[petsc-users] PETSc and dense matrices

[Jed Brown]

On Thu, Jan 6, 2011 at 10:04, Raeth, Peter <PRaeth at hpti.com> wrote:

> While I can not put my finger on it, I thought I saw on a man page that
> PETSc was only designed for the solution of sparse matrices.


I can try to explain:

Some choices in PETSc are not great if the problem has no "structure".  I
loosely define "structure" to mean that there is a way to store the forward
operator in less than O(N^2) space and that there is a way to multiply the
forward operator my a vector in less than O(N^2) time.  In addition to
sparse matrices, this includes operators that can be applied using fast
transforms like FFT and FMM, have tensor product structure, are the Schur
complement or a low-rank correction of something fitting the above
description, etc.

If you only solve dense problems with no additional structure, then PETSc
cannot have the absolute best performance.  But it should be perfectly
adequate for most dense problems and if you have some problems with
structure and some dense problems, it offers a uniform high-level interface
and a lot of algorithmic flexibility that you won't find in a dense-only
package.
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