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 -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20130510/f86a3f91/attachment.html>
