[petsc-users] CG or GMRES

[Matthew Knepley]

On Fri, May 10, 2013 at 8:15 AM, Alan <zhenglun.wei at gmail.com> wrote:

> Thank you so much, Dr. Brown.
> I have a minor question on the 'gamg'. As you said, 'gamg' works for
> many moderately non-symmetric problems. Does this apply for general
> algebraic MG preconditioner or just 'gamg' in PETSc. As you know, does
> 'BoomerAMG' suffer from the non-symmetric matrices problem? Should we
> only use regular MG as the preconditioner for highly non-symmetric
> problems?
>

There is nothing that prevents AMG from working on non-symmetric matrices
(unlike CG),
but there are no guarantees that it will do a good job.

   Matt


> thanks,
> Alan
>
> > "Zhenglun (Alan) Wei" <zhenglun.wei at gmail.com> writes:
> >
> >> Dear folks,
> >> I hope you're having a nice day.
> >> For the Poisson solver in /src/ksp/ksp/example/tutorial/ex45.c, I used
> >> the ksp_type = CG to solve it before; it converges very fast with
> >> pc_type = gamg. However, I was trying to check if the matrix generated
> >> by the 'ComputeMatrix' is symmetric by using "ierr = MatIsSymmetric(B,
> >> tol, &flg);". It shows that this matrix is not exact a symmetric one by
> >> setting tol = 0.0. Yet, the matrix is 'symmetric' if the tol > 0.01.
> > The matrix does not enforce boundary conditions symmetrically.
> >
> >> Does this mean that, even if the matrix is not exact symmetric, the CG
> >> could still be used.
> > You happen to be iterating in a "benign" space in which the operator is
> SPD.
> >
> >> This brings me a question. Can the CG be used to solve an actual
> >> unsymmetric matrix as long as 'MatIsSymmetric' returns a 'PETSC_TRUE'
> >> value with certain tolerance.
> > No.
> >
> >> Is there any rule of thumb for this tolerence?  Also, as a
> >> preconditioner, does 'gamg' only work for symmetric positive-definite
> >> matrix? or it works for any matrix or even with GMRES?
> > It works for many moderately non-symmetric, certainly for something that
> only
> > has non-symmetric boundary conditions.
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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