[petsc-users] Oscillations in finite difference solution

[Jed Brown]

On Wed, Feb 22, 2012 at 18:05, Patrick Alken <patrick.alken at colorado.edu>wrote:

> Hi all,
>
>  I have been trying to track down a problem for a few days with solving a
> linear system arising from a finite differenced PDE in spherical
> coordinates. I found that PETSc managed to converge to a nice solution for
> my matrix at small grid sizes and everything looks pretty good.
>
>  But when I try larger more realistic grid sizes, PETSc fails to converge.
> After trying with another direct solver library, I found that the direct
> solver found a solution which exactly solves the matrix equation,


This never happens, so what do you mean? You compute the residual and it's
similar to what you expect the rounding error to be?


> but when plotting the solution, I see that it oscillates rapidly between
> the grid points and therefore isn't a satisfactory solution. (At smaller
> grids the solution is nice and smooth)
>

What sort of PDE are you solving?


>
>  I was wondering if this phenomenon is common in PDEs? and if there is any
> way to correct for it?
>
>  I am currently using 2nd order centered differences for interior grid
> points, and 1st order forward/backward differences for edge points. Would
> it be worthwhile to try moving to 4th order differences instead? Or would
> that make the problem worse?
>
>  I've even tried smoothing the parameters which go into the matrix entries
> using moving averages...which doesn't seem to help too much.
>
>  Any advice from those who have experience with this phenomenon would be
> greatly appreciated!
>
> Thanks,
> Patrick
>
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