[petsc-users] [petsc-maint #86567] Question on KSPs

[Jed Brown]

On Tue, Sep 13, 2011 at 10:03, Michele De Stefano <
mstefano at milan.westerngeco.slb.com> wrote:

> we would like to explore more in detail the possibility to have a
> completely matrix-free preconditioner.
> May you explain which are the "few methods" that we should implement and
> that you was talking of ?
>

Matrix-free multigrid, approximate the problem with a simpler model for
which a fast solver (e.g. FMM or FFT-based) is available, the nested
iteration that Matt mentioned, low rank + identity approximations of the
inverse (e.g. built as a byproduct of an outer iteration like BFGS).

None of these are truly generic. I absolutely do not recommend trying to
build matrix-free preconditioners to avoid writing code to assemble a
matrix. Indeed, I think it's well worth having the code to assemble a matrix
even if you usually run without it because it enables you to try many
algorithms without extra effort. Having the matrix available can inform the
design of matrix-free methods.

The performance asymptotics of matrix-free methods are better for some
problems. In many cases, it makes sense to apply the Jacobian using some
matrix-free method and assemble a less expensive matrix for preconditioning.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20110913/1627dab4/attachment.htm>