Add test programs for relaxation and full multigrid.

1 files changed, 209 insertions, 0 deletions

diff --git a/relax_test.c b/relax_test.c
new file mode 100644
index 0000000..b750aba
--- /dev/null
+++ b/relax_test.c
@@ -0,0 +1,209 @@
+#include <math.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <stdint.h>
+#include <string.h>
+
+#include "ell_relax.h"
+#include "log.h"
+
+#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
+
+static double findmax(double *arr, size_t len)
+{
+    double ret = 0.0;
+    for (size_t i = 0; i < len; i++) {
+        double val = fabs(*arr++);
+        if (val > ret)
+            ret = val;
+    }
+    return ret;
+}
+
+int main(int argc, char **argv)
+{
+    EllRelaxContext *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_ell_relax_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] = 1.0 / (N - 1.0);
+    ctx->step[1] = 1.0 / (N - 1.0);
+
+    ctx->fd_stencil = 2;
+
+    {
+        EllRelaxBoundary *bnd = &ctx->boundaries[ELL_RELAX_BOUNDARY_0L];
+
+        bnd->type = ELL_RELAX_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;
+
+            for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size[1] + j; k++)
+                dst[k] = sol(-j * ctx->step[0], k * ctx->step[1]);
+        }
+    }
+    {
+        EllRelaxBoundary *bnd = &ctx->boundaries[ELL_RELAX_BOUNDARY_0U];
+
+        bnd->type = ELL_RELAX_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;
+
+            for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size[1] + j; k++)
+                dst[k] = sol((N - 1 + j) * ctx->step[0], k * ctx->step[1]);
+        }
+    }
+    {
+        EllRelaxBoundary *bnd = &ctx->boundaries[ELL_RELAX_BOUNDARY_1L];
+
+        bnd->type = ELL_RELAX_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;
+
+            for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size[0] + j; k++)
+                dst[k] = sol(k * ctx->step[0], -j * ctx->step[1]);
+        }
+    }
+    {
+        EllRelaxBoundary *bnd = &ctx->boundaries[ELL_RELAX_BOUNDARY_1U];
+
+        bnd->type = ELL_RELAX_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;
+
+            for (ptrdiff_t k = -j; k < (ptrdiff_t)ctx->domain_size[0] + j; k++)
+                dst[k] = sol(k * ctx->step[0], (N - 1 + j) * ctx->step[1]);
+        }
+    }
+
+    for (size_t y = 0; y < ctx->domain_size[1]; y++) {
+        const double y_coord = y * ctx->step[1];
+
+        memset(ctx->u + y * ctx->u_stride, 0, sizeof(*ctx->u) * ctx->domain_size[0]);
+
+        for (size_t x = 0; x < ctx->domain_size[0]; x++) {
+            const double x_coord = x * ctx->step[0];
+
+            ctx->diff_coeffs[ELL_RELAX_DIFF_COEFF_02][ctx->diff_coeffs_stride * y + x] = 1.0;
+            ctx->diff_coeffs[ELL_RELAX_DIFF_COEFF_20][ctx->diff_coeffs_stride * y + x] = 1.0;
+            ctx->diff_coeffs[ELL_RELAX_DIFF_COEFF_11][ctx->diff_coeffs_stride * y + x] = 1.0;
+
+            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[ELL_RELAX_DIFF_COEFF_00] + y * ctx->diff_coeffs_stride, 0,
+               sizeof(*ctx->diff_coeffs[0]) * ctx->domain_size[0]);
+        memset(ctx->diff_coeffs[ELL_RELAX_DIFF_COEFF_01] + y * ctx->diff_coeffs_stride, 0,
+               sizeof(*ctx->diff_coeffs[0]) * ctx->domain_size[0]);
+        memset(ctx->diff_coeffs[ELL_RELAX_DIFF_COEFF_10] + y * ctx->diff_coeffs_stride, 0,
+               sizeof(*ctx->diff_coeffs[0]) * ctx->domain_size[0]);
+    }
+
+    ret = mg2di_ell_relax_init(ctx);
+    if (ret < 0) {
+        fprintf(stderr, "Error initializing the solver context: %d\n", ret);
+        ret = 1;
+        goto fail;
+    }
+
+    res_old = findmax(ctx->residual, ctx->residual_stride * ctx->domain_size[1]);
+
+    for (int i = 0; i < maxiter; i++) {
+        ret = mg2di_ell_relax_step(ctx);
+        if (ret < 0) {
+            fprintf(stderr, "Error during relaxation\n");
+            ret = 1;
+            goto fail;
+        }
+        res_new = findmax(ctx->residual, ctx->residual_stride * ctx->domain_size[1]);
+        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[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);
+    }
+
+fail:
+    mg2di_ell_relax_free(&ctx);
+    return ret;
+}