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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
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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
62 changes: 32 additions & 30 deletions include/GMGPolar/solver.h
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Original file line number Diff line number Diff line change
Expand Up @@ -95,9 +95,20 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solve(const BoundaryC
/* ---------------------------------------------- */
LIKWID_STOP("Solver");
auto start_check_exact_error = std::chrono::high_resolution_clock::now();
// fill exact solution on host to avoid repeat same computation
HostVector<double> exact_sol("exact_sol", level.solution().size());
const PolarGrid& grid = level.grid();
Kokkos::parallel_for(
"fill exact sol on host",
Kokkos::MDRangePolicy<Kokkos::DefaultHostExecutionSpace, Kokkos::Rank<2>>({0, 0}, {grid.nr(), grid.ntheta()}),
[&](const int i_r, const int i_theta) {
double r = grid.radius(i_r);
double theta = grid.theta(i_theta);
exact_sol(grid.index(i_r, i_theta)) = exact_solution_->exact_solution(r, theta);
});

if (exact_solution_ != nullptr)
evaluateExactError(level, *exact_solution_);
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();
Expand All @@ -121,15 +132,15 @@ 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 @@ -170,7 +181,7 @@ 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_);
computeExactError(level, level.solution(), level.residual(), exact_sol);
writeToVTK("output_error", level, level.residual());
}
}
Expand Down Expand Up @@ -215,7 +226,8 @@ 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 @@ -245,7 +257,7 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solveMultigrid(double
auto start_check_exact_error = std::chrono::high_resolution_clock::now();

if (exact_solution_ != nullptr)
evaluateExactError(level, *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 +300,8 @@ 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 @@ -355,7 +368,7 @@ void GMGPolar<DomainGeometry, DensityProfileCoefficients>::solvePCG(double& init
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_));
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 +587,7 @@ 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 @@ -584,35 +597,24 @@ 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();
const LevelCache<DomainGeometry, DensityProfileCoefficients>& levelCache = level.levelCache();

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++) {
Kokkos::parallel_for(
"compute error on host",
Kokkos::MDRangePolicy<Kokkos::DefaultHostExecutionSpace, Kokkos::Rank<2>>({0, 0}, {grid.nr(), grid.ntheta()}),
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@julianlitz julianlitz May 20, 2026

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Less cache efficient access, but for this purpose ok.

[&](const int i_r, const int i_theta) {
double r = grid.radius(i_r);
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)];
}
}
}
error[grid.index(i_r, i_theta)] =
exact_solution(grid.index(i_r, i_theta)) - solution[grid.index(i_r, i_theta)];
});

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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