On Sun, 27 Oct 2013 21:11:18 -0400 Ben Thompson <[email protected]> wrote:
> Hello, > > Prelims: > I've been using fenics for a while now and I've had great success > getting quick results for simple problems. Now, I'm starting to move > to more complex problems. I'm going to be analyzing a variety of > coupled hyperbolic-parabolic problems where both time and space > scales range over at least 4 orders of magnitude. I will certainly be > using adaptive time-stepping and, possibly, grid refinement > techniques. However, the problem would become computationally far > more tractable if I could time-step the small-scale region > independently of the large-scale region. > > Problem: > I'd like to use local time stepping methods to allow the small length > scale and time scale to operate independently of the large > length/time scale. This is clearly possible in a specific formulation > of Discontinuous Galerkin methods: > http://onlinelibrary.wiley.com/doi/10.1111/j.1365-246X.2007.03427.x/abstract > The linked method (ADER-DG) uses a Lax-Wendroff-like process to turn > time derivatives into spatial derivatives, but extends to higher > orders. The result is that the derivatives are local to an element > and one element can time-integrate respecting only it's local > stability condition (i.e. CFL condition). I'm not an expert on the > method they describe, but it doesn't seem like it impacts the spatial > discretization at all -- standard DG. Since fenics leaves > time-integration to the user, implementing such a time integration > scheme seems entirely possible... > > Questions: > The open question in my mind is how easy it would be for me to use > local time-steps in the fenics solver. If I solve with a local deltaT > variable, will I be able to force the solver to ignore all the parts > of the system with 0 time step and just update the non-zero parts? If > not, how difficult would it be to code this? > I'm suspect I could hack something to assemble a new form each > time-step that only contains the relevant components, but that seems > extremely suboptimal. > > Finally, what would be your description of the state of support for DG > methods, especially with respect to parallelization? https://bitbucket.org/fenics-project/dolfin/issue/51/assembly-over-interior-facets-does-not Jan > > If any of this is not currently possible but would be reasonable > within the general fenics framework, I'd be interested in helping to > improve the situation. I'm an experienced software developer and am > quickly gaining background in the fenics codebase/DG methods. > > Thanks very much! > Ben Thompson _______________________________________________ fenics mailing list [email protected] http://fenicsproject.org/mailman/listinfo/fenics
