[petsc-users] 2D Poisson on nonuniform meshes

[Filippo Leonardi]

Thanks Matt,

I use the "natural scaling"  of the Laplacian Lapl * x  = b. The grid is *still* uniform.

I give you a couple of results:

1 ) This is e.g. gmres + gamg + 4 levels. As you can see it converges after 2 iterations which is 
totally strange. The solution is incorrect.

2 ) This is mg + galerkin matrices + levels. Result is incorrect

3 ) Default: works fine

4) LU: works fine

I remove the constant nullspace as usual.

I use the usual setcomputeoperator business and compute rhs.

Instead, if I scale to Lapl * dx * dy * x = b * dx * dy (things work fine also with MG). This is fine 
with uniform grid but  I do not know how to do that properly on nonuniform.

Let me know if you need code pieces or other details.

1)

 0 KSP Residual norm 1.793027353791e-05  


2)

 0 KSP Residual norm 1.010294060491e-05  


0 KSP Residual norm 2.990548680394e-08  


Linear solve converged due to CONVERGED_ITS iterations 1 


On Tuesday 01 September 2015 03:40:14 Matthew Knepley wrote:
> 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

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