[petsc-users] CG or GMRES

[Alan]

Thanks, Dr. Knepley,
      Can I treat AMG and MG like this way. To solve problems with 
non-symmetric matrices, MG needs users to provide the coarse mesh 
information. This take more complexity on coding than using AMG; but MG, 
generally, do better job than MG for non-symmetric problems.

Alan

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