refine3D.c

Test for refinement in 3D

set logscale x 2
set logscale y
set grid
set xr [17:1000]
set xlabel 'N'
set ylabel 'L_1 error'
set key box bottom left
set size square
plot 'out' u 1:2 t '1^3 stencil', '' u 1:4 t '2^3 stencil',\
 '' u 1:6 t '3^3 stencil', '' u 1:8 t '4^3 stencil', '' u 1:10 t '5^3 stencil',\
0.1*x**-1 lw 2  t'1st order', 5e3*x**-5 lw 2 t '5th order'

Average error (script)

set logscale x 2
set logscale y
set grid
set xr [ 17:1000]
set xlabel 'N'
set ylabel 'L_{\inf} error'
set key box bottom left
set size square
plot 'out' u 1:3 t '1^3 stencil', '' u 1:5 t '2^3 stencil',\
 '' u 1:7 t '3^3 stencil', '' u 1:9 t '4^3 stencil', '' u 1:11 t '5^3 stencil',\
10*x**-1 lw 2  t'1st order', 1e6*x**-5 lw 2 t '5th order'

Max. error (script)

#include "grid/multigrid3D.h"
#include "higher-order.h"
#include "utils.h"

scalar s[], w[];
int main () {
  L0 = 10;
  X0 = Y0 = Z0 = -L0/2.;
  for (int l = 4; l < 10 ; l++) {
    init_grid (1 << l);
    foreach()
      s[] = exp (-(sq(x) + sq(y) + sq(z)));
    boundary ({s});
    
    printf ("%d ", N);
    
    s.prolongation = refine_1st;
    wavelet (s, w);
    norm f = normf (w);
    printf ("%g %g ", f.avg, f.max);
    
    s.prolongation = refine_2nd;
    wavelet (s, w);
    f = normf (w);
    printf ("%g %g ", f.avg, f.max);
    
    s.prolongation = refine_3rd;
    wavelet (s, w);
    f = normf (w);
    printf ("%g %g ", f.avg, f.max);
   
    s.prolongation = refine_4th;
    wavelet (s, w);
    f = normf (w);
    printf ("%g %g ", f.avg, f.max);
   
    s.prolongation = refine_5th;
    wavelet (s, w);
    f = normf (w);
    printf ("%g %g\n", f.avg, f.max);

    fflush (stdout);
  }
}

sandbox/Antoonvh/refine3D.c

Test for refinement in 3D