[petsc-users] Oscillations in finite difference solution

[Patrick Alken]

On 02/22/2012 05:13 PM, Jed Brown wrote:
> On Wed, Feb 22, 2012 at 18:05, Patrick Alken 
> <patrick.alken at colorado.edu <mailto: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?

Yes I mean the direct solver residual is around 10e-15. The PETSc 
residual is 4e00

>     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?

The PDE is:

grad(f) . B = g

where B is a known vector field, g is a known scalar function, and f is 
the unknown scalar function to be determined (I am discretizing this 
equation for f in spherical coords)

>
>      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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