[petsc-users] Convergence on Axisymmetric Poisson matrix

[Barry Smith]

   Are you running with -ksp_monitor_true_residual to track the b - A*x residual instead of just the preconditioned residual? 

   GAMG definitely does not symmetrize the system but it is possible the preconditioner results in the solve "not seeing" the unsymmetry during the solution process and hence CG still converging; it would be dangerous to rely on this in general I think. You could also run this case with GMRES to see if that is better than the CG iterations.

   Barry

> On Oct 24, 2021, at 7:00 PM, Lionel CHENG <cheng at cerfacs.fr> wrote:
> 
> Hello everyone,
> 
> I have some questions regarding a linear system that I am solving in my plasma simulations. We have in this case a strongly non-symmetric matrix due to the cylindrical coordinates for which the Laplacian cell is given by Fig. 2 for two kinds of triangles. The different unstructured grids have from 300 000 nodes to 7 000 000 nodes.
> 
> To my understanding, CG should not work properly on this matrix but BiCGStab(1) should. When using SOR preconditioner it is indeed the case: -ksp_type cg -pc_type sor yields solutions in 10 to 20 times more iterations than -ksp_type bcgs -pc_type sor.
> 
> However, when switching to -ksp_type cg -pc_type gamg the convergence is great and even slightly better than -ksp_type bcgs. I do not understand how CG is able to make the system converge when using GAMG although the matrix is non-symmetric ? Is GAMG able to somehow symmetrize the system? I have the impression that when using -pc_type gamg the Krylov solver is actually the Pre-relaxation and post-relaxation of the initial grid, is that right?
> 
> For GAMG since the matrix is non-symmetric -mg_levels_pc_type sor for and -mg_levels_ksp_type richardson have been used and yields better results than the original chebychev solver.
> 
> Sincerely yours,
> 
> Lionel Cheng
> <main.pdf>

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