On 07/22/2012 08:17 PM, Jed Brown wrote: > On Sun, Jul 22, 2012 at 1:11 PM, Umut Tabak <u.tabak at tudelft.nl > <mailto:u.tabak at tudelft.nl>> wrote: > > Well, basically, I am not interested in time domain response. What > I would like to do is to find the eigenvalues/vectors of the > system so it is in the frequency domain. What I was doing it > generally is the fact that I first factorize the operator matrix > with the normal factorization operation and use it to do multiple > solves in my Block Lanczos eigenvalue solver. Then in my > performance evaluations I saw that this is the point that I should > make faster, then I realized that I could solve this particular > system, that is pinned in your words, faster with iterative > methods almost %20 percent faster. And this is the reason why I am > trying to dig under. > > > How many grid points per wavelength? I am not sure at the moment I should check it further but the mesh is fine enough that this should not be a problem in the frequency range of interest. > >> basically the operator is singular however for my problem I >> can delete one of the rows of the matrix, for this case, I >> and get a non-singular operator that I can continue my >> operations, basically, I am getting a matrix with size n-1, >> where original problem size is n. >> >> >> This is often bad for iterative solvers. See the User's Manual >> section on solving singular systems. What is the condition number >> of the original operator minus the zero eigenvalue (instead of >> "pinning" on point)? > This is not clear to me... You mean something like projecting the > original operator on the on the zero eigenvector, some kind of a > deflation. > > > See the User's Manual section. As long as the preconditioner is > stable, convergence is as good as for the nonsingular problem by > removing the null space on each iteration. Ok I will see that part, Thx. U.
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