See https://doc.comsol.com/5.5/doc/com.comsol.help.comsol/comsol_ref_solver.27.1... The Iterative Solvers - COMSOL Multiphysics<https://doc.comsol.com/5.5/doc/com.comsol.help.comsol/comsol_ref_solver.27.123.html> The relaxation factor ω to some extent controls the stability and convergence properties of a numerical solver by shifting its eigenvalue spectrum. The optimal value for the relaxation factor can improve convergence significantly — for example, for SOR when used as a solver. However, the optimal choice is typically a subtle task with arbitrary complexity. doc.comsol.com We use BCGS for constant memory while gmres without restart requires increased memory but has predictable convergence than BCGS. Hong ________________________________ From: petsc-users <[email protected]> on behalf of Jed Brown <[email protected]> Sent: Wednesday, September 29, 2021 5:28 PM To: Marco Cisternino <[email protected]>; [email protected] <[email protected]> Subject: Re: [petsc-users] FGMRES and BCGS It is not surprising. BCGS uses less memory for the Krylov vectors, but that might be a small fraction of the total memory used (considering your matrix and GAMG). FGMRES(30) needs 60 work vectors (2 per iteration). If you're using a linear (non-iterative) preconditioner, then you don't need a flexible method -- plain GMRES should be fine. FGMRES uses the unpreconditioned norm, which you can also get via -ksp_type gmres -ksp_norm_type unpreconditioned. This classic paper shows that for any class of nonsymmetric Krylov method, there are matrices in which that method outperforms every other method by at least sqrt(N). https://epubs.siam.org/doi/10.1137/0613049 Marco Cisternino <[email protected]> writes:
Good Morning, I usually solve a non-symmetric discretization of the Poisson equation using GAMG+FGMRES. In the last days I tried to use BCGS in place of FGMRES, still using GAMG as preconditioner. No problem in finding the solution but I'm experiencing something I didn't expect. The test case is a 25 millions cells domain with Dirichlet and Neumann boundary conditions. Both the solvers are able to solve the problem with an increasing number of MPI processes, but:
* FGMRES is about 25% faster than BCGS for all the processes number * Both solvers have the same scalability from 48 to 384 processes * Both solvers almost use the same amount of memory (FGMRES use a restart=30) Am I wrong expecting less memory consumption and more performance from BCGS with respect to FGMRES? Thank you in advance for any help.
Best regards, Marco Cisternino