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#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include "mg2d.h"
#include "mg2d_boundary.h"
#include "mg2d_constants.h"
#define ARRAY_ELEMS(x) (sizeof(x) / sizeof(*x))
#define MAXITER 64
#define TOL 5e-15
#define DOMAIN_SIZE 1.0
static const double pde_coeffs[MG2D_DIFF_COEFF_NB] = {
[MG2D_DIFF_COEFF_00] = 1.0,
[MG2D_DIFF_COEFF_10] = 0.9,
[MG2D_DIFF_COEFF_01] = 1.1,
[MG2D_DIFF_COEFF_20] = 1.2,
[MG2D_DIFF_COEFF_02] = 0.8,
[MG2D_DIFF_COEFF_11] = 0.7,
};
#if 1
static double sol_00(double x, double y)
{
return sin(M_PI * x) * sin(M_PI * y);
}
static double sol_10(double x, double y)
{
return M_PI * cos(M_PI * x) * sin(M_PI * y);
}
static double sol_01(double x, double y)
{
return M_PI * sin(M_PI * x) * cos(M_PI * y);
}
static double sol_20(double x, double y)
{
return -M_PI * M_PI * sol_00(x, y);
}
static double sol_02(double x, double y)
{
return -M_PI * M_PI * sol_00(x, y);
}
static double sol_11(double x, double y)
{
return M_PI * M_PI * cos(M_PI * x) * cos(M_PI * y);
}
#define BC_TYPE MG2D_BC_TYPE_FIXVAL
#else
static double sol_00(double x, double y)
{
return cos(M_PI * x) * cos(M_PI * y);
}
static double sol_10(double x, double y)
{
return -M_PI * sin(M_PI * x) * cos(M_PI * y);
}
static double sol_01(double x, double y)
{
return -M_PI * cos(M_PI * x) * sin(M_PI * y);
}
static double sol_20(double x, double y)
{
return -M_PI * M_PI * sol_00(x, y);
}
static double sol_02(double x, double y)
{
return -M_PI * M_PI * sol_00(x, y);
}
static double sol_11(double x, double y)
{
return M_PI * M_PI * sin(M_PI * x) * sin(M_PI * y);
}
#define BC_TYPE MG2D_BC_TYPE_REFLECT
#endif
static double (*sol[MG2D_DIFF_COEFF_NB])(double x, double y) = {
[MG2D_DIFF_COEFF_00] = sol_00,
[MG2D_DIFF_COEFF_10] = sol_10,
[MG2D_DIFF_COEFF_01] = sol_01,
[MG2D_DIFF_COEFF_20] = sol_20,
[MG2D_DIFF_COEFF_02] = sol_02,
[MG2D_DIFF_COEFF_11] = sol_11,
};
int main(int argc, char **argv)
{
MG2DContext *ctx;
long int gridsize;
int ret = 0;
if (argc < 2) {
fprintf(stderr, "Usage: %s <N>\n", argv[0]);
return 1;
}
gridsize = strtol(argv[1], NULL, 0);
if (gridsize <= 0) {
fprintf(stderr, "Invalid parameters: %ld\n", gridsize);
return 1;
}
ctx = mg2d_solver_alloc(gridsize);
if (!ctx) {
fprintf(stderr, "Error allocating the solver context\n");
return 1;
}
ctx->step[0] = DOMAIN_SIZE / (gridsize - 1);
ctx->step[1] = DOMAIN_SIZE / (gridsize - 1);
ctx->fd_stencil = 2;
ctx->maxiter = MAXITER;
ctx->nb_relax_pre = 2;
ctx->nb_cycles = 1;
ctx->nb_relax_post = 2;
ctx->tol = TOL / (ctx->step[0] * ctx->step[1]);
ctx->nb_threads = 1;
ctx->log_level = MG2D_LOG_INFO;
for (int bnd_loc = 0; bnd_loc < ARRAY_ELEMS(ctx->boundaries); bnd_loc++) {
MG2DBoundary *bnd = ctx->boundaries[bnd_loc];
const int ci = mg2d_bnd_coord_idx(bnd_loc);
const int bnd_dir = mg2d_bnd_out_dir(bnd_loc);
double coord[2];
bnd->type = BC_TYPE;
memset(bnd->val, 0, gridsize * sizeof(*bnd->val));
if (bnd->type == MG2D_BC_TYPE_FIXVAL) {
for (int j = 1; j < ctx->fd_stencil; j++) {
double *dst = bnd->val + j * bnd->val_stride;
coord[ci] = mg2d_bnd_is_upper(bnd_loc) * DOMAIN_SIZE + bnd_dir * j * ctx->step[ci];
for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size + j; k++) {
coord[!ci] = k * ctx->step[!ci];
dst[k] = sol[MG2D_DIFF_COEFF_00](coord[0], coord[1]);
}
}
}
}
for (size_t y = 0; y < ctx->domain_size; y++) {
const double y_coord = y * ctx->step[1];
memset(ctx->u + y * ctx->u_stride, 0, sizeof(*ctx->u) * ctx->domain_size);
for (size_t x = 0; x < ctx->domain_size; x++) {
const double x_coord = x * ctx->step[0];
double rhs = 0.0;
for (int i = 0; i < MG2D_DIFF_COEFF_NB; i++) {
ctx->diff_coeffs[i]->data[ctx->diff_coeffs[i]->stride * y + x] = pde_coeffs[i];
rhs += pde_coeffs[i] * sol[i](x_coord, y_coord);
}
ctx->rhs[y * ctx->rhs_stride + x] = rhs;
}
}
ret = mg2d_solve(ctx);
if (ret < 0) {
fprintf(stderr, "Error solving the equation\n");
ret = 1;
goto fail;
}
mg2d_print_stats(ctx, NULL);
{
double max_err = 0.0;
for (size_t y = 0; y < ctx->domain_size; y++) {
const double y_coord = y * ctx->step[1];
for (size_t x = 0; x < ctx->domain_size; x++) {
const double x_coord = x * ctx->step[0];
double err = fabs(ctx->u[y * ctx->u_stride + x] - sol[MG2D_DIFF_COEFF_00](x_coord, y_coord));
if (err > max_err)
max_err = err;
}
}
fprintf(stderr, "max(|solution - exact|): %g\n", max_err);
fprintf(stdout, "%ld %g\n", gridsize, max_err);
}
fail:
mg2d_solver_free(&ctx);
return ret;
}
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