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#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include "mg2d.h"
#define MAXITER 64
#define TOL 1e-9
#if 1
static double sol(double x, double y)
{
return sin(M_PI * x) * sin(M_PI * y);
}
static double sol_dx(double x, double y)
{
return M_PI * cos(M_PI * x) * sin(M_PI * y);
}
static double sol_dy(double x, double y)
{
return M_PI * sin(M_PI * x) * cos(M_PI * y);
}
static double sol_dxx(double x, double y)
{
return -M_PI * M_PI * sol(x, y);
}
static double sol_dyy(double x, double y)
{
return -M_PI * M_PI * sol(x, y);
}
static double sol_dxy(double x, double y)
{
return M_PI * M_PI * cos(M_PI * x) * cos(M_PI * y);
}
#endif
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] = 1.0 / (gridsize - 1);
ctx->step[1] = 1.0 / (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->nb_threads = 1;
{
MG2DBoundary *bnd = ctx->boundaries[MG2D_BOUNDARY_0L];
bnd->type = MG2D_BC_TYPE_FIXVAL;
memset(bnd->val, 0, gridsize * sizeof(*bnd->val));
for (int j = 1; j < ctx->fd_stencil; j++) {
double *dst = bnd->val + j * bnd->val_stride;
for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size + j; k++)
dst[k] = sol(-j * ctx->step[0], k * ctx->step[1]);
}
}
{
MG2DBoundary *bnd = ctx->boundaries[MG2D_BOUNDARY_0U];
bnd->type = MG2D_BC_TYPE_FIXVAL;
memset(bnd->val, 0, gridsize * sizeof(*bnd->val));
for (int j = 1; j < ctx->fd_stencil; j++) {
double *dst = bnd->val + j * bnd->val_stride;
for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size + j; k++)
dst[k] = sol((gridsize - 1 + j) * ctx->step[0], k * ctx->step[1]);
}
}
{
MG2DBoundary *bnd = ctx->boundaries[MG2D_BOUNDARY_1L];
bnd->type = MG2D_BC_TYPE_FIXVAL;
memset(bnd->val, 0, gridsize * sizeof(*bnd->val));
for (int j = 1; j < ctx->fd_stencil; j++) {
double *dst = bnd->val + j * bnd->val_stride;
for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size + j; k++)
dst[k] = sol(k * ctx->step[0], -j * ctx->step[1]);
}
}
{
MG2DBoundary *bnd = ctx->boundaries[MG2D_BOUNDARY_1U];
bnd->type = MG2D_BC_TYPE_FIXVAL;
memset(bnd->val, 0, gridsize * sizeof(*bnd->val));
for (int j = 1; j < ctx->fd_stencil; j++) {
double *dst = bnd->val + j * bnd->val_stride;
for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size + j; k++)
dst[k] = sol(k * ctx->step[0], (gridsize - 1 + j) * ctx->step[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);
//memset(ctx->rhs + y * ctx->rhs_stride, 0, sizeof(*ctx->rhs) * ctx->domain_size[0]);
for (size_t x = 0; x < ctx->domain_size; x++) {
const double x_coord = x * ctx->step[0];
ctx->diff_coeffs[MG2D_DIFF_COEFF_02][ctx->diff_coeffs_stride * y + x] = 1.0;
ctx->diff_coeffs[MG2D_DIFF_COEFF_20][ctx->diff_coeffs_stride * y + x] = 1.0;
ctx->diff_coeffs[MG2D_DIFF_COEFF_11][ctx->diff_coeffs_stride * y + x] = 1.0;
//ctx->diff_coeffs[ELL_RELAX_DIFF_COEFF_00][ctx->diff_coeffs_stride * y + x] = 2.0 * M_PI;
ctx->rhs[y * ctx->rhs_stride + x] = sol_dxx(x_coord, y_coord) + sol_dyy(x_coord, y_coord) + sol_dxy(x_coord, y_coord);
}
memset(ctx->diff_coeffs[MG2D_DIFF_COEFF_00] + y * ctx->diff_coeffs_stride, 0,
sizeof(*ctx->diff_coeffs[0]) * ctx->domain_size);
memset(ctx->diff_coeffs[MG2D_DIFF_COEFF_01] + y * ctx->diff_coeffs_stride, 0,
sizeof(*ctx->diff_coeffs[0]) * ctx->domain_size);
memset(ctx->diff_coeffs[MG2D_DIFF_COEFF_10] + y * ctx->diff_coeffs_stride, 0,
sizeof(*ctx->diff_coeffs[0]) * ctx->domain_size);
}
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(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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