[petsc-users] GMRES with matrix-free method and preconditioning matrix for higher performance.

[Choi Kyungjun]

Dear Petsc.

I am implementing Petsc library for my CFD flow code.

Thanks to Matt, I got what I wanted last week.

It was the GMRES with matrix-free method, no preconditioning matrix and
command line options are below.

*-snes_mf    -pc_type none    -..monitor   -..converged_reason*

The solve worked, but performed very poorly.


I learned that the efficiency of Krylov-subspace methods depends strongly
depends on a good preconditioner.

And in the Petsc manual, the matrix-free method is allowed only with no
preconditioning, a user-provided preconditioner matrix, or a user-provided
preconditioner shell.


Here are my questions.

1) To improve the solver performance using GMRES, is there any way using
snes_mf without preconditioning matrix?

2) For user-provided preconditioner matrix, I saw some example codes that
provide approx. Jacobian matrix as preconditioner matrix. But this means
that I should derive approx. Jacobian mat for system, am I right?

3) I'd like to know which is the fastest way to solve with GMRES method.
Could you tell me or let me know any other examples?

Thank you very much for your help.

Sincerely,

Kyungjun.
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