[petsc-users] 2D Poisson on nonuniform meshes

[Barry Smith]

   You need to get the nonuniform finite difference stencil right and the refinement right and the interpolation right. For example when you refine are you putting the new grid points 1/2 way between the coarser 2 or defined by the "grading" of the coarse mesh.  I recommend doing the problem with 1d to understand exactly what you are doing, get it working there. Once you understand it doing 2 or 3d is easy.

  Barry



> On Sep 1, 2015, at 2:22 AM, Filippo Leonardi <filippo.leonardi at sam.math.ethz.ch> wrote:
> 
> Dear PETSc Users,
>  
> I want to use multigrid to solve uniform (just Laplace) poisson in 2D/3D on cartesian, non-uniform meshes with a standard 5 (7)-points stencil FD.
>  
> I always scaled my Poisson matrix like in the doc examples, i.e. multiplying by dx*dy (so that in ComputeRHS I need to scale b, in A*x = b, as well). This always worked properly with both MG/GAMG and with galerkin matrices.
>  
> Now I'd like to use non-uniform meshes, therefore the scaling is non-uniform. However I cannot get my matrices to scale properly with any sort of multigrid.
>  
> One would think that without scaling, i.e. solving the original system, at least MG+galerkin or GAMG should work anyways provided the matrix A and b are consistent.
>  
> I tried without boundaries (i.e. torus), so this is not the problem.
>  
> Anyone did/knows how to do this properly?
>  
> Thanks,
> F