[petsc-dev] Contribution proposal about the application of PCShell as left and right preconditioner

[Sylvain Mercier]

Dear PETSc team,

During my phd thesis, I have worked on solving sequences of linear
systems with slowly varying matrices using GMRES(restart). In
particular, I have developed a preconditioning technique to improve
the action of an existing "first-level preconditioner". This new
method is usually applied as right preconditioner with a PCShell, although
the first preconditioner is applied on the left.

That is why I have developed routines in PETSc to be able to apply
simultaneously a left and a right PCShells when we use a PC_SYMMETRIC
PCSIDE. In fact, I have add two routines: PCShellSetApplySymmetricLeft and
PCShellSetApplySymmetricRight (similarly to the routine PCShellSetApply).

Moreover, I have added the possibility to use a PC_SYMMETRIC preconditioner
within GMRES.

I gently request your position on the integration of these developments in
PETSc. I have some problems to provide a pull-request via a fork so I
propose a patch. Let me know if you want extra integration work.

Best regards,
Sylvain.
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