Re: [Libmesh-devel] New Predictor-Corrector implementation for DiffSystem framework

[John P. <jwp...@gm...>]

On Thu, Oct 2, 2008 at 1:41 PM, Nasser Mohieddin Abukhdeir
<nas...@mc...> wrote:
> Hello all:
>    After some enlightening conversations with Roy, I am going to be
> implementing a predictor/corrector AdaptiveTimeSolver class that does
> the following:
>
> 1) An explicit solve (just an EulerSolver step with theta=0) yields the
> "predictor" which is stored.
>
> 2) The explicit solve solution is used as the starting iterate for a
> full nonlinear implicit solve , which is done to the user's tolerances
> or maximum step count.
>
> 3) The implicit solution is compared with the copy of the explicit
> solution to get an error estimate and adapt the time step.

While this algorithm will work in practice for certain problems, I
have a few doubts about its robustness.  In particular, the explicit
solve step need not be 1.) a good initial guess for the implicit
solve, or 2.) useful as an error estimate when compared with the
implicit solve solution.

You might be interested in ABTR (Adams-Bashforth/Trapezoidal Rule,
though I have my doubts about it for the same reasons) or possibly the
predictor-multicorrector methods suggested by Hughes et al (CMAME v.
17/18, 1979, p. 159-182) although these do not necessarily update the
timestep.  I think Ben may have also implemented some interesting
adaptive timestep selection algorithms in his dissertation work on
compressible flows, but I can't remember for sure.  I don't want to
discourage you from trying any particular algorithm, but I think we
should be somewhat careful about what goes in the library.

-- 
John