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 > > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120222/0be21e08/attachment.htm>
