// This function only works for max. compact 9-point stencils
NumericArray DendyInterpolation::prolongate(
const NumericArray& u,
const Stencil& stencil,
const Index nx,
const Index ny) const
{
const Index nxNew=2*nx;
const Index nyNew=2*ny;
NumericArray result((nxNew+1)*(nyNew+1));
NumericArray stencilL;
Precision scale=0;
Precision weight1=0;
Precision weight2=0;
Precision erg=0;
// linear interpolation on the borders
for (Index sy=0; sy<=ny; sy++)
{
result[2*sy*(nxNew+1)]=u[sy*(nx+1)];
result[2*sy*(nxNew+1)+2*nx]=u[sy*(nx+1)+nx];
}
for (Index sx=0; sx<=nx; sx++)
{
result[2*sx]=u[sx];
result[2*ny*(nxNew+1)+2*sx]=u[ny*(nx+1)+sx];
}
for (Index sy=0; sy<=ny-1; sy++)
{
result[(2*sy+1)*(nxNew+1)] = 0.5 * (result[2*sy*(nxNew+1)] + result[2*(sy+1)*(nxNew+1)]);
result[(2*sy+1)*(nxNew+1)+2*nx] = 0.5 * (result[2*sy*(nxNew+1)+2*nx] + result[2*(sy+1)*(nxNew+1)+2*nx]);
}
for (Index sx=0; sx<=nx-1; sx++)
{
result[2*sx+1] = 0.5 * (result[2*sx] + result[2*sx+2]);
result[2*ny*(nxNew+1)+2*sx+1] = 0.5 * (result[2*ny*(nxNew+1)+2*sx] + result[2*ny*(nxNew+1)+2*sx+2]);
}
//copy coarse grid points
for (Index sy=1; sy<=ny-1; sy++)
for (Index sx=1; sx<=nx-1; sx++)
result[2*sy*(nxNew+1)+2*sx]=u[sy*(nx+1)+sx];
stencilL.resize( stencil.getLInSize(C,2,1,nxNew,nyNew, 1).size());
//interpolation of fine grid points on coarse grid lines
for (Index sy=2; sy<=nyNew-2; sy+=2)
for (Index sx=1; sx<=nxNew-1; sx+=2)
{
stencilL=stencil.getLInSize(C,sx,sy,nxNew,nyNew, 1);
scale=0;
scale-=stencilL[C];
scale-=stencilL[S];
scale-=stencilL[N];
weight1=0;
weight1+=stencilL[W];
weight1+=stencilL[SW];
weight1+=stencilL[NW];
weight2=0;
weight2+=stencilL[E];
weight2+=stencilL[SE];
weight2+=stencilL[NE];
result[sy*(nxNew+1)+sx]=
( weight1*result[sy*(nxNew+1)+sx-1]
+weight2*result[sy*(nxNew+1)+sx+1]
)/scale;
}
//interpolation of fine grid points on fine grid lines and coarse grid columns
for (Index sy=1; sy<=nyNew-1; sy+=2)
for (Index sx=2; sx<=nxNew-2; sx+=2)
{
stencilL=stencil.getLInSize(C,sx,sy,nxNew,nyNew,1);
scale=0;
scale-=stencilL[C];
scale-=stencilL[W];
scale-=stencilL[E];
weight1=0;
weight1+=stencilL[S];
weight1+=stencilL[SW];
weight1+=stencilL[SE];
weight2=0;
weight2+=stencilL[N];
weight2+=stencilL[NW];
weight2+=stencilL[NE];
result[sy*(nxNew+1)+sx]=
( weight1*result[(sy-1)*(nxNew+1)+sx]
+weight2*result[(sy+1)*(nxNew+1)+sx]
)/scale;
}
//interpolation of fine grid points on fine grid lines and fine grid columns
for (Index sy=1; sy<=nyNew-1; sy+=2)
for (Index sx=1; sx<=nxNew-1; sx+=2)
{
stencilL=stencil.getLInSize(C,sx,sy,nxNew,nyNew,1);
erg=0;
scale=-stencilL[0];
erg+=stencilL[W] *result[ sy *(nxNew+1)+sx-1];
erg+=stencilL[E] *result[ sy *(nxNew+1)+sx+1];
erg+=stencilL[S] *result[(sy-1)*(nxNew+1)+sx ];
erg+=stencilL[SW]*result[(sy-1)*(nxNew+1)+sx-1];
erg+=stencilL[SE]*result[(sy-1)*(nxNew+1)+sx+1];
erg+=stencilL[N] *result[(sy+1)*(nxNew+1)+sx ];
erg+=stencilL[NW]*result[(sy+1)*(nxNew+1)+sx-1];
erg+=stencilL[NE]*result[(sy+1)*(nxNew+1)+sx+1];
result[sy*(nxNew+1)+sx]=erg/scale;
}
return result;
}
