[petsc-users] incomplete cholesky with a drop tolerance

[Jed Brown]

On Sun, Jul 22, 2012 at 10:17 AM, Umut Tabak <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?


> 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)?


> However, this application is pretty problem specific, then I can use this
> full-rank matrix in linear solutions. The condition number estimate belongs
> to this full-rank matrix that is extracted from the original singular
> operator...
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