On Tue, 2 Mar 2010 11:19:04 -0700, Derek Gaston <[email protected]> wrote: > Any other comments about this? I'm still thinking about it. > > Also... does anyone (Jed?) know how to advance and explicit system alongside > an implicit system with TSGL?
There are multiple levels of coupling that you could use. Starting from the loosest coupling: * Decoupled with no interpolation during stages, not better than first order accurate. * Fix the explicit system at the start of the implicit time step, solve all the stages of the implicit system, then integrate the explicit system up to the current state using the interpolated solution of the implicit system. This is likely to be a much more robust scheme, and I wouldn't be surprised if you see better than first-order accuracy here (despite this not holding in all regimes). * At each stage of the implicit system, integrate the explicit system up to the current stage using interpolated values of the implicit system. If the final abscissa is 1 and the implicit method has full stage order, then I think this is nominally of full accuracy (i.e. min(implicit_order,explicit order)). This is burying the explicit integrator in function evaluation for the implicit system. Dana told me that he has actually done this in the past, albeit for simpler implicit integrators. TSGL is not currently set up to offer the high-order interpolation at arbitrary points within the interval, especially before all the stages have been solved, but the method can supply these values (I or (preferably) the inventors of the method just need to work out the details for this operation). I would like to have it anyway for integration of continuous adjoints (discrete adjoints don't need interpolation). Jed ------------------------------------------------------------------------------ Download Intel® Parallel Studio Eval Try the new software tools for yourself. Speed compiling, find bugs proactively, and fine-tune applications for parallel performance. See why Intel Parallel Studio got high marks during beta. http://p.sf.net/sfu/intel-sw-dev _______________________________________________ Libmesh-devel mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-devel
