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Merged
AbdelhadiKara merged 13 commits into from
May 21, 2026
Merged

Reduce amount of calculation for exact solution #277

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8d46fd6
fill exact solution on host
AbdelhadiKara May 19, 2026
a215fe6
compute and store exact solution once, pass it as a Vector
AbdelhadiKara May 19, 2026
e7baa1e
fix typo
AbdelhadiKara May 19, 2026
90dad33
Merge remote-tracking branch 'origin/main' into akara_compute_exact_s…
AbdelhadiKara May 19, 2026
65a99dc
use class_lambda for host parallel loop
AbdelhadiKara May 20, 2026
678e915
pass by reference in cpu loops
AbdelhadiKara May 20, 2026
71e5482
Merge branch 'main' into akara_compute_exact_solution_vector
AbdelhadiKara May 21, 2026
494289e
iterate over grid index, create if condition and allocate exact_sol …
AbdelhadiKara May 21, 2026
bd98e90
harmonize exact_solution condition with the rest of the code
AbdelhadiKara May 21, 2026
cb33567
return to use of multi dimensional loop for exact solution fill
AbdelhadiKara May 21, 2026
af6c2cd
split filling into 2 loops, use subtract function
AbdelhadiKara May 21, 2026
457cff1
fix outer word typo
AbdelhadiKara May 21, 2026
26da51e
allocate exact solution only if needed
AbdelhadiKara May 21, 2026
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9 changes: 5 additions & 4 deletions include/GMGPolar/gmgpolar.h
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Original file line number Diff line number Diff line change
Expand Up @@ -134,7 +134,7 @@ class GMGPolar : public IGMGPolar
std::vector<std::pair<double, double>> exact_errors_;
std::pair<double, double> computeExactError(Level<DomainGeometry, DensityProfileCoefficients>& level,
HostConstVector<double> solution, HostVector<double> error,
const ExactSolution& exact_solution);
HostConstVector<double> exact_solution);

/* --------------- */
/* Setup Functions */
Expand All @@ -153,13 +153,14 @@ class GMGPolar : public IGMGPolar
/* Solve Functions */
void fullMultigridApproximation(MultigridCycleType FMG_cycle, int FMG_iterations);
void solveMultigrid(double& initial_residual_norm, double& current_residual_norm,
double& current_relative_residual_norm);
void solvePCG(double& initial_residual_norm, double& current_residual_norm, double& current_relative_residual_norm);
double& current_relative_residual_norm, HostConstVector<double> exact_solution);
void solvePCG(double& initial_residual_norm, double& current_residual_norm, double& current_relative_residual_norm,
HostConstVector<double> exact_solution);
double residualNorm(const ResidualNormType& norm_type,
const Level<DomainGeometry, DensityProfileCoefficients>& level,
HostConstVector<double> residual) const;
void evaluateExactError(Level<DomainGeometry, DensityProfileCoefficients>& level,
const ExactSolution& exact_solution);
HostConstVector<double> exact_solution);
void updateResidualNorms(Level<DomainGeometry, DensityProfileCoefficients>& level, int iteration,
double& initial_residual_norm, double& current_residual_norm,
double& current_relative_residual_norm);
Expand Down
82 changes: 45 additions & 37 deletions include/GMGPolar/solver.h
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Original file line number Diff line number Diff line change
Expand Up @@ -95,10 +95,33 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solve(const BoundaryC
/* ---------------------------------------------- */
LIKWID_STOP("Solver");
auto start_check_exact_error = std::chrono::high_resolution_clock::now();

if (exact_solution_ != nullptr)
evaluateExactError(level, *exact_solution_);

HostAllocatableVector<double> exact_sol;
if (exact_solution_) {
exact_sol = HostVector<double>("exact_sol", level.solution().size());
// fill exact solution on host to avoid repeat same computation
const PolarGrid& grid = level.grid();

Kokkos::parallel_for("fill exact sol outer loop on r",
Kokkos::MDRangePolicy<Kokkos::DefaultHostExecutionSpace, Kokkos::Rank<2>>(
{0, 0}, {grid.numberSmootherCircles(), grid.ntheta()}),
[&](const int i_r, const int i_theta) {
double r = grid.radius(i_r);
double theta = grid.theta(i_theta);
const int grid_idx = grid.index(i_r, i_theta);
exact_sol(grid_idx) = exact_solution_->exact_solution(r, theta);
});
Kokkos::parallel_for("fill exact sol outer loop on theta",
Kokkos::MDRangePolicy<Kokkos::DefaultHostExecutionSpace, Kokkos::Rank<2>>(
{0, grid.numberSmootherCircles()}, {grid.ntheta(), grid.nr()}),
[&](const int i_theta, const int i_r) {
double r = grid.radius(i_r);
double theta = grid.theta(i_theta);
const int grid_idx = grid.index(i_r, i_theta);
exact_sol(grid_idx) = exact_solution_->exact_solution(r, theta);
});

evaluateExactError(level, exact_sol);
}
auto end_check_exact_error = std::chrono::high_resolution_clock::now();
t_check_exact_error_ += std::chrono::duration<double>(end_check_exact_error - start_check_exact_error).count();
LIKWID_START("Solver");
Expand All @@ -121,15 +144,15 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solve(const BoundaryC
if (!PCG_) {
// Solve A*x = b directly using multigrid cycles (V/W/F-cycle)
// until convergence or max_iterations_ is reached.
solveMultigrid(initial_residual_norm, current_residual_norm, current_relative_residual_norm);
solveMultigrid(initial_residual_norm, current_residual_norm, current_relative_residual_norm, exact_sol);
}
else {
// Solve A*x = b using Preconditioned Conjugate Gradient (PCG),
// with multigrid cycles as the preconditioner (i.e., one multigrid
// cycle approximates the action of A^{-1} at each PCG iteration).
auto start_conjugate_gradient = std::chrono::high_resolution_clock::now();

solvePCG(initial_residual_norm, current_residual_norm, current_relative_residual_norm);
solvePCG(initial_residual_norm, current_residual_norm, current_relative_residual_norm, exact_sol);

auto end_conjugate_gradient = std::chrono::high_resolution_clock::now();
t_conjugate_gradient_ +=
Expand Down Expand Up @@ -169,8 +192,8 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solve(const BoundaryC

if (paraview_) {
writeToVTK("output_solution", level, level.solution());
if (exact_solution_ != nullptr) {
computeExactError(level, level.solution(), level.residual(), *exact_solution_);
if (exact_solution_) {
computeExactError(level, level.solution(), level.residual(), exact_sol);
writeToVTK("output_error", level, level.residual());
}
}
Expand Down Expand Up @@ -215,7 +238,8 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::fullMultigridApproxim
template <concepts::DomainGeometry DomainGeometry, concepts::DensityProfileCoefficients DensityProfileCoefficients>
void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solveMultigrid(double& initial_residual_norm,
double& current_residual_norm,
double& current_relative_residual_norm)
double& current_relative_residual_norm,
HostConstVector<double> exact_solution)
{
Level<DomainGeometry, DensityProfileCoefficients>& level = levels_[0];

Expand Down Expand Up @@ -244,8 +268,8 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solveMultigrid(double
LIKWID_STOP("Solver");
auto start_check_exact_error = std::chrono::high_resolution_clock::now();

if (exact_solution_ != nullptr)
evaluateExactError(level, *exact_solution_);
if (exact_solution_)
evaluateExactError(level, exact_solution);

auto end_check_exact_error = std::chrono::high_resolution_clock::now();
t_check_exact_error_ += std::chrono::duration<double>(end_check_exact_error - start_check_exact_error).count();
Expand Down Expand Up @@ -288,7 +312,8 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solveMultigrid(double
template <concepts::DomainGeometry DomainGeometry, concepts::DensityProfileCoefficients DensityProfileCoefficients>
void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solvePCG(double& initial_residual_norm,
double& current_residual_norm,
double& current_relative_residual_norm)
double& current_relative_residual_norm,
HostConstVector<double> exact_solution)
{
Level<DomainGeometry, DensityProfileCoefficients>& level = levels_[0];

Expand Down Expand Up @@ -354,8 +379,8 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solvePCG(double& init
LIKWID_STOP("Solver");
auto start_check_exact_error = std::chrono::high_resolution_clock::now();

if (exact_solution_ != nullptr)
exact_errors_.push_back(computeExactError(level, pcg_solution_, level.residual(), *exact_solution_));
if (exact_solution_)
exact_errors_.push_back(computeExactError(level, pcg_solution_, level.residual(), exact_solution));

auto end_check_exact_error = std::chrono::high_resolution_clock::now();
t_check_exact_error_ += std::chrono::duration<double>(end_check_exact_error - start_check_exact_error).count();
Expand Down Expand Up @@ -574,7 +599,7 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::initRhsHierarchy(Host

template <concepts::DomainGeometry DomainGeometry, concepts::DensityProfileCoefficients DensityProfileCoefficients>
void GMGPolar<DomainGeometry, DensityProfileCoefficients>::evaluateExactError(
Level<DomainGeometry, DensityProfileCoefficients>& level, const ExactSolution& exact_solution)
Level<DomainGeometry, DensityProfileCoefficients>& level, HostConstVector<double> exact_solution)
{
// Compute the weighted L2 norm and infinity norm of the error between the numerical and exact solution.
// The results are stored as a pair: (weighted L2 error, infinity error).
Expand All @@ -584,34 +609,17 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::evaluateExactError(
template <concepts::DomainGeometry DomainGeometry, concepts::DensityProfileCoefficients DensityProfileCoefficients>
std::pair<double, double> GMGPolar<DomainGeometry, DensityProfileCoefficients>::computeExactError(
Level<DomainGeometry, DensityProfileCoefficients>& level, HostConstVector<double> solution,
HostVector<double> error, const ExactSolution& exact_solution)
HostVector<double> error, HostConstVector<double> exact_solution)
{
const PolarGrid& grid = level.grid();

assert(solution.size() == error.size());
assert(std::ssize(solution) == grid.numberOfNodes());

#pragma omp parallel
{
#pragma omp for nowait
for (int i_r = 0; i_r < grid.numberSmootherCircles(); i_r++) {
double r = grid.radius(i_r);
for (int i_theta = 0; i_theta < grid.ntheta(); i_theta++) {
double theta = grid.theta(i_theta);
error[grid.index(i_r, i_theta)] =
exact_solution.exact_solution(r, theta) - solution[grid.index(i_r, i_theta)];
}
}
#pragma omp for nowait
for (int i_theta = 0; i_theta < grid.ntheta(); i_theta++) {
double theta = grid.theta(i_theta);
for (int i_r = grid.numberSmootherCircles(); i_r < grid.nr(); i_r++) {
double r = grid.radius(i_r);
error[grid.index(i_r, i_theta)] =
exact_solution.exact_solution(r, theta) - solution[grid.index(i_r, i_theta)];
}
}
}
Kokkos::deep_copy(error, solution);
// Compute the error as the difference between exact and numerical solution
subtract(error, exact_solution);

HostConstVector<double> c_error = error;
double weighted_euclidean_error = l2_norm(c_error) / std::sqrt(grid.numberOfNodes());
double infinity_error = infinity_norm(c_error);
Expand Down
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