[petsc-dev] future pull request about multipreconditioned solvers

[Smith, Barry F.]

  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 <petsc-dev at mcs.anl.gov> 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
>