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#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>
#include <string.h>
#include <mpi.h>
#include <ndarray.h>
#include "components.h"
#include "ell_grid_solve.h"
#include "log.h"
#include "mg2d_boundary.h"
#include "mg2d_constants.h"
#define DOMAIN_SIZE 1.0
#define FD_STENCIL 2
#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;
DomainGeometry *dg = NULL;
DomainComponent *dc = NULL;
long int log2N, log2maxiter;
long int N, maxiter;
double res_old, res_new;
int ret = 0;
char processor_name[MPI_MAX_PROCESSOR_NAME];
int nb_processes, rank, processor_name_len;
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;
MPI_Init(NULL, NULL);
MPI_Comm_size(MPI_COMM_WORLD, &nb_processes);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
MPI_Get_processor_name(processor_name, &processor_name_len);
fprintf(stderr, "This is process %d out of %d, running on %s\n",
rank, nb_processes, processor_name);
dg = mg2di_dg_alloc(nb_processes);
if (!dg) {
fprintf(stderr, "Error allocating domain geometry\n");
ret = 1;
goto fail;
}
dg->domain_size[0] = N;
dg->domain_size[1] = N;
for (unsigned int i = 0; i < dg->nb_components; i++) {
size_t patch_start, patch_end, patch_size_y;
patch_size_y = (N + nb_processes - 1) / nb_processes;
patch_start = i * patch_size_y;
patch_end = MIN((i + 1) * patch_size_y, N);
patch_size_y = patch_end - patch_start;
if (patch_size_y <= 0) {
fprintf(stderr, "Too many processes for grid size %ld: %d\n", N, nb_processes);
ret = 1;
goto fail;
}
dg->components[i].interior.start[0] = 0;
dg->components[i].interior.start[1] = patch_start;
dg->components[i].interior.size[0] = N;
dg->components[i].interior.size[1] = patch_size_y;
dg->components[i].exterior.start[0] = -FD_STENCIL_MAX;
dg->components[i].exterior.start[1] = i ? patch_start : -FD_STENCIL_MAX;
dg->components[i].exterior.size[0] = N + 2 * FD_STENCIL_MAX;
dg->components[i].exterior.size[1] = patch_size_y + ((i == 0) * FD_STENCIL_MAX) + ((i == nb_processes - 1) * FD_STENCIL_MAX);
dg->components[i].bnd_is_outer[MG2D_BOUNDARY_0L] = 1;
dg->components[i].bnd_is_outer[MG2D_BOUNDARY_0U] = 1;
dg->components[i].bnd_is_outer[MG2D_BOUNDARY_1L] = i == 0;
dg->components[i].bnd_is_outer[MG2D_BOUNDARY_1U] = i == nb_processes - 1;
}
dc = &dg->components[rank];
ctx = mg2di_egs_alloc_mpi(MPI_COMM_WORLD, dg);
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 = FD_STENCIL;
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];
if (!dc->bnd_is_outer[bnd_loc])
continue;
bnd->type = MG2D_BC_TYPE_FIXVAL;
memset(bnd->val, 0, ctx->domain_size[!ci] * 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 < (ptrdiff_t)ctx->domain_size[!ci] + j; k++) {
coord[!ci] = (k + dc->interior.start[!ci]) * 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 + dc->interior.start[1]) * ctx->step[1];
memset(NDA_PTR2D(ctx->u, 0, y), 0, sizeof(*ctx->u->data) * ctx->domain_size[0]);
for (size_t x = 1; 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 (rank == 0) {
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 + dc->interior.start[1]) * 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;
}
}
MPI_Reduce(rank ? &max_err : MPI_IN_PLACE, &max_err, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
if (rank == 0)
fprintf(stderr, "max(|solution - exact|): %g\n", max_err);
}
fail:
mg2di_egs_free(&ctx);
mg2di_dg_free(&dg);
MPI_Finalize();
return ret;
}
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