new feature 'overset grids'

[nfehn]

This PR introduces the feature of overset grids by the example of the Poisson module. Two domains overlap and ExaDG's interface coupling functionality is used to couple the two domains via Dirichlet BCs. A very simple outer iteration is currently used to obtain convergence for the coupled problem.

This PR is currently a draft, since several aspects have been encountered which first need to be generalized in ExaDG. Here is a list of main points:

• InterfaceCoupling/FunctionCached does currently not work for scalar quantities. -> see commit 69a89d8
• Hence, I set up a vectorial Poisson problem. However, I had to deactivate the error calculation in Poisson::Postprocessor since this seems to work only for scalar problems. <\del>
• The setup of multigrid (map of dirichlet boundary IDs passed to MultigridPreconditionerBase) does not take into account Dirichlet cached BCs. In case all boundary conditions are of type DirichletCached, multigrid even crashes. It is remarkable that multigrid seems to work if we have both Dirichlet and DirichletCached BCs (as in some FSI examples). This is a bug. -> See PR take DirichletCached BCs into account for multigrid setup #188.
• InterfaceCoupling needs to be generalized in case that the two domains do not touch each other along a boundary, but intersect each other (-> marked_vertices and setup of InterfaceCoupling needs to be generalized). -> See PR improve robustness of InterfaceCoupling regarding marked_vertices #187 as a first remedy.
• The design of the related base application class and the driver class needs to be improved to avoid code duplication. -> first part resolved in commit f469412, second part in commit 7cb2daa

Example: Scalar Poisson problem with constant right-hand side, homogeneous DBC's, DirichletCachedBC's at the overlapping boundaries: Domain1 = [0,1]^2; Domain2 = [0.5, 1.5] x [0, 1]. -> overlap from x_1 = 0.5 to 1.0.

Solution after initialization with zero

and after 1, 2, 3 iterations (visually converged after 3 iterations).

[peterrum]

Nice, some domain-decomposition method! The next step would be to compute the traditional Schwarz setup: union of rectangle and circle. That was one of the first tests of RPE. I'll try to take a look at the PR later today.

[nfehn]

Nice, some domain-decomposition method! The next step would be to compute the traditional Schwarz setup: union of rectangle and circle. That was one of the first tests of RPE. I'll try to take a look at the PR later today.

Yes, I already thought of this setup, did not realize it so far since some functionality is missing. Can you point me to that test case? Is it part of deal.II? I need functionality like tria_1->contains(face) (in the bangerth-favorite naming ;) and interpreted purely geometrically; face belonging to another triangulation tria_2) to detect automatically on which boundary faces to set DirichletCached boundary conditions.

[peterrum]

This is the test: https://github.com/dealii/dealii/blob/master/tests/remote_point_evaluation/vector_tools_evaluate_at_points_02.cc

Not very nice. What I do is to only check if the quadrature points are inside of the domain or not.

[nfehn]

This is the test: https://github.com/dealii/dealii/blob/master/tests/remote_point_evaluation/vector_tools_evaluate_at_points_02.cc

Not very nice. What I do is to only check if the quadrature points are inside of the domain or not.

I do not find the place where you check whether the q-points are inside the other triangulation. Does this happen inside RemotePointEvaluation? For me the code looks like you are collecting all points on the boundary, do the evaluation, and set constraints for all the points afterwards?

[peterrum]

Does this happen inside RemotePointEvaluation? For me the code looks like you are collecting all points on the boundary, do the evaluation, and set constraints for all the points afterwards?

Yes. If the point is not found in the other domain, the value has its default value (0.0).

[peterrum]

Looks good to me!

[nfehn]

Yes. If the point is not found in the other domain, the value has its default value (0.0).

Does this mean that you impose a constraint with a value of 0.0 for faces that are not found? This would be restrictive since one might want to impose other inhomogeneous boundary conditions for those faces that are outside the other tria.

[nfehn]

i would merge once the checks completed