On Fri, Oct 3, 2008 at 12:40 PM, Adam C Powell IV <[EMAIL PROTECTED]> wrote: > On Fri, 2008-10-03 at 10:50 -0500, Roy Stogner wrote: >> On Thu, 2 Oct 2008, Nasser Mohieddin Abukhdeir wrote: >> >> > Moving back to John's point about the previously mentioned >> > Predictor/Corrector algorithm (assuming we compute everything >> > correctly), I'm assuming that idea is trashed. >> >> The idea that we can use the first Newton step as an explicit solution >> is wrong, but using a forward Euler solve for the predictor and >> following it up by a backward Euler Newton solve for the corrector >> should still work just fine. > > Are you sure about that? It seems that if delta t is significantly > larger than the forward Euler stability criterion, this would make an > awful predictor. In the past I've used a linear projection of the > previous two timesteps into the new time as the predictor, and saved a > couple of Newton iterations vs. using the previous timestep alone, which > is more stable than a forward Euler step, but doesn't always work well > either...
I think this is an interesting question to investigate. As we all know explicit Euler is unstable when applied repeatedly but just how "unstable" it is for a single step, and whether a single step is possibly useful, I'm not so sure. Therefore, both as a coding exercise and to settle this question for practical problems, it might be interesting to implement an explicit/implicit predictor/corrector solver... This is essentially what ABTR is, and explicit AB2 should have an even smaller region of stability than explicit Euler given that it's higher-order. -- John ------------------------------------------------------------------------- This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world http://moblin-contest.org/redirect.php?banner_id=100&url=/ _______________________________________________ Libmesh-devel mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-devel
