[petsc-users] Multigrid with PML

[Barry Smith]

   This is a very difficult problem. I am not surprised that GAMG performs poorly, I would be surprised if it performed well at all.

   I think you need to do some googling of   "helmholtz PML linear system solve" to find what other people have used. The first hit I got was this http://www.math.tau.ac.il/services/phd/dissertations/Singer_Ido.pdf and every iterative method he tried ended up requiring MANY iterations with refinement. This is 14 years old so there will be better suggestions out there. One that caught my eye was http://www.sciencedirect.com/science/article/pii/S0022247X11005063


  Barry

Just looking at the matrix makes it clear to me that conventional iterative methods are not going to work well, many of the diagonal entries are zero and even in rows with a diagonal entry it is much smaller in magnitude than the diagonal entries. 

> On Jul 13, 2016, at 2:30 PM, Safin, Artur <aks084000 at utdallas.edu> wrote:
> 
> Dear PETSc community,
> 
> I am working on solving a Helmholtz problem with PML. The issue is that I am finding it very hard to deal with the resulting matrix system; I can get the correct solution for coarse meshes, but it takes roughly 2-4 times as long to converge for each successively refined mesh. I've noticed that without PML, I do not have problems with convergence speed.
> 
> I am using the GMRES solver with GAMG as the preconditioner (with block-Jacobi preconditioner for the multigrid solves). I have also tried to assemble a separate preconditioning matrix with the complex shift 1+0.5i, that does not seem to improve the results. Currently I am running with
> 
>    -ksp_type fgmres \
>    -pc_type gamg \
>    -mg_levels_pc_type bjacobi \
>    -pc_mg_type full \
>    -ksp_gmres_restart 150 \
> 
> Can anyone suggest some way of speeding up the convergence? Any help would be appreciated. I am attaching the output from kspview.
> 
> Best,
> 
> Artur
> 
> <kspview>