[petsc-users] Oscillations in finite difference solution

[Patrick Alken]

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, 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)

   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