[petsc-users] 2D Poisson on nonuniform meshes

[Matthew Knepley]

On Tue, 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.
>

The point of that scaling is to make the boundary values the same size as
the residuals. If you have
no boundary values, the problem is scale invariant since its linear. It
would be nice to scale it so everything
is about size 1.

When asking about convergence always run with -ksp_view
-ksp_monitor_true_residual -ksp_converged_reason

  Thanks,

     Matt


> Anyone did/knows how to do this properly?
>
>
>
> Thanks,
>
> F
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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