[petsc-users] Questions about TS

[Jed Brown]

On Wed, Oct 19, 2011 at 21:39, Blaise Bourdin <bourdin at lsu.edu> wrote:

> OK, this is clear. It will be really nice indeed when everything is
> reorganized this way.
>

Note that most methods work this way already. The main hole right now is
that explicit methods don't support nontrivial mass matrices. The best error
control is currently in the Rosenbrock-W methods (TSROSW), but the other
methods will also grow support (via extrapolation for those methods that
don't have any embedded error estimators).

One aspect that we haven't settled on an API for is user-provided stability
requirements (especially for explicit methods or for the explicit part of an
IMEX scheme, sometimes strong stability). Often the user can cheaply
characterize some extreme eigenvalues of their system in which case we could
use those estimates to limit step size instead of needing to reject steps
only after the error estimator decides the accuracy is unacceptable.

Specifically, the user-provided stability limits are sharper and don't
require tuning the tolerances on the time integrator so that it detects
instability immediately, but does not shorten the steps excessively.
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