[petsc-dev] Question About Petsc ILU

[Jed Brown]

On Thu, Dec 29, 2011 at 11:01, Dave Nystrom <dnystrom1 at comcast.net> wrote:

> I have recently added the capability to have a separate preconditioning
> matrix in the petsc interface for the code I am working with.  I have two
> types of preconditioning matrices that I have questions about.  One is
> tridiagonal and the other is 7 diagonals.  In both cases, the the diagonals
> are all lexically adjacent.  Or phrased differently, the tridiagonal matrix
> has a bandwidth of 3 and the 7 diagonal matrix has a bandwidth of 7 and so
> they are compact or dense band systems.
>
> I was wondering what petsc ilu will do for preconditioning matrices like
> these.  Will it produce an exact lu factorization or a nearly exact
> factorization?
>

Yes


>  I'm interested in the answer to this question because I am
> thinking I might be able to run this preconditioner on the gpu using the
> txpetscgpu package.
>

Likely pointless because this solve is probably not a big part of run-time.
The bigger concern is the convergence rate that you lose by using this
approximation. Matt and I mentioned this the last time you brought it up,
but I recommend getting familiar with the literature. Then, get the math
straight before looking for ways to transform into problems that you can
run fast on a GPU or whatever. If you just optimize kernels, you're likely
to optimize something that takes a small part of run-time and isn't really
helping you anyway.
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