Just to clarify things, my understanding of the backwards Euler method that is implemented now is such that for the initial u' = f(theta*u_new + (1-theta)*u_old), so the first iteration of the nonlinear solver should be equivalent to an explicit solve, assuming u_new = u_old during the first step. Please correct me if I'm wrong.
My goal to get an adaptive time solver working such that it is less costly than the current implementation. I am very much *not* and expert, but am very committed to using LibMesh, so if there can be a consensus on a) if there needs to be a faster/less accurate adaptive time solver implementation and b) if so, what would be the best implementation, I will do my best to implement it. 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/ John Peterson wrote: > On Thu, Oct 2, 2008 at 1:41 PM, Nasser Mohieddin Abukhdeir > <[EMAIL PROTECTED]> 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 > ------------------------------------------------------------------------- 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
