# [petsc-users] incomplete cholesky with a drop tolerance

Umut Tabak u.tabak at tudelft.nl
Sun Jul 22 13:11:32 CDT 2012

```On 07/22/2012 05:28 PM, Jed Brown wrote:
> On Sun, Jul 22, 2012 at 10:17 AM, Umut Tabak <u.tabak at tudelft.nl
> <mailto:u.tabak at tudelft.nl>> wrote:
>
>     Helmholtz equation, 3d discretization of a fluid domain,
>
>
> Do you mean indefinite Helmholtz (frequency-domain) or time-domain
> (definite)? Sorry, I have to ask...
>
> What is the wave number? How many grid points per wavelength?
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.
>
>     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.
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