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#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include <ndarray.h>
#include "ell_grid_solve.h"
#include "log.h"
#include "mg2d_boundary.h"
#include "mg2d_constants.h"
#define ARRAY_ELEMS(x) (sizeof(x) / sizeof(*x))
#define DOMAIN_SIZE 1.0
#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)
{
EGSContext *ctx;
long int log2N, log2maxiter;
long int N, maxiter;
double res_old, res_new;
int ret = 0;
if (argc < 3) {
fprintf(stderr, "Usage: %s <log2 N> <log2 maxiter>\n", argv[0]);
return 1;
}
log2N = strtol(argv[1], NULL, 0);
log2maxiter = strtol(argv[2], NULL, 0);
if (log2N <= 0 || log2maxiter < 0 ||
log2N >= sizeof(N) * 8 || log2maxiter >= sizeof(maxiter) * 8) {
fprintf(stderr, "Invalid log2N/log2maxiter values: %ld/%ld\n",
log2N, log2maxiter);
return 1;
}
N = (1L << log2N) + 1;
maxiter = 1L << log2maxiter;
ctx = mg2di_egs_alloc((size_t [2]){N, N});
if (!ctx) {
fprintf(stderr, "Error allocating the solver context\n");
return 1;
}
ctx->logger.log = mg2di_log_default_callback;
ctx->step[0] = DOMAIN_SIZE / (N - 1.0);
ctx->step[1] = DOMAIN_SIZE / (N - 1.0);
ctx->fd_stencil = 2;
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 = MG2D_BC_TYPE_FIXVAL;
memset(bnd->val, 0, N * sizeof(*bnd->val));
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 < N + j; k++) {
coord[!ci] = k * ctx->step[!ci];
dst[k] = sol(coord[0], coord[1]);
}
}
}
for (size_t y = 0; y < ctx->domain_size[1]; y++) {
const double y_coord = y * ctx->step[1];
memset(NDA_PTR2D(ctx->u, 0, y), 0, sizeof(*ctx->u->data) * ctx->domain_size[0]);
for (size_t x = 0; x < ctx->domain_size[0]; x++) {
const double x_coord = x * ctx->step[0];
*NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_02], x, y) = 1.0;
*NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_20], x, y) = 1.0;
*NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_11], x, y) = 1.0;
*NDA_PTR2D(ctx->rhs, x, y) = sol_dxx(x_coord, y_coord) + sol_dyy(x_coord, y_coord) + sol_dxy(x_coord, y_coord);
}
memset(NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_00], 0, y), 0,
sizeof(*ctx->diff_coeffs[0]->data) * ctx->domain_size[0]);
memset(NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_01], 0, y), 0,
sizeof(*ctx->diff_coeffs[0]->data) * ctx->domain_size[0]);
memset(NDA_PTR2D(ctx->diff_coeffs[MG2D_DIFF_COEFF_10], 0, y), 0,
sizeof(*ctx->diff_coeffs[0]->data) * ctx->domain_size[0]);
}
ret = mg2di_egs_init(ctx, 0);
if (ret < 0) {
fprintf(stderr, "Error initializing the solver context: %d\n", ret);
ret = 1;
goto fail;
}
res_old = ctx->residual_max;
for (int i = 0; i < maxiter; i++) {
ret = mg2di_egs_solve(ctx, EGS_SOLVE_RELAXATION, 0);
if (ret < 0) {
fprintf(stderr, "Error during relaxation\n");
ret = 1;
goto fail;
}
res_new = ctx->residual_max;
if (res_new > 1e3) {
fprintf(stderr, "Diverged at step %d: %g -> %g\n", i, res_old, res_new);
goto fail;
}
fprintf(stderr, "Step %d: %g -> %g (%g)\n", i, res_old, res_new, res_old / res_new);
res_old = res_new;
}
{
double max_err = 0.0;
for (size_t y = 0; y < ctx->domain_size[1]; y++) {
const double y_coord = y * ctx->step[1];
for (size_t x = 0; x < ctx->domain_size[0]; x++) {
const double x_coord = x * ctx->step[0];
double err = fabs(ctx->u->data[y * ctx->u->stride[0] + x] - sol(x_coord, y_coord));
if (err > max_err)
max_err = err;
}
}
fprintf(stderr, "max(|solution - exact|): %g\n", max_err);
}
fail:
mg2di_egs_free(&ctx);
return ret;
}
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