ok, John's explanation was very helpful, did the math (a few times :) and have a better grasp on the problem then I did before, sorry about that.
What now confuses me is whether or not EulerSolver with theta=0.5 is actually Crank-Nicolson. It makes sense to me that Euler2Solver with theta=0.5 is...but not EulerSolver. 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. I did some digging around, looked up the methods that John suggested, and found a variable coefficient multistep method (allows for unequally spaced data): Chapter 12 http://books.google.com/books?id=aqfMgehyGnEC That might fit the bill. Everything is detailed in this chapter, and while this is neither straighforward nor easy to code, it looks like it might be worth the effort, but it would probably need to rely on Roy's FemContext change do to all of the overhead data being kept from previous steps. Anyway, I'm in no hurry, lots of other more simple details to work out with my simulations, but as I said before, if the need is there and a suitable method identified, I'll do the work. Nasser Mohieddin Abukhdeir Graduate Student (Materials Modeling Research Group) McGill University - Department of Chemical Engineering http://webpages.mcgill.ca/students/nabukh/web/ http://mmrg.chemeng.mcgill.ca/ Roy Stogner wrote: > On Thu, 2 Oct 2008, John Peterson wrote: > > >> This was probably a confusing description but try it for >> a simple example to convince yourself the first Newton step is not the >> same as an explicit solve. >> > > John's right - in fact, consider the case where f(U) is linear. Then > Newton will obviously hit the correct solution after one step, but > (presuming you're using an implicit time discretization) that correct > solution is still the result of an implicit, not an explicit, solve. > --- > Roy > ------------------------------------------------------------------------- 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
