Implement MappingDoFVector (ALE) for ElementType::Simplex

[nfehn]

To enable ALE methods for ElementType::Simplex, we need to extend

1. class MappingDoFVector:

• function fill_grid_coordinates_vector() (in order to translate a Mapping into a DoFVector)
• function initialize_mapping_from_dof_vector() (in order to translate a DoFVector into a Mapping)

2. utility functions in namespace MappingTools:

• functions initialize_coarse_mappings_from_mapping_dof_vector() to construct coarse mappings of type MappingDoFVector for use in h-multigrid methods
• There are two functions with this name, differing in the number of arguments. The variant with only one triangulation object for all h-levels is not relevant for ElementType::Simplex (@peterrum)?

@dominiktassilostill FYI

[nfehn]

The first commit shows which places we need to extend / re-implement for simplex by introducing if-else-branches depending on the ElementType and by introducing asserts for element types not supported so far.

[nfehn]

@kronbichler as discussed in person, the current implementation of MappingDoFVector might be problematic, because dof_handler (and the underlying FE and degree) passed to the function fill_grid_coordinates_vector() (and initialize_mapping_from_dof_vector()) can be independent of the mapping_degree passed to the constructor of MappingDoFVector. I removed the constructor argument and used dof_handler.get_fe().degree instead; the hierarchic/lexicographic indexing becomes a local variable instead of the member variable used previously. Could you please check commits 32efd75 and b6e3210?

[kronbichler]

I had a close look at the code now. I think the new approach looks good. For the simplices, we do not have the equivalent of MappingQCache anyway, so all routines are more expensive. I think the longer-term solution will be to let all mapping-related code use the evaluators of solution fields, but that needs modification in deal.II as well; that is not part of the present PR in either case.

[nfehn]

@kronbichler thanks for your review.

We need some more refactoring in order to integrate Simplex elements easily without having to touch several classes (see 923958b and 7fbcbe8).

[nfehn]

This change was not actually intended and might cause the test to fail.