[petsc-users] incomplete cholesky with a drop tolerance

[Jed Brown]

On Sun, Jul 22, 2012 at 1:11 PM, Umut Tabak <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?

>
>
>> 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.
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