx = idx_test - idxrange_singular.front();
    -
    499 const int col_idx = idx_trial - idxrange_singular.front();
    -
    500 const int csr_idx_singular_area = nnz_per_row_csr_host(row_idx + 1);
    -
    501 //Fill the C matrix corresponding to the splines on the singular point
    -
    502 col_idx_csr_host(csr_idx_singular_area) = col_idx;
    -
    503 values_csr_host(m_batch_idx, csr_idx_singular_area) = element;
    -
    504 nnz_per_row_csr_host(row_idx + 1)++;
    -
    505 });
    -
    506 });
    -
    507
    -
    508 // Create index ranges associated with the 2D splines
    -
    509 IdxRangeBSR central_radial_bspline_idx_range(
    -
    510 m_idxrange_bsplines_r.take_first(IdxStep<BSplinesR> {BSplinesR::degree()}));
    -
    511
    -
    512 IdxRangeBSRTheta idxrange_non_singular_near_centre(
    -
    513 central_radial_bspline_idx_range,
    -
    514 m_idxrange_bsplines_theta);
    -
    515
    -
    516 // Calculate the matrix elements where bspline products overlap the bsplines which cover the singular point
    -
    517 ddc::for_each(idxrange_singular, [&](IdxBSPolar const idx_test) {
    -
    518 ddc::for_each(idxrange_non_singular_near_centre, [&](IdxBSRTheta const idx_trial) {
    -
    519 const IdxBSPolar idx_trial_polar(
    -
    520 PolarBSplinesRTheta::template get_polar_index<PolarBSplinesRTheta>(
    -
    521 idx_trial));
    -
    522 const Idx<BSplinesR> idx_trial_r(ddc::select<BSplinesR>(idx_trial));
    -
    523 const Idx<BSplinesTheta> idx_trial_theta(ddc::select<BSplinesTheta>(idx_trial));
    -
    524
    -
    525 // Find the index range covering the cells where both the test and trial functions are non-zero
    -
    526 const Idx<RCellDim> first_overlap_element_r(
    -
    527 idx_trial_r.uid() < BSplinesR::degree()
    -
    528 ? 0
    -
    529 : idx_trial_r.uid() - BSplinesR::degree());
    -
    530 const Idx<ThetaCellDim> first_overlap_element_theta(
    -
    531 theta_mod(idx_trial_theta.uid() - BSplinesTheta::degree()));
    -
    532
    -
    533 const IdxStep<RCellDim> n_overlap_r(
    -
    534 m_n_overlap_cells - first_overlap_element_r.uid());
    -
    535 const IdxStep<ThetaCellDim> n_overlap_theta(BSplinesTheta::degree() + 1);
    -
    536
    -
    537 const IdxRange<RCellDim> r_cells(first_overlap_element_r, n_overlap_r);
    -
    538 const IdxRange<ThetaCellDim>
    -
    539 theta_cells(first_overlap_element_theta, n_overlap_theta);
    -
    540 const IdxRange<RCellDim, ThetaCellDim> non_zero_cells(r_cells, theta_cells);
    -
    541
    -
    542 if (n_overlap_r > 0) {
    -
    543 double element = 0.0;
    -
    544
    -
    545 ddc::for_each(non_zero_cells, [&](IdxCell const cell_idx) {
    -
    546 const int cell_idx_r(ddc::select<RCellDim>(cell_idx).uid());
    -
    547 const int cell_idx_theta(
    -
    548 theta_mod(ddc::select<ThetaCellDim>(cell_idx).uid()));
    -
    549
    -
    550 const IdxRangeQuadratureRTheta cell_quad_points(
    -
    551 get_quadrature_points_in_cell(cell_idx_r, cell_idx_theta));
    -
    552 // Find the column where the non-zero data is stored
    -
    553 Idx<RBasisSubset> ib_trial_r(idx_trial_r.uid() - cell_idx_r);
    -
    554 Idx<ThetaBasisSubset> ib_trial_theta(
    -
    555 theta_mod(idx_trial_theta.uid() - cell_idx_theta));
    -
    556 // Calculate the weak integral
    -
    557 element += ddc::transform_reduce(
    -
    558 cell_quad_points,
    -
    559 0.0,
    -
    560 ddc::reducer::sum<double>(),
    -
    561 [&](IdxQuadratureRTheta const idx_quad) {
    -
    562 IdxQuadratureR const idx_r = ddc::select<QDimRMesh>(idx_quad);
    -
    563 IdxQuadratureTheta const idx_theta
    -
    564 = ddc::select<QDimThetaMesh>(idx_quad);
    -
    565 return weak_integral_element<Mapping>(
    -
    566 idx_r,
    -
    567 idx_theta,
    -
    568 m_singular_basis_vals_and_derivs(
    -
    569 idx_test,
    -
    570 idx_r,
    -
    571 idx_theta),
    -
    572 r_basis_vals_and_derivs(ib_trial_r, idx_r),
    -
    573 m_theta_basis_vals_and_derivs(
    -
    574 ib_trial_theta,
    -
    575 idx_theta),
    -
    576 coeff_alpha,
    -
    577 coeff_beta,
    -
    578 spline_evaluator,
    -
    579 mapping);
    -
    580 });
    -
    581 });
    -
    582
    -
    583 int const row_idx = idx_test - idxrange_singular.front();
    -
    584 int const col_idx = idx_trial_polar - idxrange_singular.front();
    -
    585 //a_ij
    -
    586 col_idx_csr_host(nnz_per_row_csr_host(row_idx + 1)) = col_idx;
    -
    587 values_csr_host(m_batch_idx, nnz_per_row_csr_host(row_idx + 1)) = element;
    -
    588 nnz_per_row_csr_host(row_idx + 1)++;
    -
    589 //a_ji
    -
    590 col_idx_csr_host(nnz_per_row_csr_host(col_idx + 1)) = row_idx;
    -
    591 values_csr_host(m_batch_idx, nnz_per_row_csr_host(col_idx + 1)) = element;
    -
    592 nnz_per_row_csr_host(col_idx + 1)++;
    -
    593 }
    -
    594 });
    -
    595 });
    -
    596
    -
    597 // Calculate the matrix elements following a stencil
    -
    598 ddc::for_each(m_idxrange_fem_non_singular, [&](IdxBSPolar const idx_test_polar) {
    -
    599 const IdxBSRTheta idx_test(PolarBSplinesRTheta::get_2d_index(idx_test_polar));
    -
    600 const std::size_t idx_test_r(ddc::select<BSplinesR>(idx_test).uid());
    -
    601 const std::size_t idx_test_theta(ddc::select<BSplinesTheta>(idx_test).uid());
    -
    602
    -
    603 // Calculate the index of the elements that are already filled
    -
    604 IdxRangeBSTheta remaining_theta(
    -
    605 Idx<BSplinesTheta> {idx_test_theta},
    -
    606 IdxStep<BSplinesTheta> {BSplinesTheta::degree() + 1});
    -
    607 ddc::for_each(remaining_theta, [&](Idx<BSplinesTheta> const idx_trial_theta) {
    -
    608 IdxBSRTheta idx_trial(Idx<BSplinesR>(idx_test_r), idx_trial_theta);
    -
    609 IdxBSPolar idx_trial_polar(
    -
    610 PolarBSplinesRTheta::template get_polar_index<PolarBSplinesRTheta>(
    -
    611 IdxBSRTheta(idx_test_r, theta_mod(idx_trial_theta.uid()))));
    -
    612 double element = get_matrix_stencil_element(
    -
    613 idx_test,
    -
    614 idx_trial,
    -
    615 coeff_alpha,
    -
    616 coeff_beta,
    -
    617 spline_evaluator,
    -
    618 mapping);
    -
    619 int const int_polar_idx_test = idx_test_polar - idxrange_singular.front();
    -
    620 if (idx_test_polar == idx_trial_polar) {
    -
    621 const int idx = nnz_per_row_csr_host(int_polar_idx_test + 1);
    -
    622 col_idx_csr_host(idx) = int_polar_idx_test;
    -
    623 values_csr_host(m_batch_idx, idx) = element;
    -
    624 nnz_per_row_csr_host(int_polar_idx_test + 1)++;
    -
    625 } else {
    -
    626 int const int_polar_idx_trial = idx_trial_polar - idxrange_singular.front();
    -
    627
    -
    628 const int aij_idx = nnz_per_row_csr_host(int_polar_idx_test + 1);
    -
    629 col_idx_csr_host(aij_idx) = int_polar_idx_trial;
    -
    630 values_csr_host(m_batch_idx, aij_idx) = element;
    -
    631 nnz_per_row_csr_host(int_polar_idx_test + 1)++;
    -
    632
    -
    633 const int aji_idx = nnz_per_row_csr_host(int_polar_idx_trial + 1);
    -
    634 col_idx_csr_host(aji_idx) = int_polar_idx_test;
    -
    635 values_csr_host(m_batch_idx, aji_idx) = element;
    -
    636 nnz_per_row_csr_host(int_polar_idx_trial + 1)++;
    -
    637 }
    -
    638 });
    -
    639 IdxRangeBSR remaining_r(
    -
    640 ddc::select<BSplinesR>(idx_test) + 1,
    -
    641 IdxStep<BSplinesR> {
    -
    642 min(BSplinesR::degree(),
    -
    643 ddc::discrete_space<BSplinesR>().nbasis() - 2 - idx_test_r)});
    -
    644 IdxRangeBSTheta relevant_theta(
    -
    645 Idx<BSplinesTheta> {
    -
    646 idx_test_theta + ddc::discrete_space<BSplinesTheta>().nbasis()
    -
    647 - BSplinesTheta::degree()},
    -
    648 IdxStep<BSplinesTheta> {2 * BSplinesTheta::degree() + 1});
    -
    649
    -
    650 IdxRangeBSRTheta trial_idx_range(remaining_r, relevant_theta);
    -
    651
    -
    652 ddc::for_each(trial_idx_range, [&](IdxBSRTheta const idx_trial) {
    -
    653 const int idx_trial_r(ddc::select<BSplinesR>(idx_trial).uid());
    -
    654 const int idx_trial_theta(ddc::select<BSplinesTheta>(idx_trial).uid());
    -
    655 IdxBSPolar idx_trial_polar(
    -
    656 PolarBSplinesRTheta::template get_polar_index<PolarBSplinesRTheta>(
    -
    657 IdxBSRTheta(idx_trial_r, theta_mod(idx_trial_theta))));
    -
    658 double element = get_matrix_stencil_element(
    -
    659 idx_test,
    -
    660 idx_trial,
    -
    661 coeff_alpha,
    -
    662 coeff_beta,
    -
    663 spline_evaluator,
    -
    664 mapping);
    -
    665 int const int_polar_idx_test = idx_test_polar - idxrange_singular.front();
    -
    666 if (idx_test_polar == idx_trial_polar) {
    -
    667 const int idx = nnz_per_row_csr_host(int_polar_idx_test + 1);
    -
    668 col_idx_csr_host(idx) = int_polar_idx_test;
    -
    669 values_csr_host(m_batch_idx, idx) = element;
    -
    670 nnz_per_row_csr_host(int_polar_idx_test + 1)++;
    -
    671 } else {
    -
    672 int const int_polar_idx_trial = idx_trial_polar - idxrange_singular.front();
    -
    673 const int aij_idx = nnz_per_row_csr_host(int_polar_idx_test + 1);
    -
    674 col_idx_csr_host(aij_idx) = int_polar_idx_trial;
    -
    675 values_csr_host(m_batch_idx, aij_idx) = element;
    -
    676 nnz_per_row_csr_host(int_polar_idx_test + 1)++;
    -
    677
    -
    678 const int aji_idx = nnz_per_row_csr_host(int_polar_idx_trial + 1);
    -
    679 col_idx_csr_host(aji_idx) = int_polar_idx_test;
    -
    680 values_csr_host(m_batch_idx, aji_idx) = element;
    -
    681 nnz_per_row_csr_host(int_polar_idx_trial + 1)++;
    -
    682 }
    -
    683 });
    -
    684 });
    -
    685 assert(nnz_per_row_csr_host(matrix_size) == n_matrix_elements);
    -
    686 m_gko_matrix = std::make_unique<MatrixBatchCsr<
    -
    687 Kokkos::DefaultExecutionSpace,
    -
    688 MatrixBatchCsrSolver::CG>>(1, matrix_size, n_matrix_elements);
    -
    689
    -
    690 auto [values, col_idx, nnz_per_row] = m_gko_matrix->get_batch_csr();
    -
    691 Kokkos::deep_copy(values, values_csr_host);
    -
    692 Kokkos::deep_copy(col_idx, col_idx_csr_host);
    -
    693 Kokkos::deep_copy(nnz_per_row, nnz_per_row_csr_host);
    -
    694 m_gko_matrix->setup_solver();
    -
    695 Kokkos::Profiling::popRegion();
    -
    696 }
    +
    337 ddc::for_each(idxrange_r_edges, [&](Idx<KnotsR> i) { breaks_r(i) = ddc::coordinate(i); });
    +
    338 ddc::for_each(idxrange_theta_edges, [&](Idx<KnotsTheta> i) {
    +
    339 breaks_theta(i) = ddc::coordinate(i);
    +
    340 });
    +
    341
    +
    342 // Define quadrature points and weights
    +
    343 GaussLegendre<R> gl_coeffs_r(m_n_gauss_legendre_r);
    +
    344 GaussLegendre<Theta> gl_coeffs_theta(m_n_gauss_legendre_theta);
    +
    345 gl_coeffs_r.compute_points_and_weights_on_mesh(
    +
    346 get_field(m_points_r),
    +
    347 get_field(m_weights_r),
    +
    348 get_const_field(breaks_r));
    +
    349 gl_coeffs_theta.compute_points_and_weights_on_mesh(
    +
    350 get_field(m_points_theta),
    +
    351 get_field(m_weights_theta),
    +
    352 get_const_field(breaks_theta));
    +
    353
    +
    354 std::vector<double> vect_points_r(m_points_r.size());
    +
    355 for (IdxQuadratureR i : m_idxrange_quadrature_r) {
    +
    356 vect_points_r[i - m_idxrange_quadrature_r.front()] = m_points_r(i);
    +
    357 }
    +
    358 std::vector<double> vect_points_theta(m_points_theta.size());
    +
    359 for (IdxQuadratureTheta i : m_idxrange_quadrature_theta) {
    +
    360 vect_points_theta[i - m_idxrange_quadrature_theta.front()] = m_points_theta(i);
    +
    361 }
    +
    362
    +
    363 // Create quadrature index range
    +
    364 ddc::init_discrete_space<QDimRMesh>(vect_points_r);
    +
    365 ddc::init_discrete_space<QDimThetaMesh>(vect_points_theta);
    +
    366
    +
    367 // Find value and derivative of 1D bsplines in radial direction
    +
    368 ddc::for_each(m_idxrange_quadrature_r, [&](IdxQuadratureR const idx_r) {
    +
    369 std::array<double, 2 * m_n_non_zero_bases_r> data;
    +
    370 DSpan2D vals(data.data(), m_n_non_zero_bases_r, 2);
    +
    371 ddc::discrete_space<BSplinesR>()
    +
    372 .eval_basis_and_n_derivs(vals, ddc::coordinate(idx_r), 1);
    +
    373 for (auto ib : m_non_zero_bases_r) {
    +
    374 const int ib_idx = ib - m_non_zero_bases_r.front();
    +
    375 m_r_basis_vals_and_derivs(ib, idx_r).value = vals(ib_idx, 0);
    +
    376 m_r_basis_vals_and_derivs(ib, idx_r).derivative = vals(ib_idx, 1);
    +
    377 }
    +
    378 });
    +
    379
    +
    380 // Find value and derivative of 1D bsplines in poloidal direction
    +
    381 ddc::for_each(m_idxrange_quadrature_theta, [&](IdxQuadratureTheta const idx_theta) {
    +
    382 std::array<double, 2 * m_n_non_zero_bases_theta> data;
    +
    383 DSpan2D vals(data.data(), m_n_non_zero_bases_theta, 2);
    +
    384 ddc::discrete_space<BSplinesTheta>()
    +
    385 .eval_basis_and_n_derivs(vals, ddc::coordinate(idx_theta), 1);
    +
    386 for (auto ib : m_non_zero_bases_theta) {
    +
    387 const int ib_idx = ib - m_non_zero_bases_theta.front();
    +
    388 m_theta_basis_vals_and_derivs(ib, idx_theta).value = vals(ib_idx, 0);
    +
    389 m_theta_basis_vals_and_derivs(ib, idx_theta).derivative = vals(ib_idx, 1);
    +
    390 }
    +
    391 });
    +
    392
    +
    393 IdxRangeBSPolar idxrange_singular
    +
    394 = PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>();
    +
    395
    +
    396 // Find value and derivative of 2D bsplines covering the singular point
    +
    397 ddc::for_each(m_idxrange_quadrature_singular, [&](IdxQuadratureRTheta const irp) {
    +
    398 std::array<double, PolarBSplinesRTheta::n_singular_basis()> singular_data;
    +
    399 std::array<double, m_n_non_zero_bases_r * m_n_non_zero_bases_theta> data;
    +
    400 // Values of the polar basis splines around the singular point
    +
    401 // at a given coordinate
    +
    402 DSpan1D singular_vals(singular_data.data(), PolarBSplinesRTheta::n_singular_basis());
    +
    403 // Values of the polar basis splines, that do not cover the singular point,
    +
    404 // at a given coordinate
    +
    405 DSpan2D vals(data.data(), m_n_non_zero_bases_r, m_n_non_zero_bases_theta);
    +
    406 IdxQuadratureR const idx_r(irp);
    +
    407 IdxQuadratureTheta const idx_theta(irp);
    +
    408
    +
    409 const CoordRTheta coord(ddc::coordinate(irp));
    +
    410
    +
    411 // Calculate the value
    +
    412 ddc::discrete_space<PolarBSplinesRTheta>().eval_basis(singular_vals, vals, coord);
    +
    413 for (IdxBSPolar ib : idxrange_singular) {
    +
    414 m_singular_basis_vals_and_derivs(ib, idx_r, idx_theta).value
    +
    415 = singular_vals[ib - idxrange_singular.front()];
    +
    416 }
    +
    417
    +
    418 // Calculate the radial derivative
    +
    419 ddc::discrete_space<PolarBSplinesRTheta>().eval_deriv_r(singular_vals, vals, coord);
    +
    420 for (IdxBSPolar ib : idxrange_singular) {
    +
    421 m_singular_basis_vals_and_derivs(ib, idx_r, idx_theta).radial_derivative
    +
    422 = singular_vals[ib - idxrange_singular.front()];
    +
    423 }
    +
    424
    +
    425 // Calculate the poloidal derivative
    +
    426 ddc::discrete_space<PolarBSplinesRTheta>().eval_deriv_theta(singular_vals, vals, coord);
    +
    427 for (IdxBSPolar ib : idxrange_singular) {
    +
    428 m_singular_basis_vals_and_derivs(ib, idx_r, idx_theta).poloidal_derivative
    +
    429 = singular_vals[ib - idxrange_singular.front()];
    +
    430 }
    +
    431 });
    +
    432
    +
    433 // Number of elements in the matrix that correspond to the splines
    +
    434 // that cover the singular point
    +
    435 constexpr int n_elements_singular
    +
    436 = PolarBSplinesRTheta::n_singular_basis() * PolarBSplinesRTheta::n_singular_basis();
    +
    437 // Number of non-zero elements in the matrix corresponding to the inner product of
    +
    438 // polar splines at the singular point and the other splines
    +
    439 const int n_elements_overlap = 2
    +
    440 * (PolarBSplinesRTheta::n_singular_basis()
    +
    441 * BSplinesR::degree() * m_nbasis_theta);
    +
    442 const int n_stencil_theta
    +
    443 = m_nbasis_theta * min(int(1 + 2 * BSplinesTheta::degree()), m_nbasis_theta);
    +
    444 const int n_stencil_r = m_nbasis_r * (1 + 2 * BSplinesR::degree())
    +
    445 - (1 + BSplinesR::degree()) * BSplinesR::degree();
    +
    446 // Number of non-zero elements in the matrix corresponding to the inner product of
    +
    447 // non-central splines. These have a tensor product structure
    +
    448 const int n_elements_stencil = n_stencil_r * n_stencil_theta;
    +
    449
    +
    450 const int batch_size = 1;
    +
    451
    +
    452 const int n_matrix_elements = n_elements_singular + n_elements_overlap + n_elements_stencil;
    +
    453
    +
    454 //CSR data storage
    +
    455 Kokkos::View<double**, Kokkos::LayoutRight, Kokkos::HostSpace>
    +
    456 values_csr_host("values_csr", batch_size, n_matrix_elements);
    +
    457 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace>
    +
    458 col_idx_csr_host("idx_csr", n_matrix_elements);
    +
    459 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::DefaultExecutionSpace>
    +
    460 nnz_per_row_csr("nnz_per_row_csr", m_matrix_size + 1);
    +
    461 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace>
    +
    462 nnz_per_row_csr_host("nnz_per_row_csr", m_matrix_size + 1);
    +
    463
    +
    464 fill_int_volume(mapping);
    +
    465
    +
    466 m_gko_matrix = std::make_unique<MatrixBatchCsr<
    +
    467 Kokkos::DefaultExecutionSpace,
    +
    468 MatrixBatchCsrSolver::CG>>(1, m_matrix_size, n_matrix_elements);
    +
    469 auto [values, col_idx, nnz_per_row] = m_gko_matrix->get_batch_csr();
    +
    470 init_nnz_per_line(nnz_per_row);
    +
    471 Kokkos::deep_copy(nnz_per_row_csr_host, nnz_per_row);
    +
    472
    +
    473 compute_singular_elements(
    +
    474 coeff_alpha,
    +
    475 coeff_beta,
    +
    476 mapping,
    +
    477 spline_evaluator,
    +
    478 values_csr_host,
    +
    479 col_idx_csr_host,
    +
    480 nnz_per_row_csr_host);
    +
    481 compute_overlapping_singular_elements(
    +
    482 coeff_alpha,
    +
    483 coeff_beta,
    +
    484 mapping,
    +
    485 spline_evaluator,
    +
    486 values_csr_host,
    +
    487 col_idx_csr_host,
    +
    488 nnz_per_row_csr_host);
    +
    489 compute_stencil_elements(
    +
    490 coeff_alpha,
    +
    491 coeff_beta,
    +
    492 mapping,
    +
    493 spline_evaluator,
    +
    494 values_csr_host,
    +
    495 col_idx_csr_host,
    +
    496 nnz_per_row_csr_host);
    +
    497
    +
    498 assert(nnz_per_row_csr_host(m_matrix_size) == n_matrix_elements);
    +
    499 Kokkos::deep_copy(values, values_csr_host);
    +
    500 Kokkos::deep_copy(col_idx, col_idx_csr_host);
    +
    501 Kokkos::deep_copy(nnz_per_row, nnz_per_row_csr_host);
    +
    502 m_gko_matrix->setup_solver();
    +
    503 }
    +
    +
    504
    +
    514 template <class Mapping>
    +
    +
    515 void fill_int_volume(Mapping const& mapping)
    +
    516 {
    +
    517 auto weights_r_alloc = ddc::create_mirror_view_and_copy(
    +
    518 Kokkos::DefaultExecutionSpace(),
    +
    519 get_field(m_weights_r));
    +
    520 auto weights_theta_alloc = ddc::create_mirror_view_and_copy(
    +
    521 Kokkos::DefaultExecutionSpace(),
    +
    522 get_field(m_weights_theta));
    +
    523 DField<IdxRangeQuadratureR> weights_r = get_field(weights_r_alloc);
    +
    524 DField<IdxRangeQuadratureTheta> weights_theta = get_field(weights_theta_alloc);
    +
    525 // Find the integral volume associated with each point used in the quadrature scheme
    +
    526 IdxRangeQuadratureRTheta const
    +
    527 all_quad_points(m_idxrange_quadrature_r, m_idxrange_quadrature_theta);
    +
    528 auto int_volume_alloc = ddc::create_mirror_view_and_copy(
    +
    529 Kokkos::DefaultExecutionSpace(),
    +
    530 get_field(m_int_volume));
    +
    531 auto int_volume = get_field(int_volume_alloc);
    +
    532 ddc::parallel_for_each(
    +
    533 Kokkos::DefaultExecutionSpace(),
    +
    534 all_quad_points,
    +
    535 KOKKOS_LAMBDA(IdxQuadratureRTheta const irp) {
    +
    536 IdxQuadratureR const idx_r(irp);
    +
    537 IdxQuadratureTheta const idx_theta(irp);
    +
    538 CoordRTheta coord(ddc::coordinate(irp));
    +
    539 int_volume(idx_r, idx_theta) = Kokkos::abs(mapping.jacobian(coord))
    +
    540 * weights_r(idx_r) * weights_theta(idx_theta);
    +
    541 });
    +
    542 }
    +
    +
    543
    +
    566 template <class Mapping>
    +
    +
    567 void compute_singular_elements(
    +
    568 ConstSpline2D coeff_alpha,
    +
    569 ConstSpline2D coeff_beta,
    +
    570 Mapping const& mapping,
    +
    571 SplineRThetaEvaluatorNullBound const& spline_evaluator,
    +
    572 Kokkos::View<double**, Kokkos::LayoutRight, Kokkos::HostSpace> const values_csr_host,
    +
    573 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace> const col_idx_csr_host,
    +
    574 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace> const nnz_per_row_csr_host)
    +
    575 {
    +
    576 IdxRangeBSPolar idxrange_singular
    +
    577 = PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>();
    +
    578 IdxRangeQuadratureRTheta idxrange_quadrature_singular = m_idxrange_quadrature_singular;
    +
    579
    +
    580 auto singular_basis_vals_and_derivs_alloc = ddc::create_mirror_view_and_copy(
    +
    581 Kokkos::DefaultExecutionSpace(),
    +
    582 get_field(m_singular_basis_vals_and_derivs));
    +
    583 auto r_basis_vals_and_derivs_alloc = ddc::create_mirror_view_and_copy(
    +
    584 Kokkos::DefaultExecutionSpace(),
    +
    585 get_field(m_r_basis_vals_and_derivs));
    +
    586 Field<EvalDeriv2DType, IdxRange<PolarBSplinesRTheta, QDimRMesh, QDimThetaMesh>>
    +
    587 singular_basis_vals_and_derivs = get_field(singular_basis_vals_and_derivs_alloc);
    +
    588 DField<IdxRangeQuadratureRTheta> int_volume_proxy = get_field(m_int_volume);
    +
    589
    +
    590 Kokkos::Profiling::pushRegion("PolarPoissonFillFemMatrix");
    +
    591 // Calculate the matrix elements corresponding to the bsplines which cover the singular point
    +
    592 ddc::for_each(idxrange_singular, [&](IdxBSPolar const idx_test) {
    +
    593 ddc::for_each(idxrange_singular, [&](IdxBSPolar const idx_trial) {
    +
    594 // Calculate the weak integral
    +
    595 double const element = ddc::parallel_transform_reduce(
    +
    596 Kokkos::DefaultExecutionSpace(),
    +
    597 idxrange_quadrature_singular,
    +
    598 0.0,
    +
    599 ddc::reducer::sum<double>(),
    +
    600 KOKKOS_LAMBDA(Idx<QDimRMesh, QDimThetaMesh> const& idx_quad) {
    +
    601 Idx<QDimRMesh> const idx_r(idx_quad);
    +
    602 Idx<QDimThetaMesh> const idx_theta(idx_quad);
    +
    603 return weak_integral_element(
    +
    604 idx_r,
    +
    605 idx_theta,
    +
    606 singular_basis_vals_and_derivs(idx_test, idx_r, idx_theta),
    +
    607 singular_basis_vals_and_derivs(idx_trial, idx_r, idx_theta),
    +
    608 coeff_alpha,
    +
    609 coeff_beta,
    +
    610 spline_evaluator,
    +
    611 mapping,
    +
    612 int_volume_proxy);
    +
    613 });
    +
    614 const int row_idx = idx_test - idxrange_singular.front();
    +
    615 const int col_idx = idx_trial - idxrange_singular.front();
    +
    616 const int csr_idx_singular_area = nnz_per_row_csr_host(row_idx + 1);
    +
    617 //Fill the C matrix corresponding to the splines on the singular point
    +
    618 col_idx_csr_host(csr_idx_singular_area) = col_idx;
    +
    619 values_csr_host(m_batch_idx, csr_idx_singular_area) = element;
    +
    620 nnz_per_row_csr_host(row_idx + 1)++;
    +
    621 });
    +
    622 });
    +
    623 }
    -
    697
    -
    711 template <class RHSFunction>
    -
    -
    712 void operator()(RHSFunction const& rhs, host_t<SplinePolar>& spline) const
    -
    713 {
    -
    714 Kokkos::Profiling::pushRegion("PolarPoissonRHS");
    -
    715
    -
    716 static_assert(
    -
    717 std::is_invocable_r_v<double, RHSFunction, CoordRTheta>,
    -
    718 "RHSFunction must have an operator() which takes a coordinate and returns a "
    -
    719 "double");
    -
    720 const int b_size = ddc::discrete_space<PolarBSplinesRTheta>().nbasis()
    -
    721 - ddc::discrete_space<BSplinesTheta>().nbasis();
    -
    722 const int batch_size = 1;
    -
    723 // Create b for rhs
    -
    724 Kokkos::View<double**, Kokkos::LayoutRight, Kokkos::HostSpace>
    -
    725 b_host("b_host", batch_size, b_size);
    -
    726 //Create an initial guess
    -
    727 Kokkos::View<double**, Kokkos::LayoutRight, Kokkos::HostSpace>
    -
    728 x_init_host("x_init_host", batch_size, b_size);
    -
    729 // Fill b
    -
    730 ddc::for_each(
    -
    731 PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>(),
    -
    732 [&](IdxBSPolar const idx) {
    -
    733 const int bspl_idx = idx
    -
    734 - PolarBSplinesRTheta::template singular_idx_range<
    -
    735 PolarBSplinesRTheta>()
    -
    736 .front();
    -
    737 b_host(0, bspl_idx) = ddc::transform_reduce(
    -
    738 m_idxrange_quadrature_singular,
    -
    739 0.0,
    -
    740 ddc::reducer::sum<double>(),
    -
    741 [&](IdxQuadratureRTheta const idx_quad) {
    -
    742 IdxQuadratureR const idx_r = ddc::select<QDimRMesh>(idx_quad);
    -
    743 IdxQuadratureTheta const idx_theta
    -
    744 = ddc::select<QDimThetaMesh>(idx_quad);
    -
    745 CoordRTheta coord(ddc::coordinate(idx_quad));
    -
    746 return rhs(coord)
    -
    747 * m_singular_basis_vals_and_derivs(idx, idx_r, idx_theta)
    -
    748 .value
    -
    749 * m_int_volume(idx_r, idx_theta);
    -
    750 });
    -
    751 });
    -
    752 const std::size_t ncells_r = ddc::discrete_space<BSplinesR>().ncells();
    -
    753 ddc::for_each(m_idxrange_fem_non_singular, [&](IdxBSPolar const idx) {
    -
    754 const IdxBSRTheta idx_2d(PolarBSplinesRTheta::get_2d_index(idx));
    -
    755 const std::size_t idx_r(ddc::select<BSplinesR>(idx_2d).uid());
    -
    756 const std::size_t idx_theta(ddc::select<BSplinesTheta>(idx_2d).uid());
    -
    757
    -
    758 // Find the cells on which the bspline is non-zero
    -
    759 int first_cell_r(idx_r - BSplinesR::degree());
    -
    760 int first_cell_theta(idx_theta - BSplinesTheta::degree());
    -
    761 std::size_t last_cell_r(idx_r + 1);
    -
    762 if (first_cell_r < 0)
    -
    763 first_cell_r = 0;
    -
    764 if (last_cell_r > ncells_r)
    -
    765 last_cell_r = ncells_r;
    -
    766 IdxStep<RCellDim> const r_length(last_cell_r - first_cell_r);
    -
    767 IdxStep<ThetaCellDim> const theta_length(BSplinesTheta::degree() + 1);
    -
    768
    -
    769
    -
    770 Idx<RCellDim> const start_r(first_cell_r);
    -
    771 Idx<ThetaCellDim> const start_theta(theta_mod(first_cell_theta));
    -
    772 const IdxRange<RCellDim> r_cells(start_r, r_length);
    -
    773 const IdxRange<ThetaCellDim> theta_cells(start_theta, theta_length);
    -
    774 const IdxRange<RCellDim, ThetaCellDim> non_zero_cells(r_cells, theta_cells);
    -
    775 assert(r_length * theta_length > 0);
    -
    776 double element = 0.0;
    -
    777 ddc::for_each(non_zero_cells, [&](IdxCell const cell_idx) {
    -
    778 const int cell_idx_r(ddc::select<RCellDim>(cell_idx).uid());
    -
    779 const int cell_idx_theta(theta_mod(ddc::select<ThetaCellDim>(cell_idx).uid()));
    -
    780
    -
    781 const IdxRangeQuadratureRTheta cell_quad_points(
    -
    782 get_quadrature_points_in_cell(cell_idx_r, cell_idx_theta));
    -
    783
    -
    784 // Find the column where the non-zero data is stored
    -
    785 Idx<RBasisSubset> ib_r(idx_r - cell_idx_r);
    -
    786 Idx<ThetaBasisSubset> ib_theta(theta_mod(idx_theta - cell_idx_theta));
    -
    787
    -
    788 // Calculate the weak integral
    -
    789 element += ddc::transform_reduce(
    -
    790 cell_quad_points,
    -
    791 0.0,
    -
    792 ddc::reducer::sum<double>(),
    -
    793 [&](IdxQuadratureRTheta const idx_quad) {
    -
    794 IdxQuadratureR const idx_r = ddc::select<QDimRMesh>(idx_quad);
    -
    795 IdxQuadratureTheta const idx_theta
    -
    796 = ddc::select<QDimThetaMesh>(idx_quad);
    -
    797 CoordRTheta coord(ddc::coordinate(idx_quad));
    -
    798 double rb = r_basis_vals_and_derivs(ib_r, idx_r).value;
    -
    799 double pb = m_theta_basis_vals_and_derivs(ib_theta, idx_theta).value;
    -
    800 return rhs(coord) * rb * pb * m_int_volume(idx_r, idx_theta);
    -
    801 });
    -
    802 });
    -
    803 const std::size_t singular_index
    -
    804 = idx - ddc::discrete_space<PolarBSplinesRTheta>().full_domain().front();
    -
    805 b_host(0, singular_index) = element;
    -
    806 });
    -
    807
    -
    808 Kokkos::View<double**, Kokkos::LayoutRight> b("b", batch_size, b_size);
    -
    809 Kokkos::deep_copy(b, b_host);
    -
    810 Kokkos::Profiling::popRegion();
    -
    811
    -
    812 Kokkos::deep_copy(m_x_init, x_init_host);
    -
    813 // Solve the matrix equation
    -
    814 Kokkos::Profiling::pushRegion("PolarPoissonSolve");
    -
    815 m_gko_matrix->solve(m_x_init, b);
    -
    816 Kokkos::deep_copy(x_init_host, m_x_init);
    -
    817 //-----------------
    -
    818 IdxRangeBSRTheta dirichlet_boundary_idx_range(
    -
    819 m_idxrange_bsplines_r.take_last(IdxStep<BSplinesR> {1}),
    -
    820 m_idxrange_bsplines_theta);
    -
    821 IdxRangeBSTheta idxrange_polar(ddc::discrete_space<BSplinesTheta>().full_domain());
    -
    822
    -
    823
    -
    824 // Fill the spline
    -
    825 ddc::for_each(
    -
    826 PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>(),
    -
    827 [&](IdxBSPolar const idx) {
    -
    828 const int bspl_idx = idx
    -
    829 - PolarBSplinesRTheta::template singular_idx_range<
    -
    830 PolarBSplinesRTheta>()
    -
    831 .front();
    -
    832 spline.singular_spline_coef(idx) = x_init_host(0, bspl_idx);
    -
    833 });
    -
    834 ddc::for_each(m_idxrange_fem_non_singular, [&](IdxBSPolar const idx) {
    -
    835 const IdxBSRTheta idx_2d(PolarBSplinesRTheta::get_2d_index(idx));
    -
    836 spline.spline_coef(idx_2d) = x_init_host(0, idx.uid());
    -
    837 });
    -
    838 ddc::for_each(dirichlet_boundary_idx_range, [&](IdxBSRTheta const idx) {
    -
    839 spline.spline_coef(idx) = 0.0;
    -
    840 });
    -
    841
    -
    842 // Copy the periodic elements
    -
    843 IdxRangeBSRTheta copy_idx_range(
    -
    844 m_idxrange_bsplines_r,
    -
    845 idxrange_polar.remove_first(
    -
    846 IdxStep<BSplinesTheta>(ddc::discrete_space<BSplinesTheta>().nbasis())));
    -
    847 ddc::for_each(copy_idx_range, [&](IdxBSRTheta const idx_2d) {
    -
    848 spline.spline_coef(ddc::select<BSplinesR>(idx_2d), ddc::select<BSplinesTheta>(idx_2d))
    -
    849 = spline.spline_coef(
    -
    850 ddc::select<BSplinesR>(idx_2d),
    -
    851 ddc::select<BSplinesTheta>(idx_2d)
    -
    852 - ddc::discrete_space<BSplinesTheta>().nbasis());
    -
    853 });
    -
    854 Kokkos::Profiling::popRegion();
    -
    855 }
    +
    624
    +
    647 template <class Mapping>
    +
    +
    648 void compute_overlapping_singular_elements(
    +
    649 ConstSpline2D coeff_alpha,
    +
    650 ConstSpline2D coeff_beta,
    +
    651 Mapping const& mapping,
    +
    652 SplineRThetaEvaluatorNullBound const& spline_evaluator,
    +
    653 Kokkos::View<double**, Kokkos::LayoutRight, Kokkos::HostSpace> const values_csr_host,
    +
    654 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace> const col_idx_csr_host,
    +
    655 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace> const nnz_per_row_csr_host)
    +
    656 {
    +
    657 // Create index ranges associated with the 2D splines
    +
    658 IdxRangeBSPolar idxrange_singular
    +
    659 = PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>();
    +
    660 IdxRangeBSR central_radial_bspline_idx_range(
    +
    661 m_idxrange_bsplines_r.take_first(IdxStep<BSplinesR> {BSplinesR::degree()}));
    +
    662
    +
    663 IdxRangeBSRTheta idxrange_non_singular_near_centre(
    +
    664 central_radial_bspline_idx_range,
    +
    665 m_idxrange_bsplines_theta);
    +
    666
    +
    667 auto singular_basis_vals_and_derivs_alloc = ddc::create_mirror_view_and_copy(
    +
    668 Kokkos::DefaultExecutionSpace(),
    +
    669 get_field(m_singular_basis_vals_and_derivs));
    +
    670 auto r_basis_vals_and_derivs_alloc = ddc::create_mirror_view_and_copy(
    +
    671 Kokkos::DefaultExecutionSpace(),
    +
    672 get_field(m_r_basis_vals_and_derivs));
    +
    673 auto theta_basis_vals_and_derivs_alloc = ddc::create_mirror_view_and_copy(
    +
    674 Kokkos::DefaultExecutionSpace(),
    +
    675 get_field(m_theta_basis_vals_and_derivs));
    +
    676 DField<IdxRangeQuadratureRTheta> int_volume_proxy = get_field(m_int_volume);
    +
    677 Field<EvalDeriv2DType, IdxRange<PolarBSplinesRTheta, QDimRMesh, QDimThetaMesh>>
    +
    678 singular_basis_vals_and_derivs = get_field(singular_basis_vals_and_derivs_alloc);
    +
    679 Field<EvalDeriv1DType, IdxRange<RBasisSubset, QDimRMesh>> r_basis_vals_and_derivs
    +
    680 = get_field(r_basis_vals_and_derivs_alloc);
    +
    681 Field<EvalDeriv1DType, IdxRange<ThetaBasisSubset, QDimThetaMesh>>
    +
    682 theta_basis_vals_and_derivs = get_field(theta_basis_vals_and_derivs_alloc);
    +
    683 // Calculate the matrix elements where bspline products overlap the bsplines which cover the singular point
    +
    684 ddc::for_each(idxrange_singular, [&](IdxBSPolar const idx_test) {
    +
    685 ddc::for_each(idxrange_non_singular_near_centre, [&](IdxBSRTheta const idx_trial) {
    +
    686 const IdxBSPolar idx_trial_polar(
    +
    687 PolarBSplinesRTheta::template get_polar_index<PolarBSplinesRTheta>(
    +
    688 idx_trial));
    +
    689 const Idx<BSplinesR> idx_trial_r(ddc::select<BSplinesR>(idx_trial));
    +
    690 const Idx<BSplinesTheta> idx_trial_theta(ddc::select<BSplinesTheta>(idx_trial));
    +
    691
    +
    692 // Find the index range covering the cells where both the test and trial functions are non-zero
    +
    693 const Idx<RCellDim> first_overlap_element_r(
    +
    694 idx_trial_r.uid() < BSplinesR::degree()
    +
    695 ? 0
    +
    696 : idx_trial_r.uid() - BSplinesR::degree());
    +
    697 const Idx<ThetaCellDim> first_overlap_element_theta(
    +
    698 theta_mod(idx_trial_theta.uid() - BSplinesTheta::degree()));
    +
    699
    +
    700 const IdxStep<RCellDim> n_overlap_r(
    +
    701 m_n_overlap_cells - first_overlap_element_r.uid());
    +
    702 const IdxStep<ThetaCellDim> n_overlap_theta(BSplinesTheta::degree() + 1);
    +
    703
    +
    704 const IdxRange<RCellDim> r_cells(first_overlap_element_r, n_overlap_r);
    +
    705 const IdxRange<ThetaCellDim>
    +
    706 theta_cells(first_overlap_element_theta, n_overlap_theta);
    +
    707 const IdxRange<RCellDim, ThetaCellDim> non_zero_cells(r_cells, theta_cells);
    +
    708
    +
    709 if (n_overlap_r > 0) {
    +
    710 double element = 0.0;
    +
    711
    +
    712 ddc::for_each(non_zero_cells, [&](IdxCell const cell_idx) {
    +
    713 const int cell_idx_r(ddc::select<RCellDim>(cell_idx).uid());
    +
    714 const int cell_idx_theta(
    +
    715 theta_mod(ddc::select<ThetaCellDim>(cell_idx).uid()));
    +
    716
    +
    717 const IdxRangeQuadratureRTheta cell_quad_points(
    +
    718 get_quadrature_points_in_cell(cell_idx_r, cell_idx_theta));
    +
    719 // Find the column where the non-zero data is stored
    +
    720 Idx<RBasisSubset> ib_trial_r(idx_trial_r.uid() - cell_idx_r);
    +
    721 Idx<ThetaBasisSubset> ib_trial_theta(
    +
    722 theta_mod(idx_trial_theta.uid() - cell_idx_theta));
    +
    723 // Calculate the weak integral
    +
    724 element += ddc::parallel_transform_reduce(
    +
    725 Kokkos::DefaultExecutionSpace(),
    +
    726 cell_quad_points,
    +
    727 0.0,
    +
    728 ddc::reducer::sum<double>(),
    +
    729 KOKKOS_LAMBDA(IdxQuadratureRTheta const idx_quad) {
    +
    730 IdxQuadratureR const idx_r(idx_quad);
    +
    731 IdxQuadratureTheta const idx_theta(idx_quad);
    +
    732 return weak_integral_element<Mapping>(
    +
    733 idx_r,
    +
    734 idx_theta,
    +
    735 singular_basis_vals_and_derivs(
    +
    736 idx_test,
    +
    737 idx_r,
    +
    738 idx_theta),
    +
    739 r_basis_vals_and_derivs(ib_trial_r, idx_r),
    +
    740 theta_basis_vals_and_derivs(ib_trial_theta, idx_theta),
    +
    741 coeff_alpha,
    +
    742 coeff_beta,
    +
    743 spline_evaluator,
    +
    744 mapping,
    +
    745 int_volume_proxy);
    +
    746 });
    +
    747 });
    +
    748
    +
    749 int const row_idx = idx_test - idxrange_singular.front();
    +
    750 int const col_idx = idx_trial_polar - idxrange_singular.front();
    +
    751 //a_ij
    +
    752 col_idx_csr_host(nnz_per_row_csr_host(row_idx + 1)) = col_idx;
    +
    753 values_csr_host(m_batch_idx, nnz_per_row_csr_host(row_idx + 1)) = element;
    +
    754 nnz_per_row_csr_host(row_idx + 1)++;
    +
    755 //a_ji
    +
    756 col_idx_csr_host(nnz_per_row_csr_host(col_idx + 1)) = row_idx;
    +
    757 values_csr_host(m_batch_idx, nnz_per_row_csr_host(col_idx + 1)) = element;
    +
    758 nnz_per_row_csr_host(col_idx + 1)++;
    +
    759 }
    +
    760 });
    +
    761 });
    +
    762 }
    -
    856
    -
    857
    -
    871 template <class RHSFunction>
    -
    -
    872 void operator()(RHSFunction const& rhs, host_t<DFieldRTheta> phi) const
    -
    873 {
    -
    874 static_assert(
    -
    875 std::is_invocable_r_v<double, RHSFunction, CoordRTheta>,
    -
    876 "RHSFunction must have an operator() which takes a coordinate and returns a "
    -
    877 "double");
    -
    878
    +
    763
    +
    786 template <class Mapping>
    +
    +
    787 void compute_stencil_elements(
    +
    788 ConstSpline2D coeff_alpha,
    +
    789 ConstSpline2D coeff_beta,
    +
    790 Mapping const& mapping,
    +
    791 SplineRThetaEvaluatorNullBound const& spline_evaluator,
    +
    792 Kokkos::View<double**, Kokkos::LayoutRight, Kokkos::HostSpace> const values_csr_host,
    +
    793 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace> const col_idx_csr_host,
    +
    794 Kokkos::View<int*, Kokkos::LayoutRight, Kokkos::HostSpace> const nnz_per_row_csr_host)
    +
    795 {
    +
    796 IdxRangeBSPolar idxrange_singular
    +
    797 = PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>();
    +
    798
    +
    799 // Calculate the matrix elements following a stencil
    +
    800 ddc::for_each(m_idxrange_fem_non_singular, [&](IdxBSPolar const idx_test_polar) {
    +
    801 const IdxBSRTheta idx_test(PolarBSplinesRTheta::get_2d_index(idx_test_polar));
    +
    802 const std::size_t idx_test_r(ddc::select<BSplinesR>(idx_test).uid());
    +
    803 const std::size_t idx_test_theta(ddc::select<BSplinesTheta>(idx_test).uid());
    +
    804
    +
    805 // Calculate the index of the elements that are already filled
    +
    806 IdxRangeBSTheta remaining_theta(
    +
    807 Idx<BSplinesTheta> {idx_test_theta},
    +
    808 IdxStep<BSplinesTheta> {BSplinesTheta::degree() + 1});
    +
    809 ddc::for_each(remaining_theta, [&](Idx<BSplinesTheta> const idx_trial_theta) {
    +
    810 IdxBSRTheta idx_trial(Idx<BSplinesR>(idx_test_r), idx_trial_theta);
    +
    811 IdxBSPolar idx_trial_polar(
    +
    812 PolarBSplinesRTheta::template get_polar_index<PolarBSplinesRTheta>(
    +
    813 IdxBSRTheta(idx_test_r, theta_mod(idx_trial_theta.uid()))));
    +
    814 double element = get_matrix_stencil_element(
    +
    815 idx_test,
    +
    816 idx_trial,
    +
    817 coeff_alpha,
    +
    818 coeff_beta,
    +
    819 spline_evaluator,
    +
    820 mapping);
    +
    821 int const int_polar_idx_test = idx_test_polar - idxrange_singular.front();
    +
    822 if (idx_test_polar == idx_trial_polar) {
    +
    823 const int idx = nnz_per_row_csr_host(int_polar_idx_test + 1);
    +
    824 col_idx_csr_host(idx) = int_polar_idx_test;
    +
    825 values_csr_host(m_batch_idx, idx) = element;
    +
    826 nnz_per_row_csr_host(int_polar_idx_test + 1)++;
    +
    827 } else {
    +
    828 int const int_polar_idx_trial = idx_trial_polar - idxrange_singular.front();
    +
    829
    +
    830 const int aij_idx = nnz_per_row_csr_host(int_polar_idx_test + 1);
    +
    831 col_idx_csr_host(aij_idx) = int_polar_idx_trial;
    +
    832 values_csr_host(m_batch_idx, aij_idx) = element;
    +
    833 nnz_per_row_csr_host(int_polar_idx_test + 1)++;
    +
    834
    +
    835 const int aji_idx = nnz_per_row_csr_host(int_polar_idx_trial + 1);
    +
    836 col_idx_csr_host(aji_idx) = int_polar_idx_test;
    +
    837 values_csr_host(m_batch_idx, aji_idx) = element;
    +
    838 nnz_per_row_csr_host(int_polar_idx_trial + 1)++;
    +
    839 }
    +
    840 });
    +
    841 IdxRangeBSR remaining_r(
    +
    842 ddc::select<BSplinesR>(idx_test) + 1,
    +
    843 IdxStep<BSplinesR> {
    +
    844 min(BSplinesR::degree(),
    +
    845 ddc::discrete_space<BSplinesR>().nbasis() - 2 - idx_test_r)});
    +
    846 IdxRangeBSTheta relevant_theta(
    +
    847 Idx<BSplinesTheta> {
    +
    848 idx_test_theta + ddc::discrete_space<BSplinesTheta>().nbasis()
    +
    849 - BSplinesTheta::degree()},
    +
    850 IdxStep<BSplinesTheta> {2 * BSplinesTheta::degree() + 1});
    +
    851
    +
    852 IdxRangeBSRTheta trial_idx_range(remaining_r, relevant_theta);
    +
    853
    +
    854 ddc::for_each(trial_idx_range, [&](IdxBSRTheta const idx_trial) {
    +
    855 const int idx_trial_r(ddc::select<BSplinesR>(idx_trial).uid());
    +
    856 const int idx_trial_theta(ddc::select<BSplinesTheta>(idx_trial).uid());
    +
    857 IdxBSPolar idx_trial_polar(
    +
    858 PolarBSplinesRTheta::template get_polar_index<PolarBSplinesRTheta>(
    +
    859 IdxBSRTheta(idx_trial_r, theta_mod(idx_trial_theta))));
    +
    860 double element = get_matrix_stencil_element(
    +
    861 idx_test,
    +
    862 idx_trial,
    +
    863 coeff_alpha,
    +
    864 coeff_beta,
    +
    865 spline_evaluator,
    +
    866 mapping);
    +
    867 int const int_polar_idx_test = idx_test_polar - idxrange_singular.front();
    +
    868 if (idx_test_polar == idx_trial_polar) {
    +
    869 const int idx = nnz_per_row_csr_host(int_polar_idx_test + 1);
    +
    870 col_idx_csr_host(idx) = int_polar_idx_test;
    +
    871 values_csr_host(m_batch_idx, idx) = element;
    +
    872 nnz_per_row_csr_host(int_polar_idx_test + 1)++;
    +
    873 } else {
    +
    874 int const int_polar_idx_trial = idx_trial_polar - idxrange_singular.front();
    +
    875 const int aij_idx = nnz_per_row_csr_host(int_polar_idx_test + 1);
    +
    876 col_idx_csr_host(aij_idx) = int_polar_idx_trial;
    +
    877 values_csr_host(m_batch_idx, aij_idx) = element;
    +
    878 nnz_per_row_csr_host(int_polar_idx_test + 1)++;
    879
    -
    880 (*this)(rhs, m_phi_spline_coef);
    -
    881 host_t<CoordFieldMemRTheta> coords_eval_alloc(get_idx_range(phi));
    -
    882 host_t<CoordFieldRTheta> coords_eval(get_field(coords_eval_alloc));
    -
    883 ddc::for_each(get_idx_range(phi), [&](IdxRTheta idx) {
    -
    884 coords_eval(idx) = ddc::coordinate(idx);
    -
    885 });
    -
    886 m_polar_spline_evaluator(phi, get_const_field(coords_eval), m_phi_spline_coef);
    -
    887 }
    +
    880 const int aji_idx = nnz_per_row_csr_host(int_polar_idx_trial + 1);
    +
    881 col_idx_csr_host(aji_idx) = int_polar_idx_test;
    +
    882 values_csr_host(m_batch_idx, aji_idx) = element;
    +
    883 nnz_per_row_csr_host(int_polar_idx_trial + 1)++;
    +
    884 }
    +
    885 });
    +
    886 });
    +
    887
    +
    888 Kokkos::Profiling::popRegion();
    +
    889 }
    -
    888
    -
    889private:
    -
    890 static KOKKOS_FUNCTION IdxRangeQuadratureRTheta
    -
    891 get_quadrature_points_in_cell(int cell_idx_r, int cell_idx_theta)
    -
    892 {
    -
    893 const IdxQuadratureR first_quad_point_r(cell_idx_r * m_n_gauss_legendre_r);
    -
    894 const IdxQuadratureTheta first_quad_point_theta(cell_idx_theta * m_n_gauss_legendre_theta);
    -
    895 constexpr IdxStepQuadratureR n_GL_r(m_n_gauss_legendre_r);
    -
    896 constexpr IdxStepQuadratureTheta n_GL_theta(m_n_gauss_legendre_theta);
    -
    897 const IdxRangeQuadratureR quad_points_r(first_quad_point_r, n_GL_r);
    -
    898 const IdxRangeQuadratureTheta quad_points_theta(first_quad_point_theta, n_GL_theta);
    -
    899 return IdxRangeQuadratureRTheta(quad_points_r, quad_points_theta);
    -
    900 }
    -
    901
    -
    902 template <class Mapping>
    -
    903 double weak_integral_element(
    -
    904 IdxQuadratureR idx_r,
    -
    905 IdxQuadratureTheta idx_theta,
    -
    906 EvalDeriv2DType const& test_bspline_val_and_deriv,
    -
    907 EvalDeriv2DType const& trial_bspline_val_and_deriv,
    -
    908 host_t<ConstSpline2D> coeff_alpha,
    -
    909 host_t<ConstSpline2D> coeff_beta,
    -
    910 SplineRThetaEvaluatorNullBound_host const& evaluator,
    -
    911 Mapping const& mapping)
    -
    912 {
    -
    913 return templated_weak_integral_element(
    -
    914 idx_r,
    -
    915 idx_theta,
    -
    916 test_bspline_val_and_deriv,
    -
    917 trial_bspline_val_and_deriv,
    -
    918 test_bspline_val_and_deriv,
    -
    919 trial_bspline_val_and_deriv,
    -
    920 coeff_alpha,
    -
    921 coeff_beta,
    -
    922 evaluator,
    -
    923 mapping);
    -
    924 }
    -
    925
    -
    926 template <class Mapping>
    -
    927 double weak_integral_element(
    -
    928 IdxQuadratureR idx_r,
    -
    929 IdxQuadratureTheta idx_theta,
    -
    930 EvalDeriv2DType const& test_bspline_val_and_deriv,
    -
    931 EvalDeriv1DType const& trial_bspline_val_and_deriv_r,
    -
    932 EvalDeriv1DType const& trial_bspline_val_and_deriv_theta,
    -
    933 host_t<ConstSpline2D> coeff_alpha,
    -
    934 host_t<ConstSpline2D> coeff_beta,
    -
    935 SplineRThetaEvaluatorNullBound_host const& evaluator,
    -
    936 Mapping const& mapping)
    -
    937 {
    -
    938 return templated_weak_integral_element(
    -
    939 idx_r,
    -
    940 idx_theta,
    -
    941 test_bspline_val_and_deriv,
    -
    942 trial_bspline_val_and_deriv_r,
    -
    943 test_bspline_val_and_deriv,
    -
    944 trial_bspline_val_and_deriv_theta,
    -
    945 coeff_alpha,
    -
    946 coeff_beta,
    -
    947 evaluator,
    -
    948 mapping);
    -
    949 }
    +
    903 template <class RHSFunction>
    +
    +
    904 void operator()(RHSFunction const& rhs, host_t<SplinePolar>& spline) const
    +
    905 {
    +
    906 Kokkos::Profiling::pushRegion("PolarPoissonRHS");
    +
    907
    +
    908 static_assert(
    +
    909 std::is_invocable_r_v<double, RHSFunction, CoordRTheta>,
    +
    910 "RHSFunction must have an operator() which takes a coordinate and returns a "
    +
    911 "double");
    +
    912 const int b_size = ddc::discrete_space<PolarBSplinesRTheta>().nbasis()
    +
    913 - ddc::discrete_space<BSplinesTheta>().nbasis();
    +
    914 const int batch_size = 1;
    +
    915 // Create b for rhs
    +
    916 Kokkos::View<double**, Kokkos::LayoutRight, Kokkos::HostSpace>
    +
    917 b_host("b_host", batch_size, b_size);
    +
    918 //Create an initial guess
    +
    919 Kokkos::View<double**, Kokkos::LayoutRight, Kokkos::HostSpace>
    +
    920 x_init_host("x_init_host", batch_size, b_size);
    +
    921 // Fill b
    +
    922 auto int_volume_host = ddc::create_mirror_view_and_copy(get_field(m_int_volume));
    +
    923 ddc::for_each(
    +
    924 PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>(),
    +
    925 [&](IdxBSPolar const idx) {
    +
    926 const int bspl_idx = idx
    +
    927 - PolarBSplinesRTheta::template singular_idx_range<
    +
    928 PolarBSplinesRTheta>()
    +
    929 .front();
    +
    930 b_host(0, bspl_idx) = ddc::transform_reduce(
    +
    931 m_idxrange_quadrature_singular,
    +
    932 0.0,
    +
    933 ddc::reducer::sum<double>(),
    +
    934 [&](IdxQuadratureRTheta const idx_quad) {
    +
    935 IdxQuadratureR const idx_r(idx_quad);
    +
    936 IdxQuadratureTheta const idx_theta(idx_quad);
    +
    937 CoordRTheta coord(ddc::coordinate(idx_quad));
    +
    938 return rhs(coord)
    +
    939 * m_singular_basis_vals_and_derivs(idx, idx_r, idx_theta)
    +
    940 .value
    +
    941 * int_volume_host(idx_r, idx_theta);
    +
    942 });
    +
    943 });
    +
    944 const std::size_t ncells_r = ddc::discrete_space<BSplinesR>().ncells();
    +
    945
    +
    946 ddc::for_each(m_idxrange_fem_non_singular, [&](IdxBSPolar const idx) {
    +
    947 const IdxBSRTheta idx_2d(PolarBSplinesRTheta::get_2d_index(idx));
    +
    948 const std::size_t idx_r(ddc::select<BSplinesR>(idx_2d).uid());
    +
    949 const std::size_t idx_theta(ddc::select<BSplinesTheta>(idx_2d).uid());
    950
    -
    951 template <class Mapping>
    -
    952 double weak_integral_element(
    -
    953 IdxQuadratureR idx_r,
    -
    954 IdxQuadratureTheta idx_theta,
    -
    955 EvalDeriv1DType const& test_bspline_val_and_deriv_r,
    -
    956 EvalDeriv2DType const& trial_bspline_val_and_deriv,
    -
    957 EvalDeriv1DType const& test_bspline_val_and_deriv_theta,
    -
    958 host_t<ConstSpline2D> coeff_alpha,
    -
    959 host_t<ConstSpline2D> coeff_beta,
    -
    960 SplineRThetaEvaluatorNullBound_host const& evaluator,
    -
    961 Mapping const& mapping)
    -
    962 {
    -
    963 return templated_weak_integral_element(
    -
    964 idx_r,
    -
    965 idx_theta,
    -
    966 test_bspline_val_and_deriv_r,
    -
    967 trial_bspline_val_and_deriv,
    -
    968 test_bspline_val_and_deriv_theta,
    -
    969 trial_bspline_val_and_deriv,
    -
    970 coeff_alpha,
    -
    971 coeff_beta,
    -
    972 evaluator,
    -
    973 mapping);
    -
    974 }
    -
    975
    -
    976 template <class Mapping>
    -
    977 double weak_integral_element(
    -
    978 IdxQuadratureR idx_r,
    -
    979 IdxQuadratureTheta idx_theta,
    -
    980 EvalDeriv1DType const& test_bspline_val_and_deriv_r,
    -
    981 EvalDeriv1DType const& trial_bspline_val_and_deriv_r,
    -
    982 EvalDeriv1DType const& test_bspline_val_and_deriv_theta,
    -
    983 EvalDeriv1DType const& trial_bspline_val_and_deriv_theta,
    -
    984 host_t<ConstSpline2D> coeff_alpha,
    -
    985 host_t<ConstSpline2D> coeff_beta,
    -
    986 SplineRThetaEvaluatorNullBound_host const& evaluator,
    -
    987 Mapping const& mapping)
    -
    988 {
    -
    989 return templated_weak_integral_element(
    -
    990 idx_r,
    -
    991 idx_theta,
    -
    992 test_bspline_val_and_deriv_r,
    -
    993 trial_bspline_val_and_deriv_r,
    -
    994 test_bspline_val_and_deriv_theta,
    -
    995 trial_bspline_val_and_deriv_theta,
    -
    996 coeff_alpha,
    -
    997 coeff_beta,
    -
    998 evaluator,
    -
    999 mapping);
    -
    1000 }
    -
    1001
    -
    1002 inline void get_value_and_gradient(
    -
    1003 double& value,
    -
    1004 std::array<double, 2>& gradient,
    -
    1005 EvalDeriv1DType const& r_basis,
    -
    1006 EvalDeriv1DType const& theta_basis) const
    -
    1007 {
    -
    1008 value = r_basis.value * theta_basis.value;
    -
    1009 gradient = {r_basis.derivative * theta_basis.value, r_basis.value * theta_basis.derivative};
    -
    1010 }
    -
    1011
    -
    1012 inline void get_value_and_gradient(
    -
    1013 double& value,
    -
    1014 std::array<double, 2>& gradient,
    -
    1015 EvalDeriv2DType const& basis,
    -
    1016 EvalDeriv2DType const&) const // Last argument is duplicate
    -
    1017 {
    -
    1018 value = basis.value;
    -
    1019 gradient = {basis.radial_derivative, basis.poloidal_derivative};
    -
    1020 }
    -
    1021
    -
    1031 template <class Mapping, class TestValDerivType, class TrialValDerivType>
    -
    1032 double templated_weak_integral_element(
    -
    1033 IdxQuadratureR idx_r,
    -
    1034 IdxQuadratureTheta idx_theta,
    -
    1035 TestValDerivType const& test_bspline_val_and_deriv,
    -
    1036 TrialValDerivType const& trial_bspline_val_and_deriv,
    -
    1037 TestValDerivType const& test_bspline_val_and_deriv_theta,
    -
    1038 TrialValDerivType const& trial_bspline_val_and_deriv_theta,
    -
    1039 host_t<ConstSpline2D> coeff_alpha,
    -
    1040 host_t<ConstSpline2D> coeff_beta,
    -
    1041 SplineRThetaEvaluatorNullBound_host const& spline_evaluator,
    -
    1042 Mapping const& mapping)
    -
    1043 {
    -
    1044 static_assert(
    -
    1045 std::is_same_v<
    -
    1046 TestValDerivType,
    -
    1047 EvalDeriv1DType> || std::is_same_v<TestValDerivType, EvalDeriv2DType>);
    -
    1048 static_assert(
    -
    1049 std::is_same_v<
    -
    1050 TrialValDerivType,
    -
    1051 EvalDeriv1DType> || std::is_same_v<TrialValDerivType, EvalDeriv2DType>);
    -
    1052
    -
    1053 // Calculate coefficients at quadrature point
    -
    1054 CoordRTheta coord(ddc::coordinate(idx_r), ddc::coordinate(idx_theta));
    -
    1055 const double alpha = spline_evaluator(coord, coeff_alpha);
    -
    1056 const double beta = spline_evaluator(coord, coeff_beta);
    -
    1057
    -
    1058 // Define the value and gradient of the test and trial basis functions
    -
    1059 double basis_val_test_space;
    -
    1060 double basis_val_trial_space;
    -
    1061 std::array<double, 2> basis_gradient_test_space;
    -
    1062 std::array<double, 2> basis_gradient_trial_space;
    -
    1063 get_value_and_gradient(
    -
    1064 basis_val_test_space,
    -
    1065 basis_gradient_test_space,
    -
    1066 test_bspline_val_and_deriv,
    -
    1067 test_bspline_val_and_deriv_theta);
    -
    1068 get_value_and_gradient(
    -
    1069 basis_val_trial_space,
    -
    1070 basis_gradient_trial_space,
    -
    1071 trial_bspline_val_and_deriv,
    -
    1072 trial_bspline_val_and_deriv_theta);
    -
    1073
    -
    1074 MetricTensor<Mapping, CoordRTheta> metric_tensor(mapping);
    -
    1075
    -
    1076 // Assemble the weak integral element
    -
    1077 return m_int_volume(idx_r, idx_theta)
    -
    1078 * (alpha
    -
    1079 * dot_product(
    -
    1080 basis_gradient_test_space,
    -
    1081 metric_tensor.to_covariant(basis_gradient_trial_space, coord))
    -
    1082 + beta * basis_val_test_space * basis_val_trial_space);
    +
    951 // Find the cells on which the bspline is non-zero
    +
    952 int first_cell_r(idx_r - BSplinesR::degree());
    +
    953 int first_cell_theta(idx_theta - BSplinesTheta::degree());
    +
    954 std::size_t last_cell_r(idx_r + 1);
    +
    955 if (first_cell_r < 0)
    +
    956 first_cell_r = 0;
    +
    957 if (last_cell_r > ncells_r)
    +
    958 last_cell_r = ncells_r;
    +
    959 IdxStep<RCellDim> const r_length(last_cell_r - first_cell_r);
    +
    960 IdxStep<ThetaCellDim> const theta_length(BSplinesTheta::degree() + 1);
    +
    961
    +
    962
    +
    963 Idx<RCellDim> const start_r(first_cell_r);
    +
    964 Idx<ThetaCellDim> const start_theta(theta_mod(first_cell_theta));
    +
    965 const IdxRange<RCellDim> r_cells(start_r, r_length);
    +
    966 const IdxRange<ThetaCellDim> theta_cells(start_theta, theta_length);
    +
    967 const IdxRange<RCellDim, ThetaCellDim> non_zero_cells(r_cells, theta_cells);
    +
    968 assert(r_length * theta_length > 0);
    +
    969 double element = 0.0;
    +
    970 ddc::for_each(non_zero_cells, [&](IdxCell const cell_idx) {
    +
    971 const int cell_idx_r(ddc::select<RCellDim>(cell_idx).uid());
    +
    972 const int cell_idx_theta(theta_mod(ddc::select<ThetaCellDim>(cell_idx).uid()));
    +
    973
    +
    974 const IdxRangeQuadratureRTheta cell_quad_points(
    +
    975 get_quadrature_points_in_cell(cell_idx_r, cell_idx_theta));
    +
    976
    +
    977 // Find the column where the non-zero data is stored
    +
    978 Idx<RBasisSubset> ib_r(idx_r - cell_idx_r);
    +
    979 Idx<ThetaBasisSubset> ib_theta(theta_mod(idx_theta - cell_idx_theta));
    +
    980
    +
    981 // Calculate the weak integral
    +
    982 element += ddc::transform_reduce(
    +
    983 cell_quad_points,
    +
    984 0.0,
    +
    985 ddc::reducer::sum<double>(),
    +
    986 [&](IdxQuadratureRTheta const idx_quad) {
    +
    987 IdxQuadratureR const idx_r(idx_quad);
    +
    988 IdxQuadratureTheta const idx_theta(idx_quad);
    +
    989 CoordRTheta coord(ddc::coordinate(idx_quad));
    +
    990 double rb = m_r_basis_vals_and_derivs(ib_r, idx_r).value;
    +
    991 double pb = m_theta_basis_vals_and_derivs(ib_theta, idx_theta).value;
    +
    992 return rhs(coord) * rb * pb * int_volume_host(idx_r, idx_theta);
    +
    993 });
    +
    994 });
    +
    995 const std::size_t singular_index
    +
    996 = idx - ddc::discrete_space<PolarBSplinesRTheta>().full_domain().front();
    +
    997 b_host(0, singular_index) = element;
    +
    998 });
    +
    999
    +
    1000 Kokkos::View<double**, Kokkos::LayoutRight> b("b", batch_size, b_size);
    +
    1001 Kokkos::deep_copy(b, b_host);
    +
    1002 Kokkos::Profiling::popRegion();
    +
    1003
    +
    1004 Kokkos::deep_copy(m_x_init, x_init_host);
    +
    1005 // Solve the matrix equation
    +
    1006 Kokkos::Profiling::pushRegion("PolarPoissonSolve");
    +
    1007 m_gko_matrix->solve(m_x_init, b);
    +
    1008 Kokkos::deep_copy(x_init_host, m_x_init);
    +
    1009 //-----------------
    +
    1010 IdxRangeBSRTheta dirichlet_boundary_idx_range(
    +
    1011 m_idxrange_bsplines_r.take_last(IdxStep<BSplinesR> {1}),
    +
    1012 m_idxrange_bsplines_theta);
    +
    1013 IdxRangeBSTheta idxrange_polar(ddc::discrete_space<BSplinesTheta>().full_domain());
    +
    1014
    +
    1015 // Fill the spline
    +
    1016 ddc::for_each(
    +
    1017 PolarBSplinesRTheta::template singular_idx_range<PolarBSplinesRTheta>(),
    +
    1018 [&](IdxBSPolar const idx) {
    +
    1019 const int bspl_idx = idx
    +
    1020 - PolarBSplinesRTheta::template singular_idx_range<
    +
    1021 PolarBSplinesRTheta>()
    +
    1022 .front();
    +
    1023 spline.singular_spline_coef(idx) = x_init_host(0, bspl_idx);
    +
    1024 });
    +
    1025 ddc::for_each(m_idxrange_fem_non_singular, [&](IdxBSPolar const idx) {
    +
    1026 const IdxBSRTheta idx_2d(PolarBSplinesRTheta::get_2d_index(idx));
    +
    1027 spline.spline_coef(idx_2d) = x_init_host(0, idx.uid());
    +
    1028 });
    +
    1029 ddc::for_each(dirichlet_boundary_idx_range, [&](IdxBSRTheta const idx) {
    +
    1030 spline.spline_coef(idx) = 0.0;
    +
    1031 });
    +
    1032
    +
    1033 // Copy the periodic elements
    +
    1034 IdxRangeBSRTheta copy_idx_range(
    +
    1035 m_idxrange_bsplines_r,
    +
    1036 idxrange_polar.remove_first(
    +
    1037 IdxStep<BSplinesTheta>(ddc::discrete_space<BSplinesTheta>().nbasis())));
    +
    1038 ddc::for_each(copy_idx_range, [&](IdxBSRTheta const idx_2d) {
    +
    1039 spline.spline_coef(ddc::select<BSplinesR>(idx_2d), ddc::select<BSplinesTheta>(idx_2d))
    +
    1040 = spline.spline_coef(
    +
    1041 ddc::select<BSplinesR>(idx_2d),
    +
    1042 ddc::select<BSplinesTheta>(idx_2d)
    +
    1043 - ddc::discrete_space<BSplinesTheta>().nbasis());
    +
    1044 });
    +
    1045 Kokkos::Profiling::popRegion();
    +
    1046 }
    +
    +
    1047
    +
    1061 template <class RHSFunction>
    +
    +
    1062 void operator()(RHSFunction const& rhs, DFieldRTheta phi) const
    +
    1063 {
    +
    1064 static_assert(
    +
    1065 std::is_invocable_r_v<double, RHSFunction, CoordRTheta>,
    +
    1066 "RHSFunction must have an operator() which takes a coordinate and returns a "
    +
    1067 "double");
    +
    1068
    +
    1069 (*this)(rhs, m_phi_spline_coef);
    +
    1070 CoordFieldMemRTheta coords_eval_alloc(get_idx_range(phi));
    +
    1071 CoordFieldRTheta coords_eval(get_field(coords_eval_alloc));
    +
    1072 ddc::parallel_for_each(
    +
    1073 Kokkos::DefaultExecutionSpace(),
    +
    1074 get_idx_range(phi),
    +
    1075 KOKKOS_LAMBDA(IdxRTheta idx) { coords_eval(idx) = ddc::coordinate(idx); });
    +
    1076 auto coords_eval_host = ddc::create_mirror_and_copy(coords_eval);
    +
    1077 auto phi_host = ddc::create_mirror_and_copy(phi);
    +
    1078 m_polar_spline_evaluator(
    +
    1079 get_field(phi_host),
    +
    1080 get_const_field(coords_eval_host),
    +
    1081 get_const_field(m_phi_spline_coef));
    +
    1082 ddc::parallel_deepcopy(phi, phi_host);
    1083 }
    +
    1084
    -
    1089 template <class Mapping>
    -
    1090 double get_matrix_stencil_element(
    -
    1091 IdxBSRTheta idx_test,
    -
    1092 IdxBSRTheta idx_trial,
    -
    1093 host_t<ConstSpline2D> coeff_alpha,
    -
    1094 host_t<ConstSpline2D> coeff_beta,
    -
    1095 SplineRThetaEvaluatorNullBound_host const& evaluator,
    -
    1096 Mapping const& mapping)
    +
    1095 static KOKKOS_FUNCTION IdxRangeQuadratureRTheta
    +
    +
    1096 get_quadrature_points_in_cell(int cell_idx_r, int cell_idx_theta)
    1097 {
    -
    1098 // 0 <= idx_test_r < 8
    -
    1099 // 0 <= idx_trial_r < 8
    -
    1100 // idx_test_r < idx_trial_r
    -
    1101 const int idx_test_r(ddc::select<BSplinesR>(idx_test).uid());
    -
    1102 const int idx_trial_r(ddc::select<BSplinesR>(idx_trial).uid());
    -
    1103 // 0 <= idx_test_theta < 8
    -
    1104 // 0 <= idx_trial_theta < 8
    -
    1105 int idx_test_theta(theta_mod(ddc::select<BSplinesTheta>(idx_test).uid()));
    -
    1106 int idx_trial_theta(theta_mod(ddc::select<BSplinesTheta>(idx_trial).uid()));
    -
    1107
    -
    1108 const std::size_t ncells_r = ddc::discrete_space<BSplinesR>().ncells();
    -
    1109
    -
    1110 // 0<= r_offset <= degree_r
    -
    1111 // -degree_theta <= theta_offset <= degree_theta
    -
    1112 const int r_offset = idx_trial_r - idx_test_r;
    -
    1113 int theta_offset = theta_mod(idx_trial_theta - idx_test_theta);
    -
    1114 if (theta_offset >= int(m_nbasis_theta - BSplinesTheta::degree())) {
    -
    1115 theta_offset -= m_nbasis_theta;
    -
    1116 }
    -
    1117 assert(r_offset >= 0);
    -
    1118 assert(r_offset <= int(BSplinesR::degree()));
    -
    1119 assert(theta_offset >= -int(BSplinesTheta::degree()));
    -
    1120 assert(theta_offset <= int(BSplinesTheta::degree()));
    -
    1121
    -
    1122 // Find the index range covering the cells where both the test and trial functions are non-zero
    -
    1123 int n_overlap_stencil_r(BSplinesR::degree() + 1 - r_offset);
    -
    1124 int first_overlap_r(idx_trial_r - BSplinesR::degree());
    -
    1125
    -
    1126 int first_overlap_theta;
    -
    1127 int n_overlap_stencil_theta;
    -
    1128 if (theta_offset > 0) {
    -
    1129 n_overlap_stencil_theta = BSplinesTheta::degree() + 1 - theta_offset;
    -
    1130 first_overlap_theta = theta_mod(idx_trial_theta - BSplinesTheta::degree());
    -
    1131 } else {
    -
    1132 n_overlap_stencil_theta = BSplinesTheta::degree() + 1 + theta_offset;
    -
    1133 first_overlap_theta = theta_mod(idx_test_theta - BSplinesTheta::degree());
    -
    1134 }
    -
    1135
    -
    1136 if (first_overlap_r < 0) {
    -
    1137 const int n_compact = first_overlap_r;
    -
    1138 first_overlap_r = 0;
    -
    1139 n_overlap_stencil_r += n_compact;
    -
    1140 }
    -
    1141
    -
    1142 const int n_to_edge_r(ncells_r - first_overlap_r);
    -
    1143
    -
    1144 const IdxStep<RCellDim> n_overlap_r(min(n_overlap_stencil_r, n_to_edge_r));
    -
    1145 const IdxStep<ThetaCellDim> n_overlap_theta(n_overlap_stencil_theta);
    -
    1146
    -
    1147 const Idx<RCellDim> first_overlap_element_r(first_overlap_r);
    -
    1148 const Idx<ThetaCellDim> first_overlap_element_theta(first_overlap_theta);
    -
    1149
    -
    1150 const IdxRange<RCellDim> r_cells(first_overlap_element_r, n_overlap_r);
    -
    1151 const IdxRange<ThetaCellDim> theta_cells(first_overlap_element_theta, n_overlap_theta);
    -
    1152 const IdxRange<RCellDim, ThetaCellDim> non_zero_cells(r_cells, theta_cells);
    -
    1153
    -
    1154 assert(n_overlap_r * n_overlap_theta > 0);
    -
    1155 return ddc::transform_reduce(
    -
    1156 non_zero_cells,
    -
    1157 0.0,
    -
    1158 ddc::reducer::sum<double>(),
    -
    1159 [&](IdxCell const cell_idx) {
    -
    1160 const int cell_idx_r(ddc::select<RCellDim>(cell_idx).uid());
    -
    1161 const int cell_idx_theta(theta_mod(ddc::select<ThetaCellDim>(cell_idx).uid()));
    -
    1162
    -
    1163 const IdxRangeQuadratureRTheta cell_quad_points(
    -
    1164 get_quadrature_points_in_cell(cell_idx_r, cell_idx_theta));
    -
    1165
    -
    1166 int ib_test_theta_idx = idx_test_theta - cell_idx_theta;
    -
    1167 int ib_trial_theta_idx = idx_trial_theta - cell_idx_theta;
    -
    1168
    -
    1169 // Find the column where the non-zero data is stored
    -
    1170 Idx<RBasisSubset> ib_test_r(idx_test_r - cell_idx_r);
    -
    1171 Idx<ThetaBasisSubset> ib_test_theta(theta_mod(ib_test_theta_idx));
    -
    1172 Idx<RBasisSubset> ib_trial_r(idx_trial_r - cell_idx_r);
    -
    1173 Idx<ThetaBasisSubset> ib_trial_theta(theta_mod(ib_trial_theta_idx));
    -
    1174
    -
    1175 assert(ib_test_r.uid() < BSplinesR::degree() + 1);
    -
    1176 assert(ib_test_theta.uid() < BSplinesTheta::degree() + 1);
    -
    1177 assert(ib_trial_r.uid() < BSplinesR::degree() + 1);
    -
    1178 assert(ib_trial_theta.uid() < BSplinesTheta::degree() + 1);
    -
    1179
    -
    1180 // Calculate the weak integral
    -
    1181 return ddc::transform_reduce(
    -
    1182 cell_quad_points,
    -
    1183 0.0,
    -
    1184 ddc::reducer::sum<double>(),
    -
    1185 [&](IdxQuadratureRTheta const idx_quad) {
    -
    1186 IdxQuadratureR const idx_r = ddc::select<QDimRMesh>(idx_quad);
    -
    1187 IdxQuadratureTheta const idx_theta
    -
    1188 = ddc::select<QDimThetaMesh>(idx_quad);
    -
    1189 return weak_integral_element(
    -
    1190 idx_r,
    -
    1191 idx_theta,
    -
    1192 r_basis_vals_and_derivs(ib_test_r, idx_r),
    -
    1193 r_basis_vals_and_derivs(ib_trial_r, idx_r),
    -
    1194 m_theta_basis_vals_and_derivs(ib_test_theta, idx_theta),
    -
    1195 m_theta_basis_vals_and_derivs(ib_trial_theta, idx_theta),
    -
    1196 coeff_alpha,
    -
    1197 coeff_beta,
    -
    1198 evaluator,
    -
    1199 mapping);
    -
    1200 });
    -
    1201 });
    -
    1202 }
    -
    1203
    -
    1204 static KOKKOS_FUNCTION int theta_mod(int idx_theta)
    -
    1205 {
    -
    1206 int ncells_theta = ddc::discrete_space<BSplinesTheta>().ncells();
    -
    1207 while (idx_theta < 0)
    -
    1208 idx_theta += ncells_theta;
    -
    1209 while (idx_theta >= ncells_theta)
    -
    1210 idx_theta -= ncells_theta;
    -
    1211 return idx_theta;
    -
    1212 }
    -
    1213
    -
    1214public:
    -
    -
    1228 void init_nnz_per_line(Kokkos::View<int*, Kokkos::LayoutRight> nnz) const
    -
    1229 {
    -
    1230 Kokkos::Profiling::pushRegion("PolarPoissonInitNnz");
    -
    1231 size_t const mat_size = nnz.extent(0) - 1;
    -
    1232 size_t constexpr n_singular_basis = PolarBSplinesRTheta::n_singular_basis();
    -
    1233 size_t constexpr degree = BSplinesR::degree();
    -
    1234 size_t constexpr radial_overlap = 2 * degree + 1;
    -
    1235 size_t const nbasis_theta_proxy = m_nbasis_theta;
    -
    1236
    -
    1237 // overlap between singular domain splines and radial splines
    -
    1238 Kokkos::parallel_for(
    -
    1239 "overlap singular radial",
    -
    1240 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(1, n_singular_basis + 1),
    -
    1241 KOKKOS_LAMBDA(const int k) {
    -
    1242 nnz(k + 1) = n_singular_basis + degree * nbasis_theta_proxy;
    -
    1243 });
    -
    1244
    -
    1245 // going from the internal boundary the overlapping possiblities between two radial splines increase
    -
    1246 Kokkos::parallel_for(
    -
    1247 "inner overlap",
    -
    1248 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(1, degree + 2),
    -
    1249 KOKKOS_LAMBDA(const int i) {
    -
    1250 for (size_t k = n_singular_basis + (i - 1) * nbasis_theta_proxy;
    -
    1251 k < n_singular_basis + i * nbasis_theta_proxy;
    -
    1252 k++) {
    -
    1253 nnz(k + 2) = n_singular_basis + (degree + i) * radial_overlap;
    -
    1254 }
    -
    1255 });
    -
    1256
    -
    1257 // Stencil with maximum possible overlap from two sides for radial spline
    -
    1258 Kokkos::parallel_for(
    -
    1259 "Inner Stencil",
    -
    1260 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(
    -
    1261 n_singular_basis + degree * nbasis_theta_proxy,
    -
    1262 mat_size - degree * nbasis_theta_proxy),
    -
    1263 KOKKOS_LAMBDA(const int k) { nnz(k + 2) = radial_overlap * radial_overlap; });
    +
    1098 const IdxQuadratureR first_quad_point_r(cell_idx_r * m_n_gauss_legendre_r);
    +
    1099 const IdxQuadratureTheta first_quad_point_theta(cell_idx_theta * m_n_gauss_legendre_theta);
    +
    1100 constexpr IdxStepQuadratureR n_GL_r(m_n_gauss_legendre_r);
    +
    1101 constexpr IdxStepQuadratureTheta n_GL_theta(m_n_gauss_legendre_theta);
    +
    1102 const IdxRangeQuadratureR quad_points_r(first_quad_point_r, n_GL_r);
    +
    1103 const IdxRangeQuadratureTheta quad_points_theta(first_quad_point_theta, n_GL_theta);
    +
    1104 return IdxRangeQuadratureRTheta(quad_points_r, quad_points_theta);
    +
    1105 }
    +
    +
    1106
    +
    1134 template <class Mapping>
    +
    +
    1135 static KOKKOS_FUNCTION double weak_integral_element(
    +
    1136 IdxQuadratureR idx_r,
    +
    1137 IdxQuadratureTheta idx_theta,
    +
    1138 EvalDeriv2DType const& test_bspline_val_and_deriv,
    +
    1139 EvalDeriv2DType const& trial_bspline_val_and_deriv,
    +
    1140 ConstSpline2D coeff_alpha,
    +
    1141 ConstSpline2D coeff_beta,
    +
    1142 SplineRThetaEvaluatorNullBound const& evaluator,
    +
    1143 Mapping const& mapping,
    +
    1144 DField<IdxRangeQuadratureRTheta> int_volume)
    +
    1145 {
    +
    1146 return templated_weak_integral_element(
    +
    1147 idx_r,
    +
    1148 idx_theta,
    +
    1149 test_bspline_val_and_deriv,
    +
    1150 trial_bspline_val_and_deriv,
    +
    1151 test_bspline_val_and_deriv,
    +
    1152 trial_bspline_val_and_deriv,
    +
    1153 coeff_alpha,
    +
    1154 coeff_beta,
    +
    1155 evaluator,
    +
    1156 mapping,
    +
    1157 int_volume);
    +
    1158 }
    +
    +
    1159
    +
    1161 template <class Mapping>
    +
    1162 static KOKKOS_FUNCTION double weak_integral_element(
    +
    1163 IdxQuadratureR idx_r,
    +
    1164 IdxQuadratureTheta idx_theta,
    +
    1165 EvalDeriv2DType const& test_bspline_val_and_deriv,
    +
    1166 EvalDeriv1DType const& trial_bspline_val_and_deriv_r,
    +
    1167 EvalDeriv1DType const& trial_bspline_val_and_deriv_theta,
    +
    1168 ConstSpline2D coeff_alpha,
    +
    1169 ConstSpline2D coeff_beta,
    +
    1170 SplineRThetaEvaluatorNullBound const& evaluator,
    +
    1171 Mapping const& mapping,
    +
    1172 DField<IdxRangeQuadratureRTheta> int_volume)
    +
    1173 {
    +
    1174 return templated_weak_integral_element(
    +
    1175 idx_r,
    +
    1176 idx_theta,
    +
    1177 test_bspline_val_and_deriv,
    +
    1178 trial_bspline_val_and_deriv_r,
    +
    1179 test_bspline_val_and_deriv,
    +
    1180 trial_bspline_val_and_deriv_theta,
    +
    1181 coeff_alpha,
    +
    1182 coeff_beta,
    +
    1183 evaluator,
    +
    1184 mapping,
    +
    1185 int_volume);
    +
    1186 }
    +
    1187
    +
    1188 template <class Mapping>
    +
    1189 static KOKKOS_FUNCTION double weak_integral_element(
    +
    1190 IdxQuadratureR idx_r,
    +
    1191 IdxQuadratureTheta idx_theta,
    +
    1192 EvalDeriv1DType const& test_bspline_val_and_deriv_r,
    +
    1193 EvalDeriv2DType const& trial_bspline_val_and_deriv,
    +
    1194 EvalDeriv1DType const& test_bspline_val_and_deriv_theta,
    +
    1195 ConstSpline2D coeff_alpha,
    +
    1196 ConstSpline2D coeff_beta,
    +
    1197 SplineRThetaEvaluatorNullBound const& evaluator,
    +
    1198 Mapping const& mapping,
    +
    1199 DField<IdxRangeQuadratureRTheta> int_volume)
    +
    1200 {
    +
    1201 return templated_weak_integral_element(
    +
    1202 idx_r,
    +
    1203 idx_theta,
    +
    1204 test_bspline_val_and_deriv_r,
    +
    1205 trial_bspline_val_and_deriv,
    +
    1206 test_bspline_val_and_deriv_theta,
    +
    1207 trial_bspline_val_and_deriv,
    +
    1208 coeff_alpha,
    +
    1209 coeff_beta,
    +
    1210 evaluator,
    +
    1211 mapping,
    +
    1212 int_volume);
    +
    1213 }
    +
    1214
    +
    1215 template <class Mapping>
    +
    1216 static KOKKOS_FUNCTION double weak_integral_element(
    +
    1217 IdxQuadratureR idx_r,
    +
    1218 IdxQuadratureTheta idx_theta,
    +
    1219 EvalDeriv1DType const& test_bspline_val_and_deriv_r,
    +
    1220 EvalDeriv1DType const& trial_bspline_val_and_deriv_r,
    +
    1221 EvalDeriv1DType const& test_bspline_val_and_deriv_theta,
    +
    1222 EvalDeriv1DType const& trial_bspline_val_and_deriv_theta,
    +
    1223 ConstSpline2D coeff_alpha,
    +
    1224 ConstSpline2D coeff_beta,
    +
    1225 SplineRThetaEvaluatorNullBound const& evaluator,
    +
    1226 Mapping const& mapping,
    +
    1227 DField<IdxRangeQuadratureRTheta> int_volume)
    +
    1228 {
    +
    1229 return templated_weak_integral_element(
    +
    1230 idx_r,
    +
    1231 idx_theta,
    +
    1232 test_bspline_val_and_deriv_r,
    +
    1233 trial_bspline_val_and_deriv_r,
    +
    1234 test_bspline_val_and_deriv_theta,
    +
    1235 trial_bspline_val_and_deriv_theta,
    +
    1236 coeff_alpha,
    +
    1237 coeff_beta,
    +
    1238 evaluator,
    +
    1239 mapping,
    +
    1240 int_volume);
    +
    1241 }
    +
    1243
    +
    +
    1255 static KOKKOS_INLINE_FUNCTION void get_value_and_gradient(
    +
    1256 double& value,
    +
    1257 std::array<double, 2>& gradient,
    +
    1258 EvalDeriv1DType const& r_basis,
    +
    1259 EvalDeriv1DType const& theta_basis)
    +
    1260 {
    +
    1261 value = r_basis.value * theta_basis.value;
    +
    1262 gradient = {r_basis.derivative * theta_basis.value, r_basis.value * theta_basis.derivative};
    +
    1263 }
    +
    1264
    -
    1265 // Approaching the external boundary the overlapping possiblities between two radial splines decrease
    -
    1266 Kokkos::parallel_for(
    -
    1267 "outer overlap",
    -
    1268 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(1, degree + 1),
    -
    1269 KOKKOS_LAMBDA(const int i) {
    -
    1270 for (size_t k = mat_size - i * nbasis_theta_proxy;
    -
    1271 k < mat_size - (i - 1) * nbasis_theta_proxy;
    -
    1272 k++) {
    -
    1273 nnz(k + 2) = (degree + i) * radial_overlap;
    -
    1274 }
    -
    1275 });
    -
    1276
    -
    1277 // sum non-zero elements count
    -
    1278 Kokkos::parallel_for(
    -
    1279 "Sum over lines",
    -
    1280 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(0, 1),
    -
    1281 KOKKOS_LAMBDA(const int idx) {
    -
    1282 for (size_t k = 1; k < mat_size; k++) {
    -
    1283 nnz(k + 1) += nnz(k);
    -
    1284 }
    -
    1285 nnz(0) = 0;
    -
    1286 nnz(1) = 0;
    -
    1287 });
    -
    1288 Kokkos::Profiling::popRegion();
    -
    1289 }
    +
    +
    1275 static KOKKOS_INLINE_FUNCTION void get_value_and_gradient(
    +
    1276 double& value,
    +
    1277 std::array<double, 2>& gradient,
    +
    1278 EvalDeriv2DType const& basis,
    +
    1279 EvalDeriv2DType const&) // Last argument is duplicate
    +
    1280 {
    +
    1281 value = basis.value;
    +
    1282 gradient = {basis.radial_derivative, basis.poloidal_derivative};
    +
    1283 }
    +
    +
    1284
    +
    1319 template <class Mapping, class TestValDerivType, class TrialValDerivType>
    +
    +
    1320 static KOKKOS_FUNCTION double templated_weak_integral_element(
    +
    1321 IdxQuadratureR idx_r,
    +
    1322 IdxQuadratureTheta idx_theta,
    +
    1323 TestValDerivType const& test_bspline_val_and_deriv,
    +
    1324 TrialValDerivType const& trial_bspline_val_and_deriv,
    +
    1325 TestValDerivType const& test_bspline_val_and_deriv_theta,
    +
    1326 TrialValDerivType const& trial_bspline_val_and_deriv_theta,
    +
    1327 ConstSpline2D coeff_alpha,
    +
    1328 ConstSpline2D coeff_beta,
    +
    1329 SplineRThetaEvaluatorNullBound const& spline_evaluator,
    +
    1330 Mapping const& mapping,
    +
    1331 DField<IdxRangeQuadratureRTheta> int_volume)
    +
    1332 {
    +
    1333 static_assert(
    +
    1334 std::is_same_v<
    +
    1335 TestValDerivType,
    +
    1336 EvalDeriv1DType> || std::is_same_v<TestValDerivType, EvalDeriv2DType>);
    +
    1337 static_assert(
    +
    1338 std::is_same_v<
    +
    1339 TrialValDerivType,
    +
    1340 EvalDeriv1DType> || std::is_same_v<TrialValDerivType, EvalDeriv2DType>);
    +
    1341
    +
    1342 // Calculate coefficients at quadrature point
    +
    1343 CoordRTheta coord(ddc::coordinate(idx_r), ddc::coordinate(idx_theta));
    +
    1344 const double alpha = spline_evaluator(coord, coeff_alpha);
    +
    1345 const double beta = spline_evaluator(coord, coeff_beta);
    +
    1346
    +
    1347 // Define the value and gradient of the test and trial basis functions
    +
    1348 double basis_val_test_space;
    +
    1349 double basis_val_trial_space;
    +
    1350 std::array<double, 2> basis_gradient_test_space;
    +
    1351 std::array<double, 2> basis_gradient_trial_space;
    +
    1352 get_value_and_gradient(
    +
    1353 basis_val_test_space,
    +
    1354 basis_gradient_test_space,
    +
    1355 test_bspline_val_and_deriv,
    +
    1356 test_bspline_val_and_deriv_theta);
    +
    1357 get_value_and_gradient(
    +
    1358 basis_val_trial_space,
    +
    1359 basis_gradient_trial_space,
    +
    1360 trial_bspline_val_and_deriv,
    +
    1361 trial_bspline_val_and_deriv_theta);
    +
    1362
    +
    1363 MetricTensor<Mapping, CoordRTheta> metric_tensor(mapping);
    +
    1364
    +
    1365 // Assemble the weak integral element
    +
    1366 return int_volume(idx_r, idx_theta)
    +
    1367 * (alpha
    +
    1368 * dot_product(
    +
    1369 basis_gradient_test_space,
    +
    1370 metric_tensor.to_covariant(basis_gradient_trial_space, coord))
    +
    1371 + beta * basis_val_test_space * basis_val_trial_space);
    +
    1372 }
    +
    +
    1373
    +
    1396 template <class Mapping>
    +
    +
    1397 double get_matrix_stencil_element(
    +
    1398 IdxBSRTheta idx_test,
    +
    1399 IdxBSRTheta idx_trial,
    +
    1400 ConstSpline2D coeff_alpha,
    +
    1401 ConstSpline2D coeff_beta,
    +
    1402 SplineRThetaEvaluatorNullBound const& evaluator,
    +
    1403 Mapping const& mapping)
    +
    1404 {
    +
    1405 // 0 <= idx_test_r < 8
    +
    1406 // 0 <= idx_trial_r < 8
    +
    1407 // idx_test_r < idx_trial_r
    +
    1408 const int idx_test_r(ddc::select<BSplinesR>(idx_test).uid());
    +
    1409 const int idx_trial_r(ddc::select<BSplinesR>(idx_trial).uid());
    +
    1410 // 0 <= idx_test_theta < 8
    +
    1411 // 0 <= idx_trial_theta < 8
    +
    1412 int idx_test_theta(theta_mod(ddc::select<BSplinesTheta>(idx_test).uid()));
    +
    1413 int idx_trial_theta(theta_mod(ddc::select<BSplinesTheta>(idx_trial).uid()));
    +
    1414
    +
    1415 const std::size_t ncells_r = ddc::discrete_space<BSplinesR>().ncells();
    +
    1416
    +
    1417 // 0<= r_offset <= degree_r
    +
    1418 // -degree_theta <= theta_offset <= degree_theta
    +
    1419 const int r_offset = idx_trial_r - idx_test_r;
    +
    1420 int theta_offset = theta_mod(idx_trial_theta - idx_test_theta);
    +
    1421 if (theta_offset >= int(m_nbasis_theta - BSplinesTheta::degree())) {
    +
    1422 theta_offset -= m_nbasis_theta;
    +
    1423 }
    +
    1424 assert(r_offset >= 0);
    +
    1425 assert(r_offset <= int(BSplinesR::degree()));
    +
    1426 assert(theta_offset >= -int(BSplinesTheta::degree()));
    +
    1427 assert(theta_offset <= int(BSplinesTheta::degree()));
    +
    1428
    +
    1429 // Find the index range covering the cells where both the test and trial functions are non-zero
    +
    1430 int n_overlap_stencil_r(BSplinesR::degree() + 1 - r_offset);
    +
    1431 int first_overlap_r(idx_trial_r - BSplinesR::degree());
    +
    1432
    +
    1433 int first_overlap_theta;
    +
    1434 int n_overlap_stencil_theta;
    +
    1435 if (theta_offset > 0) {
    +
    1436 n_overlap_stencil_theta = BSplinesTheta::degree() + 1 - theta_offset;
    +
    1437 first_overlap_theta = theta_mod(idx_trial_theta - BSplinesTheta::degree());
    +
    1438 } else {
    +
    1439 n_overlap_stencil_theta = BSplinesTheta::degree() + 1 + theta_offset;
    +
    1440 first_overlap_theta = theta_mod(idx_test_theta - BSplinesTheta::degree());
    +
    1441 }
    +
    1442
    +
    1443 if (first_overlap_r < 0) {
    +
    1444 const int n_compact = first_overlap_r;
    +
    1445 first_overlap_r = 0;
    +
    1446 n_overlap_stencil_r += n_compact;
    +
    1447 }
    +
    1448
    +
    1449 const int n_to_edge_r(ncells_r - first_overlap_r);
    +
    1450
    +
    1451 const IdxStep<RCellDim> n_overlap_r(min(n_overlap_stencil_r, n_to_edge_r));
    +
    1452 const IdxStep<ThetaCellDim> n_overlap_theta(n_overlap_stencil_theta);
    +
    1453
    +
    1454 const Idx<RCellDim> first_overlap_element_r(first_overlap_r);
    +
    1455 const Idx<ThetaCellDim> first_overlap_element_theta(first_overlap_theta);
    +
    1456
    +
    1457 const IdxRange<RCellDim> r_cells(first_overlap_element_r, n_overlap_r);
    +
    1458 const IdxRange<ThetaCellDim> theta_cells(first_overlap_element_theta, n_overlap_theta);
    +
    1459 const IdxRange<RCellDim, ThetaCellDim> non_zero_cells(r_cells, theta_cells);
    +
    1460
    +
    1461 auto r_basis_vals_and_derivs_alloc = ddc::create_mirror_view_and_copy(
    +
    1462 Kokkos::DefaultExecutionSpace(),
    +
    1463 get_field(m_r_basis_vals_and_derivs));
    +
    1464 auto theta_basis_vals_and_derivs_alloc = ddc::create_mirror_view_and_copy(
    +
    1465 Kokkos::DefaultExecutionSpace(),
    +
    1466 get_field(m_theta_basis_vals_and_derivs));
    +
    1467
    +
    1468 Field<EvalDeriv1DType, IdxRange<RBasisSubset, QDimRMesh>> r_basis_vals_and_derivs
    +
    1469 = get_field(r_basis_vals_and_derivs_alloc);
    +
    1470 Field<EvalDeriv1DType, IdxRange<ThetaBasisSubset, QDimThetaMesh>>
    +
    1471 theta_basis_vals_and_derivs = get_field(theta_basis_vals_and_derivs_alloc);
    +
    1472 DField<IdxRangeQuadratureRTheta> int_volume_proxy = get_field(m_int_volume);
    +
    1473
    +
    1474 assert(n_overlap_r * n_overlap_theta > 0);
    +
    1475 return ddc::transform_reduce(
    +
    1476 non_zero_cells,
    +
    1477 0.0,
    +
    1478 ddc::reducer::sum<double>(),
    +
    1479 [&](IdxCell const cell_idx) {
    +
    1480 const int cell_idx_r(ddc::select<RCellDim>(cell_idx).uid());
    +
    1481 const int cell_idx_theta(theta_mod(ddc::select<ThetaCellDim>(cell_idx).uid()));
    +
    1482
    +
    1483 const IdxRangeQuadratureRTheta cell_quad_points(
    +
    1484 get_quadrature_points_in_cell(cell_idx_r, cell_idx_theta));
    +
    1485
    +
    1486 int ib_test_theta_idx = idx_test_theta - cell_idx_theta;
    +
    1487 int ib_trial_theta_idx = idx_trial_theta - cell_idx_theta;
    +
    1488
    +
    1489 // Find the column where the non-zero data is stored
    +
    1490 Idx<RBasisSubset> ib_test_r(idx_test_r - cell_idx_r);
    +
    1491 Idx<ThetaBasisSubset> ib_test_theta(theta_mod(ib_test_theta_idx));
    +
    1492 Idx<RBasisSubset> ib_trial_r(idx_trial_r - cell_idx_r);
    +
    1493 Idx<ThetaBasisSubset> ib_trial_theta(theta_mod(ib_trial_theta_idx));
    +
    1494
    +
    1495 assert(ib_test_r.uid() < BSplinesR::degree() + 1);
    +
    1496 assert(ib_test_theta.uid() < BSplinesTheta::degree() + 1);
    +
    1497 assert(ib_trial_r.uid() < BSplinesR::degree() + 1);
    +
    1498 assert(ib_trial_theta.uid() < BSplinesTheta::degree() + 1);
    +
    1499
    +
    1500 // Calculate the weak integral
    +
    1501 return ddc::parallel_transform_reduce(
    +
    1502 Kokkos::DefaultExecutionSpace(),
    +
    1503 cell_quad_points,
    +
    1504 0.0,
    +
    1505 ddc::reducer::sum<double>(),
    +
    1506 KOKKOS_LAMBDA(IdxQuadratureRTheta const idx_quad) {
    +
    1507 IdxQuadratureR const idx_r(idx_quad);
    +
    1508 IdxQuadratureTheta const idx_theta(idx_quad);
    +
    1509 return weak_integral_element(
    +
    1510 idx_r,
    +
    1511 idx_theta,
    +
    1512 r_basis_vals_and_derivs(ib_test_r, idx_r),
    +
    1513 r_basis_vals_and_derivs(ib_trial_r, idx_r),
    +
    1514 theta_basis_vals_and_derivs(ib_test_theta, idx_theta),
    +
    1515 theta_basis_vals_and_derivs(ib_trial_theta, idx_theta),
    +
    1516 coeff_alpha,
    +
    1517 coeff_beta,
    +
    1518 evaluator,
    +
    1519 mapping,
    +
    1520 int_volume_proxy);
    +
    1521 });
    +
    1522 });
    +
    1523 }
    +
    +
    1524
    +
    +
    1532 static KOKKOS_FUNCTION int theta_mod(int idx_theta)
    +
    1533 {
    +
    1534 int ncells_theta = ddc::discrete_space<BSplinesTheta>().ncells();
    +
    1535 while (idx_theta < 0)
    +
    1536 idx_theta += ncells_theta;
    +
    1537 while (idx_theta >= ncells_theta)
    +
    1538 idx_theta -= ncells_theta;
    +
    1539 return idx_theta;
    +
    1540 }
    +
    +
    1541
    +
    +
    1555 void init_nnz_per_line(Kokkos::View<int*, Kokkos::LayoutRight> nnz) const
    +
    1556 {
    +
    1557 Kokkos::Profiling::pushRegion("PolarPoissonInitNnz");
    +
    1558 size_t const mat_size = nnz.extent(0) - 1;
    +
    1559 size_t constexpr n_singular_basis = PolarBSplinesRTheta::n_singular_basis();
    +
    1560 size_t constexpr degree = BSplinesR::degree();
    +
    1561 size_t constexpr radial_overlap = 2 * degree + 1;
    +
    1562 size_t const nbasis_theta_proxy = m_nbasis_theta;
    +
    1563
    +
    1564 // overlap between singular domain splines and radial splines
    +
    1565 Kokkos::parallel_for(
    +
    1566 "overlap singular radial",
    +
    1567 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(1, n_singular_basis + 1),
    +
    1568 KOKKOS_LAMBDA(const int k) {
    +
    1569 nnz(k + 1) = n_singular_basis + degree * nbasis_theta_proxy;
    +
    1570 });
    +
    1571
    +
    1572 // going from the internal boundary the overlapping possiblities between two radial splines increase
    +
    1573 Kokkos::parallel_for(
    +
    1574 "inner overlap",
    +
    1575 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(1, degree + 2),
    +
    1576 KOKKOS_LAMBDA(const int i) {
    +
    1577 for (size_t k = n_singular_basis + (i - 1) * nbasis_theta_proxy;
    +
    1578 k < n_singular_basis + i * nbasis_theta_proxy;
    +
    1579 k++) {
    +
    1580 nnz(k + 2) = n_singular_basis + (degree + i) * radial_overlap;
    +
    1581 }
    +
    1582 });
    +
    1583
    +
    1584 // Stencil with maximum possible overlap from two sides for radial spline
    +
    1585 Kokkos::parallel_for(
    +
    1586 "Inner Stencil",
    +
    1587 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(
    +
    1588 n_singular_basis + degree * nbasis_theta_proxy,
    +
    1589 mat_size - degree * nbasis_theta_proxy),
    +
    1590 KOKKOS_LAMBDA(const int k) { nnz(k + 2) = radial_overlap * radial_overlap; });
    +
    1591
    +
    1592 // Approaching the external boundary the overlapping possiblities between two radial splines decrease
    +
    1593 Kokkos::parallel_for(
    +
    1594 "outer overlap",
    +
    1595 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(1, degree + 1),
    +
    1596 KOKKOS_LAMBDA(const int i) {
    +
    1597 for (size_t k = mat_size - i * nbasis_theta_proxy;
    +
    1598 k < mat_size - (i - 1) * nbasis_theta_proxy;
    +
    1599 k++) {
    +
    1600 nnz(k + 2) = (degree + i) * radial_overlap;
    +
    1601 }
    +
    1602 });
    +
    1603
    +
    1604 // sum non-zero elements count
    +
    1605 Kokkos::parallel_for(
    +
    1606 "Sum over lines",
    +
    1607 Kokkos::RangePolicy<Kokkos::DefaultExecutionSpace>(0, 1),
    +
    1608 KOKKOS_LAMBDA(const int idx) {
    +
    1609 for (size_t k = 1; k < mat_size; k++) {
    +
    1610 nnz(k + 1) += nnz(k);
    +
    1611 }
    +
    1612 nnz(0) = 0;
    +
    1613 nnz(1) = 0;
    +
    1614 });
    +
    1615 Kokkos::Profiling::popRegion();
    +
    1616 }
    -
    1290};
    +
    1617};
    GaussLegendre
    Definition gauss_legendre_integration.hpp:27
    MatrixBatchCsr
    Matrix class which is able to manage and solve a batch of sparse linear systems.
    Definition matrix_batch_csr.hpp:37
    MetricTensor
    An operator for calculating the metric tensor.
    Definition metric_tensor.hpp:15
    -
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::get_2d_index
    static KOKKOS_FUNCTION tensor_product_index_type get_2d_index(ddc::DiscreteElement< DDim > const &idx)
    Get the 2D index of the tensor product bspline which, when evaluated at the same point,...
    Definition polar_bsplines.hpp:153
    -
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::BSplinesTheta_tag
    BSplinesTheta BSplinesTheta_tag
    The poloidal bspline from which the polar bsplines are constructed.
    Definition polar_bsplines.hpp:50
    -
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::n_singular_basis
    static constexpr std::size_t n_singular_basis()
    Get the number of singular bsplines i.e.
    Definition polar_bsplines.hpp:103
    -
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
    static int constexpr continuity
    The continuity enforced by the bsplines at the singular point.
    Definition polar_bsplines.hpp:61
    -
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::BSplinesR_tag
    BSplinesR BSplinesR_tag
    The radial bspline from which the polar bsplines are constructed.
    Definition polar_bsplines.hpp:47
    +
    MetricTensor::to_covariant
    KOKKOS_FUNCTION std::array< double, 2 > to_covariant(std::array< double, 2 > const &contravariant_vector, PositionCoordinate const &coord) const
    Compute the covariant vector from the contravariant vector.
    Definition metric_tensor.hpp:89
    +
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::get_2d_index
    static KOKKOS_FUNCTION tensor_product_index_type get_2d_index(ddc::DiscreteElement< DDim > const &idx)
    Get the 2D index of the tensor product bspline which, when evaluated at the same point,...
    Definition polar_bsplines.hpp:154
    +
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::BSplinesTheta_tag
    BSplinesTheta BSplinesTheta_tag
    The poloidal bspline from which the polar bsplines are constructed.
    Definition polar_bsplines.hpp:51
    +
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::n_singular_basis
    static constexpr std::size_t n_singular_basis()
    Get the number of singular bsplines i.e.
    Definition polar_bsplines.hpp:104
    +
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::continuity
    static int constexpr continuity
    The continuity enforced by the bsplines at the singular point.
    Definition polar_bsplines.hpp:62
    +
    PolarBSplines< BSplinesR, BSplinesTheta, 1 >::BSplinesR_tag
    BSplinesR BSplinesR_tag
    The radial bspline from which the polar bsplines are constructed.
    Definition polar_bsplines.hpp:48
    PolarSplineEvaluator
    Define an evaluator on polar B-splines.
    Definition polar_spline_evaluator.hpp:13
    -
    PolarSplineFEMPoissonLikeSolver
    Define a polar PDE solver for a Poisson-like equation.
    Definition polarpoissonlikesolver.hpp:50
    -
    PolarSplineFEMPoissonLikeSolver::operator()
    void operator()(RHSFunction const &rhs, host_t< DFieldRTheta > phi) const
    Solve the Poisson-like equation.
    Definition polarpoissonlikesolver.hpp:872
    -
    PolarSplineFEMPoissonLikeSolver::PolarSplineFEMPoissonLikeSolver
    PolarSplineFEMPoissonLikeSolver(host_t< ConstSpline2D > coeff_alpha, host_t< ConstSpline2D > coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound_host const &spline_evaluator)
    Instantiate a polar Poisson-like solver using FEM with B-splines.
    Definition polarpoissonlikesolver.hpp:268
    -
    PolarSplineFEMPoissonLikeSolver::operator()
    void operator()(RHSFunction const &rhs, host_t< SplinePolar > &spline) const
    Solve the Poisson-like equation.
    Definition polarpoissonlikesolver.hpp:712
    -
    PolarSplineFEMPoissonLikeSolver::init_nnz_per_line
    void init_nnz_per_line(Kokkos::View< int *, Kokkos::LayoutRight > nnz) const
    Fills the nnz data structure by computing the number of non-zero per line.
    Definition polarpoissonlikesolver.hpp:1228
    -
    PolarSplineFEMPoissonLikeSolver::RBasisSubset
    Definition polarpoissonlikesolver.hpp:64
    -
    PolarSplineFEMPoissonLikeSolver::RCellDim
    Definition polarpoissonlikesolver.hpp:70
    -
    PolarSplineFEMPoissonLikeSolver::ThetaBasisSubset
    Definition polarpoissonlikesolver.hpp:67
    -
    PolarSplineFEMPoissonLikeSolver::ThetaCellDim
    Definition polarpoissonlikesolver.hpp:73
    +
    PolarSplineFEMPoissonLikeSolver
    Define a polar PDE solver for a Poisson-like equation.
    Definition polarpoissonlikesolver.hpp:51
    +
    PolarSplineFEMPoissonLikeSolver::fill_int_volume
    void fill_int_volume(Mapping const &mapping)
    Compute the volume integrals and stores the values in a member variable.
    Definition polarpoissonlikesolver.hpp:515
    +
    PolarSplineFEMPoissonLikeSolver::get_value_and_gradient
    static KOKKOS_INLINE_FUNCTION void get_value_and_gradient(double &value, std::array< double, 2 > &gradient, EvalDeriv1DType const &r_basis, EvalDeriv1DType const &theta_basis)
    Computes the value and gradient from r_basis and theta_basis inputs.
    Definition polarpoissonlikesolver.hpp:1255
    +
    PolarSplineFEMPoissonLikeSolver::compute_stencil_elements
    void compute_stencil_elements(ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator, Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host)
    Computes the matrix element corresponding to the regular stencil ie: out to singular or overlapping a...
    Definition polarpoissonlikesolver.hpp:787
    +
    PolarSplineFEMPoissonLikeSolver::operator()
    void operator()(RHSFunction const &rhs, host_t< SplinePolar > &spline) const
    Solve the Poisson-like equation.
    Definition polarpoissonlikesolver.hpp:904
    +
    PolarSplineFEMPoissonLikeSolver::compute_overlapping_singular_elements
    void compute_overlapping_singular_elements(ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator, Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host)
    Computes the matrix element corresponding to singular elements overlapping with regular grid.
    Definition polarpoissonlikesolver.hpp:648
    +
    PolarSplineFEMPoissonLikeSolver::PolarSplineFEMPoissonLikeSolver
    PolarSplineFEMPoissonLikeSolver(ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator)
    Instantiate a polar Poisson-like solver using FEM with B-splines.
    Definition polarpoissonlikesolver.hpp:272
    +
    PolarSplineFEMPoissonLikeSolver::get_matrix_stencil_element
    double get_matrix_stencil_element(IdxBSRTheta idx_test, IdxBSRTheta idx_trial, ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, SplineRThetaEvaluatorNullBound const &evaluator, Mapping const &mapping)
    Computes the matrix element corresponding to two tensor product splines with index idx_test and idx_t...
    Definition polarpoissonlikesolver.hpp:1397
    +
    PolarSplineFEMPoissonLikeSolver::get_value_and_gradient
    static KOKKOS_INLINE_FUNCTION void get_value_and_gradient(double &value, std::array< double, 2 > &gradient, EvalDeriv2DType const &basis, EvalDeriv2DType const &)
    Computes the value and gradient from r_basis and theta_basis inputs.
    Definition polarpoissonlikesolver.hpp:1275
    +
    PolarSplineFEMPoissonLikeSolver::operator()
    void operator()(RHSFunction const &rhs, DFieldRTheta phi) const
    Solve the Poisson-like equation.
    Definition polarpoissonlikesolver.hpp:1062
    +
    PolarSplineFEMPoissonLikeSolver::templated_weak_integral_element
    static KOKKOS_FUNCTION double templated_weak_integral_element(IdxQuadratureR idx_r, IdxQuadratureTheta idx_theta, TestValDerivType const &test_bspline_val_and_deriv, TrialValDerivType const &trial_bspline_val_and_deriv, TestValDerivType const &test_bspline_val_and_deriv_theta, TrialValDerivType const &trial_bspline_val_and_deriv_theta, ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, SplineRThetaEvaluatorNullBound const &spline_evaluator, Mapping const &mapping, DField< IdxRangeQuadratureRTheta > int_volume)
    Computes a quadrature summand corresponding to the inner product.
    Definition polarpoissonlikesolver.hpp:1320
    +
    PolarSplineFEMPoissonLikeSolver::theta_mod
    static KOKKOS_FUNCTION int theta_mod(int idx_theta)
    Calculates the modulo idx_theta in relation to cells number along direction .
    Definition polarpoissonlikesolver.hpp:1532
    +
    PolarSplineFEMPoissonLikeSolver::init_nnz_per_line
    void init_nnz_per_line(Kokkos::View< int *, Kokkos::LayoutRight > nnz) const
    Fills the nnz data structure by computing the number of non-zero per line.
    Definition polarpoissonlikesolver.hpp:1555
    +
    PolarSplineFEMPoissonLikeSolver::get_quadrature_points_in_cell
    static KOKKOS_FUNCTION IdxRangeQuadratureRTheta get_quadrature_points_in_cell(int cell_idx_r, int cell_idx_theta)
    compute the quadrature range for a given pair of indices
    Definition polarpoissonlikesolver.hpp:1096
    +
    PolarSplineFEMPoissonLikeSolver::compute_singular_elements
    void compute_singular_elements(ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, Mapping const &mapping, SplineRThetaEvaluatorNullBound const &spline_evaluator, Kokkos::View< double **, Kokkos::LayoutRight, Kokkos::HostSpace > const values_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const col_idx_csr_host, Kokkos::View< int *, Kokkos::LayoutRight, Kokkos::HostSpace > const nnz_per_row_csr_host)
    Computes the matrix element corresponding to the singular area.
    Definition polarpoissonlikesolver.hpp:567
    +
    PolarSplineFEMPoissonLikeSolver::IdxCell
    Idx< RCellDim, ThetaCellDim > IdxCell
    Tag an index of cell.
    Definition polarpoissonlikesolver.hpp:187
    +
    PolarSplineFEMPoissonLikeSolver::weak_integral_element
    static KOKKOS_FUNCTION double weak_integral_element(IdxQuadratureR idx_r, IdxQuadratureTheta idx_theta, EvalDeriv2DType const &test_bspline_val_and_deriv, EvalDeriv2DType const &trial_bspline_val_and_deriv, ConstSpline2D coeff_alpha, ConstSpline2D coeff_beta, SplineRThetaEvaluatorNullBound const &evaluator, Mapping const &mapping, DField< IdxRangeQuadratureRTheta > int_volume)
    compute the weak integral value.
    Definition polarpoissonlikesolver.hpp:1135
    +
    PolarSplineFEMPoissonLikeSolver::EvalDeriv1DType
    Object storing a value and a value of the derivative of a 1D function.
    Definition polarpoissonlikesolver.hpp:168
    +
    PolarSplineFEMPoissonLikeSolver::EvalDeriv2DType
    Object storing a value and a value of the derivatives in each direction of a 2D function.
    Definition polarpoissonlikesolver.hpp:178
    +
    PolarSplineFEMPoissonLikeSolver::RBasisSubset
    Definition polarpoissonlikesolver.hpp:65
    +
    PolarSplineFEMPoissonLikeSolver::RCellDim
    Definition polarpoissonlikesolver.hpp:71
    +
    PolarSplineFEMPoissonLikeSolver::ThetaBasisSubset
    Definition polarpoissonlikesolver.hpp:68
    +
    PolarSplineFEMPoissonLikeSolver::ThetaCellDim
    Definition polarpoissonlikesolver.hpp:74
    BSplinesR
    Definition geometry.hpp:93
    BSplinesTheta
    Definition geometry.hpp:100
    GridR
    Definition geometry.hpp:116
    GridTheta
    Definition geometry.hpp:119
    PolarBSplinesRTheta
    Definition geometry.hpp:103
    -
    PolarSplineFEMPoissonLikeSolver::QDimRMesh
    Tag the first dimension for the quadrature mesh.
    Definition polarpoissonlikesolver.hpp:82
    -
    PolarSplineFEMPoissonLikeSolver::QDimThetaMesh
    Tag the second dimension for the quadrature mesh.
    Definition polarpoissonlikesolver.hpp:88
    +
    PolarSplineFEMPoissonLikeSolver::QDimRMesh
    Tag the first dimension for the quadrature mesh.
    Definition polarpoissonlikesolver.hpp:83
    +
    PolarSplineFEMPoissonLikeSolver::QDimThetaMesh
    Tag the second dimension for the quadrature mesh.
    Definition polarpoissonlikesolver.hpp:89
    PolarSpline
    A structure containing the two Chunks necessary to define a spline on a set of polar basis splines.
    Definition polar_spline.hpp:20
    R
    Define non periodic real R dimension.
    Definition geometry.hpp:31
    Theta
    Define periodic real Theta dimension.
    Definition geometry.hpp:42
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    -
    PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::QDimRMesh Struct Reference
    +
    PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::QDimRMesh Struct Reference

    Tag the first dimension for the quadrature mesh. More...

    -Inheritance diagram for PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::QDimRMesh:
    +Inheritance diagram for PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::QDimRMesh:

    Detailed Description

    -
    template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound_host, class IdxRangeFull = IdxRange<GridR, GridTheta>>
    -struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::QDimRMesh

    Tag the first dimension for the quadrature mesh.

    +
    template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound, class IdxRangeFull = IdxRange<GridR, GridTheta>>
    +struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::QDimRMesh

    Tag the first dimension for the quadrature mesh.

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    -
    PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::QDimThetaMesh Struct Reference
    +
    PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::QDimThetaMesh Struct Reference

    Tag the second dimension for the quadrature mesh. More...

    -Inheritance diagram for PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::QDimThetaMesh:
    +Inheritance diagram for PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::QDimThetaMesh:

    Detailed Description

    -
    template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound_host, class IdxRangeFull = IdxRange<GridR, GridTheta>>
    -struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host, IdxRangeFull >::QDimThetaMesh

    Tag the second dimension for the quadrature mesh.

    +
    template<class GridR, class GridTheta, class PolarBSplinesRTheta, class SplineRThetaEvaluatorNullBound, class IdxRangeFull = IdxRange<GridR, GridTheta>>
    +struct PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound, IdxRangeFull >::QDimThetaMesh

    Tag the second dimension for the quadrature mesh.

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    RotationAdvectionFieldSimulation::RotationAdvectionFieldSimulation
    RotationAdvectionFieldSimulation(Mapping const &mapping, double const rmin, double const rmax)
    Instantiate a RotationSimulation simulation.
    Definition test_cases_adv_field.hpp:427
    TranslationAdvectionFieldSimulation
    Simulation of a translated Gaussian.
    Definition test_cases_adv_field.hpp:351
    TranslationAdvectionFieldSimulation::TranslationAdvectionFieldSimulation
    TranslationAdvectionFieldSimulation(Mapping const &mapping, double const rmin, double const rmax)
    Instantiate a TranslationSimulation simulation.
    Definition test_cases_adv_field.hpp:363
    -
    Vx
    Define non periodic real X velocity dimension.
    Definition geometry.hpp:300
    -
    Vy
    Define non periodic real Y velocity dimension.
    Definition geometry.hpp:311
    +
    Vx
    Define non periodic real X velocity dimension.
    Definition geometry.hpp:341
    +
    Vy
    Define non periodic real Y velocity dimension.
    Definition geometry.hpp:352
    diff --git a/vector__mapper_8hpp_source.html b/vector__mapper_8hpp_source.html index 5ff2d17b2..2f01b35f8 100644 --- a/vector__mapper_8hpp_source.html +++ b/vector__mapper_8hpp_source.html @@ -238,8 +238,8 @@
    VectorMapper< NDTag< XIn, YIn >, NDTag< XOut, YOut >, Mapping, ExecSpace >::VectorMapper
    VectorMapper(Mapping mapping)
    A constructor for the VectorMapper.
    Definition vector_mapper.hpp:54
    VectorMapper
    The general predeclaration of VectorMapper.
    Definition vector_mapper.hpp:14
    Vector
    A type describing a vector e.g. (E_x, E_y)
    Definition ddc_aliases.hpp:82
    -
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:277
    -
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:288
    +
    X
    Define non periodic real X dimension.
    Definition geometry.hpp:318
    +
    Y
    Define non periodic real Y dimension.
    Definition geometry.hpp:329
    diff --git a/vortex__merger__equilibrium_8hpp_source.html b/vortex__merger__equilibrium_8hpp_source.html index 17f1e8d7f..a36737f4f 100644 --- a/vortex__merger__equilibrium_8hpp_source.html +++ b/vortex__merger__equilibrium_8hpp_source.html @@ -133,11 +133,11 @@
    31 GridR,
    32 GridTheta,
    33 PolarBSplinesRTheta,
    -
    34 SplineRThetaEvaluatorNullBound_host> const& m_poisson_solver;
    +
    34 SplineRThetaEvaluatorNullBound> const& m_poisson_solver;
    35
    36public:
    -
    54 VortexMergerEquilibria(
    +
    54 VortexMergerEquilibria(
    55 Mapping const& mapping,
    56 IdxRangeRTheta const& grid,
    57 SplineRThetaBuilder_host const& builder,
    @@ -146,7 +146,7 @@
    60 GridR,
    61 GridTheta,
    62 PolarBSplinesRTheta,
    -
    63 SplineRThetaEvaluatorNullBound_host> const& poisson_solver)
    +
    63 SplineRThetaEvaluatorNullBound> const& poisson_solver)
    64 : m_mapping(mapping)
    65 , m_grid(grid)
    66 , m_builder(builder)
    @@ -164,7 +164,7 @@
    110 double const tau,
    111 int count_max = 25) const
    112 {
    -
    113 host_t<DFieldMemRTheta> phi_star(m_grid);
    +
    113 DFieldMemRTheta phi_star(m_grid);
    114 host_t<DFieldMemRTheta> ci(m_grid);
    115
    116 IdxRangeBSRTheta idx_range_bsplinesRTheta = get_spline_idx_range(m_builder);
    @@ -185,91 +185,92 @@
    131 m_builder(get_field(rho_coef), get_const_field(rho_eq));
    132 PoissonLikeRHSFunction poisson_rhs(get_const_field(rho_coef), m_evaluator);
    133 m_poisson_solver(poisson_rhs, get_field(phi_star));
    -
    134
    -
    135 // STEP 3: compute c^i
    -
    136 // If phi_max is given:
    -
    137 double norm_Linf_phi_star(0.);
    -
    138 ddc::for_each(m_grid, [&](IdxRTheta const irp) {
    -
    139 double const abs_phi_star = fabs(phi_star(irp));
    -
    140 norm_Linf_phi_star
    -
    141 = norm_Linf_phi_star > abs_phi_star ? norm_Linf_phi_star : abs_phi_star;
    -
    142 });
    -
    143
    -
    144 ddc::for_each(m_grid, [&](IdxRTheta const irp) {
    -
    145 ci(irp) = phi_max / norm_Linf_phi_star;
    -
    146 });
    -
    147
    +
    134 auto phi_star_host = ddc::create_mirror_view_and_copy(get_field(phi_star));
    +
    135
    +
    136 // STEP 3: compute c^i
    +
    137 // If phi_max is given:
    +
    138 double norm_Linf_phi_star(0.);
    +
    139 ddc::for_each(m_grid, [&](IdxRTheta const irp) {
    +
    140 double const abs_phi_star = fabs(phi_star_host(irp));
    +
    141 norm_Linf_phi_star
    +
    142 = norm_Linf_phi_star > abs_phi_star ? norm_Linf_phi_star : abs_phi_star;
    +
    143 });
    +
    144
    +
    145 ddc::for_each(m_grid, [&](IdxRTheta const irp) {
    +
    146 ci(irp) = phi_max / norm_Linf_phi_star;
    +
    147 });
    148
    -
    149 // STEP 4: update sigma and phi
    -
    150 difference_sigma = 0.;
    -
    151 ddc::for_each(m_grid, [&](IdxRTheta const irp) {
    -
    152 double const abs_diff_sigma = fabs(sigma(irp) - ci(irp) * sigma(irp));
    -
    153 difference_sigma
    -
    154 = difference_sigma > abs_diff_sigma ? difference_sigma : abs_diff_sigma;
    -
    155
    -
    156 sigma(irp) = ci(irp) * sigma(irp);
    -
    157 phi_eq(irp) = ci(irp) * phi_star(irp);
    -
    158 });
    -
    159
    -
    160 } while ((difference_sigma > tau) and (count < count_max));
    -
    161
    +
    149
    +
    150 // STEP 4: update sigma and phi
    +
    151 difference_sigma = 0.;
    +
    152 ddc::for_each(m_grid, [&](IdxRTheta const irp) {
    +
    153 double const abs_diff_sigma = fabs(sigma(irp) - ci(irp) * sigma(irp));
    +
    154 difference_sigma
    +
    155 = difference_sigma > abs_diff_sigma ? difference_sigma : abs_diff_sigma;
    +
    156
    +
    157 sigma(irp) = ci(irp) * sigma(irp);
    +
    158 phi_eq(irp) = ci(irp) * phi_star_host(irp);
    +
    159 });
    +
    160
    +
    161 } while ((difference_sigma > tau) and (count < count_max));
    162
    -
    163 // STEP 1: compute rho^i
    -
    164 ddc::for_each(m_grid, [&](IdxRTheta const irp) {
    -
    165 rho_eq(irp) = sigma(irp) * function(phi_eq(irp));
    -
    166 });
    -
    167
    -
    168 // Unify at the center point:
    -
    169 IdxRangeR r_idx_range = get_idx_range<GridR>(rho_eq);
    -
    170 IdxRangeTheta theta_idx_range = get_idx_range<GridTheta>(rho_eq);
    -
    171 if (std::fabs(ddc::coordinate(r_idx_range.front())) < 1e-15) {
    -
    172 ddc::for_each(theta_idx_range, [&](const IdxTheta ip) {
    -
    173 rho_eq(r_idx_range.front(), ip)
    -
    174 = rho_eq(r_idx_range.front(), theta_idx_range.front());
    -
    175 });
    -
    176 }
    -
    177 };
    +
    163
    +
    164 // STEP 1: compute rho^i
    +
    165 ddc::for_each(m_grid, [&](IdxRTheta const irp) {
    +
    166 rho_eq(irp) = sigma(irp) * function(phi_eq(irp));
    +
    167 });
    +
    168
    +
    169 // Unify at the center point:
    +
    170 IdxRangeR r_idx_range = get_idx_range<GridR>(rho_eq);
    +
    171 IdxRangeTheta theta_idx_range = get_idx_range<GridTheta>(rho_eq);
    +
    172 if (std::fabs(ddc::coordinate(r_idx_range.front())) < 1e-15) {
    +
    173 ddc::for_each(theta_idx_range, [&](const IdxTheta ip) {
    +
    174 rho_eq(r_idx_range.front(), ip)
    +
    175 = rho_eq(r_idx_range.front(), theta_idx_range.front());
    +
    176 });
    +
    177 }
    +
    178 };
    -
    178
    179
    -
    -
    194 void set_equilibrium(
    -
    195 host_t<DFieldRTheta> rho_eq,
    -
    196 std::function<double(double const)> function,
    -
    197 double const phi_max,
    -
    198 double const tau)
    -
    199 {
    -
    200 IdxRangeRTheta grid = get_idx_range<GridR, GridTheta>(rho_eq);
    -
    201
    -
    202 // Equilibrium:
    -
    203 host_t<DFieldMemRTheta> sigma_0(grid);
    -
    204 host_t<DFieldMemRTheta> phi_eq(grid);
    -
    205 const double sig = 0.3;
    -
    206 ddc::for_each(grid, [&](IdxRTheta const irp) {
    -
    207 const CoordRTheta coord_rp(ddc::coordinate(irp));
    -
    208 const CoordXY coord_xy(m_mapping(coord_rp));
    -
    209 const double x = ddc::get<X>(coord_xy);
    -
    210 const double y = ddc::get<Y>(coord_xy);
    -
    211 sigma_0(irp) = sig;
    -
    212 phi_eq(irp) = std::exp(-(x * x + y * y) / (2 * sig * sig));
    -
    213 });
    -
    214 find_equilibrium(
    -
    215 get_field(sigma_0),
    -
    216 get_field(phi_eq),
    -
    217 get_field(rho_eq),
    -
    218 function,
    -
    219 phi_max,
    -
    220 tau);
    -
    221 };
    +
    180
    +
    +
    195 void set_equilibrium(
    +
    196 host_t<DFieldRTheta> rho_eq,
    +
    197 std::function<double(double const)> function,
    +
    198 double const phi_max,
    +
    199 double const tau)
    +
    200 {
    +
    201 IdxRangeRTheta grid = get_idx_range<GridR, GridTheta>(rho_eq);
    +
    202
    +
    203 // Equilibrium:
    +
    204 host_t<DFieldMemRTheta> sigma_0(grid);
    +
    205 host_t<DFieldMemRTheta> phi_eq(grid);
    +
    206 const double sig = 0.3;
    +
    207 ddc::for_each(grid, [&](IdxRTheta const irp) {
    +
    208 const CoordRTheta coord_rp(ddc::coordinate(irp));
    +
    209 const CoordXY coord_xy(m_mapping(coord_rp));
    +
    210 const double x = ddc::get<X>(coord_xy);
    +
    211 const double y = ddc::get<Y>(coord_xy);
    +
    212 sigma_0(irp) = sig;
    +
    213 phi_eq(irp) = std::exp(-(x * x + y * y) / (2 * sig * sig));
    +
    214 });
    +
    215 find_equilibrium(
    +
    216 get_field(sigma_0),
    +
    217 get_field(phi_eq),
    +
    218 get_field(rho_eq),
    +
    219 function,
    +
    220 phi_max,
    +
    221 tau);
    +
    222 };
    -
    222};
    +
    223};
    PoissonLikeRHSFunction
    Type of right-hand side (rhs) function of the Poisson equation.
    Definition poisson_like_rhs_function.hpp:17
    -
    PolarSplineFEMPoissonLikeSolver
    Define a polar PDE solver for a Poisson-like equation.
    Definition polarpoissonlikesolver.hpp:50
    +
    PolarSplineFEMPoissonLikeSolver
    Define a polar PDE solver for a Poisson-like equation.
    Definition polarpoissonlikesolver.hpp:51
    VortexMergerEquilibria
    Equilibrium solution of a Vlasov-Poissson equations system in polar coordinates.
    Definition vortex_merger_equilibrium.hpp:24
    -
    VortexMergerEquilibria::VortexMergerEquilibria
    VortexMergerEquilibria(Mapping const &mapping, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver)
    Instantiate a VortexMergerEquilibria.
    Definition vortex_merger_equilibrium.hpp:54
    +
    VortexMergerEquilibria::VortexMergerEquilibria
    VortexMergerEquilibria(Mapping const &mapping, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver)
    Instantiate a VortexMergerEquilibria.
    Definition vortex_merger_equilibrium.hpp:54
    VortexMergerEquilibria::find_equilibrium
    void find_equilibrium(host_t< DFieldRTheta > sigma, host_t< DFieldRTheta > phi_eq, host_t< DFieldRTheta > rho_eq, std::function< double(double const)> const &function, double const phi_max, double const tau, int count_max=25) const
    Get an equilibrium.
    Definition vortex_merger_equilibrium.hpp:104
    -
    VortexMergerEquilibria::set_equilibrium
    void set_equilibrium(host_t< DFieldRTheta > rho_eq, std::function< double(double const)> function, double const phi_max, double const tau)
    Set an equilibrium.
    Definition vortex_merger_equilibrium.hpp:194
    +
    VortexMergerEquilibria::set_equilibrium
    void set_equilibrium(host_t< DFieldRTheta > rho_eq, std::function< double(double const)> function, double const phi_max, double const tau)
    Set an equilibrium.
    Definition vortex_merger_equilibrium.hpp:195
    l_norm_tools.hpp
    File Describing useful mathematical functions to compute Lnorms.
    GridR
    Definition geometry.hpp:116
    GridTheta
    Definition geometry.hpp:119

Public Member Functions

 VortexMergerEquilibria (Mapping const &mapping, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const &poisson_solver)
 Instantiate a VortexMergerEquilibria.
 
 VortexMergerEquilibria (Mapping const &mapping, IdxRangeRTheta const &grid, SplineRThetaBuilder_host const &builder, SplineRThetaEvaluatorNullBound_host const &evaluator, PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &poisson_solver)
 Instantiate a VortexMergerEquilibria.
 
void find_equilibrium (host_t< DFieldRTheta > sigma, host_t< DFieldRTheta > phi_eq, host_t< DFieldRTheta > rho_eq, std::function< double(double const)> const &function, double const phi_max, double const tau, int count_max=25) const
 Get an equilibrium.
 
PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound_host > const & PolarSplineFEMPoissonLikeSolver< GridR, GridTheta, PolarBSplinesRTheta, SplineRThetaEvaluatorNullBound > const &  poisson_solver