Alexander,
> I have a triangulation which has been refined along some (polygonal) patch, > thus forming two non-overlapping domains (say, domain #1 and #2). My task is > to extract cells for domain #1, and solve BVP for this domain (with known > boundary conditions). The rest of the cells (domain #2) are not needed. An > example of such situation is shown attached (with land and ocean/sea being > two > domains). > > FWIW, the problem is posed in dim = 2, spacedim = 3. The solution is in H1. > > Here is what I struggle with: > > - I thought of using GridGenerator::create_triangulation_with_removed_cells, > but this one does not accept refined non-conforming meshes. Yes. You can't remove cells this way because then you would have (non-active) cells for which not all children are part of the mesh. That is not allowed. > - My next thought was to detect those edges, which domains #1 and #2 share > and > calculate face integrals on them during assembly, thus incorporating BCs. > Will > DoFTools::make_flux_sparsity_pattern be the right function for this? You mean you want to impose boundary conditions weakly? Like through the Nitsche method? You could do that. But you can also just impose them strongly. In essence, duplicate the functionality of the VectorTools::interpolate_boundary_values() function but instead of running it on only the faces at the boundary of the mesh, you run it also on the faces at the boundaries between the two subdomains. > - Next, what should I do on cells in domain #2? Logically, I should somehow > treat them with FE_Nothing... But how to get this done right? If you impose Dirichlet boundary conditions on the interface between the subdomains, then no knowledge of domain #2 leaks into domain #1. In other words, you can do whatever you please on domain #2. One option would be to just solve the same equation there -- you'd get something for the solution there, but you really don't care very much what exactly it is :-) If you wanted to reduce the numerical effort, you could just assemble a mass matrix on domain #2 instead of a stiffness matrix. Best W. -- ------------------------------------------------------------------------ Wolfgang Bangerth email: [email protected] www: http://www.math.colostate.edu/~bangerth/ -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/f37acfeb-6897-31ab-5ea1-ed67e283d461%40colostate.edu. For more options, visit https://groups.google.com/d/optout.
