Dear Bärbel,
> we would like to use ML preconditioner from Trilinos for problems where we > use cubic finite elements. Is it a good idea to use this preconditioner > for such problems? If it is: are there any suggestions how to choose the > parameters appropriate? The ML preconditioner is certainly not a bad choice - from what I've tested, it performs better than anything else I've tried for elliptic and elliptic-dominated problems (either scalar or vector-valued), except geometric multigrid. The iteration count increases if problem sizes increase, but still modestly (14, 16, 19, 24, 28 on a Laplacian problem in 3D when halving the mesh size). What explains this behavior is that ML coarsens too much because too many elements couple to each other. ML has a lot of parameters to tune, but I haven't found any real impact besides the setting TrilinosWrappers::PreconditionAMG::AdditionalData::aggregation_threshold, where you can tune the parameter somewhere in the range 1e-1 to 1e-3 in order to define which dofs should form one "coarse-grid-point". See the step-31 tutorial program in the section "build_stokes_preconditioner" for more detail. Generally, ML still works for Q3 elements in 3D, but for Q4 or Q5 it fails anyway - when there are more than a few thousand entries per row. In 2D things are a bit better. Best, Martin _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
