Pierre, Thanks for your generous offer. Maybe you could point us to a repository with the branch with your additions so we could take a look at it and see how it could be adopted into PETSc?
Barry > On Jun 7, 2019, at 11:07 AM, Pierre Gosselet via petsc-dev > <[email protected]> wrote: > > Dear Petsc developers, > > I am Pierre Gosselet, researcher in computational mechanics from France > (ENS Paris Saclay / Univ. Lille). Lately I have been working on > multipreconditioned solvers arising from domain decomposition (DD). I have > co-authored some papers with Nicole Spillane whom you probably know. > > Together with Nicolas Tardieu from EDF we have done some developments > in PetSc and we would be happy to share them. Nicolas told me I had better > send you a short notice before making a pull request. > > We have implemented a MultiPreconditioned Conjugate Gradients solver > for the SPD case and a MultiPreconditioned Orthomin solver for general > matrices. > > These solvers rely on a method with signature > PCApplyMultiPrecond(PC, Vec in, Mat out) > We proposed an implementation of this method in the (Restrictive) > Additive Schwarz (R)ASM framework: PCApplyMultiPrecond_ASM(...). > When preconditioning, each subdomain provides a column which is used to > expand the search space. There is an experimental use of the > information in NearNullSpace in order to speed up the convergence (ersatz of > Nicholaides' two-level (R)ASM). > > In practice, there are new files for the solvers (mpcg.c and mpomin.c), > some features were added in asm.c, and there are few lines added > in other files in order to declare the solvers. We tried to make a > nice implementation and integration, but we would be happy to have our > code reviewed for better performance. > > > Unfortunately, from the very limited numerical experiments that we have > conducted, we do not have tremendous examples to show, the extra costs > associated with multipreconditioning are not always compensated by the > improved convergence. In fact, it appears that multipreconditioned > solvers do not behave as well in the (R)ASM framework as in other DD > frameworks, like FETI(DP) or BDD(C), where the spectrum has a more > favorable shape and where adaptive strategies are available. > > Anyhow our developments offer opportunities to test mpcg and mpomin, to > implement new multipreconditioned solvers and new multipreconditioning > frameworks (one just need to implement PCApplyMultiPrecond_???). > > I hope you will be interested by these developments, > best regards > pierre > > > -- > Pierre Gosselet > CR CNRS (research agent) > LMT -- ENS Paris-Saclay/UMR8535 > 61 av. du président Wilson, 94235 CACHAN > tel: +33 1 47405333 >
