> I want to solve a problem in a 2D rectangle. The problem is tough only in a > small rectangle in the middle, thus I want to break the initial problem to > two problems (1st problem: a small rectangle in the middle, and 2nd > problem: the remaining domain if you remove the said rectangle from a > larger one), which I can solve independently and converge to a solution, > iteratively, through interface relaxation. > I use Dirichlet conditions on the common boundary, which I update on every > iteration. Specifically, after solving both problems (in a certain > iteration) I use the derivatives at the common boundary to update the > Dirichlet conditions.
So you are using a domain decomposition approach, but want to solve things on a single mesh, right? > 1) how can I take the derivatives at the common boundary (after solving the > problem)?, and You can use FEFaceValues and evaluate the gradients of the current solution using fe_face_values.get_function_gradients(...) > 2) can I use the boundary vector directly (in case the refinement of the > domain is such that they have the same nodes on the common boundary)? > should I probably avoid feeding the boundary data to the problem by setting > the values of the boundary vector directly, and instead interpolate my data > to create a function and use interpolate_boundary_values() to setup the > boundary vector? I don't understand this question. Are the two subdomains part of the same mesh? > Lastly, a question that has to do with both my questions above (it depends > on the answers to these questions whether an answer to the following > question is "required"): > how do I know which element of the boundary vector corresponds to what > coordinate (or the reverse)? You can ask DoFTools::map_dofs_to_support_points() for this task. Best W. ------------------------------------------------------------------------- Wolfgang Bangerth email: [email protected] www: http://www.math.tamu.edu/~bangerth/ _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
