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| // Poisson equation with variable coefficients
#include "utils.h"
#include "poisson.h"
scalar a[], b[], res[], dp[];
face vector c[];
double solution (double x, double y)
{
return sin(3.*pi*x)*sin(3.*pi*y);
}
/* Dirichlet condition on all boundaries */
a[right] = dirichlet (solution(x, y));
a[left] = dirichlet (solution(x, y));
a[top] = dirichlet (solution(x, y));
a[bottom] = dirichlet (solution(x, y));
/* homogeneous conditions for dp */
dp[right] = dirichlet(0);
dp[left] = dirichlet(0);
dp[top] = dirichlet(0);
dp[bottom] = dirichlet(0);
int main (int argc, char ** argv)
{
size (1. [0]);
origin (-0.5, -0.5);
int depth = argc < 2 ? 9 : atoi(argv[1]), nrelax = 4;
init_grid(1 << depth);
foreach() {
b[] = -18.*sq(pi)*sin(3.*pi*x)*sin(3.*pi*y)*(x + y + 2.) +
3.*pi*cos(3.*pi*x)*sin(3.*pi*y) +
3.*pi*sin(3.*pi*x)*cos(3.*pi*y);
a[] = 0.;
}
foreach_face()
c.x[] = x + y + 2.;
restriction ((scalar *){c});
const scalar lambda[] = 0.;
struct Poisson p;
p.a = a; p.b = b; p.alpha = c; p.lambda = lambda;
#define NITER 13
clock_t start = clock(), iter[NITER];
double maxres[NITER];
scalar * lres = {res};
residual ({a}, {b}, lres, &p);
for (int i = 0; i < NITER; i++) {
mg_cycle ({a}, lres, {dp}, relax, &p, nrelax, 0, depth());
residual ({a}, {b}, lres, &p);
double max = 0.;
foreach(reduction(max:max))
if (fabs(res[]) > max)
max = fabs(res[]);
iter[i] = clock();
maxres[i] = max;
}
for (int i = 0; i < NITER; i++) {
fprintf (stderr, "%d %.2g\n", i, maxres[i]);
printf ("%d %g %g\n", i, (iter[i] - start)/(double)CLOCKS_PER_SEC,
maxres[i]);
}
double max = 0;
foreach(reduction(max:max)) {
double e = a[] - solution(x, y);
if (fabs(e) > max) max = fabs(e);
// printf ("%g %g %g %g %g %g\n", x, y, a[], b[], res[], e);
}
fprintf (stderr, "# max error %g\n", max);
}
|
