MGTwoLevelTransfer (p): add fallback FE case

[peterrum]

... to allow more type of FEs (that are currently not supported by MatrixFree, e.g. RT or Nedelec).

Most changed lines are related to changed indentation (due to extra if-statements). These are the extra operations:

dealii/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h

Lines 1846 to 1866 in 468444d

	{
	lexicographic_numbering_fine[fe_index_pair.second].resize(
	dof_handler_fine.get_fe(fe_index_pair.first.second)
	.n_dofs_per_cell());
	lexicographic_numbering_coarse[fe_index_pair.second].resize(
	dof_handler_coarse.get_fe(fe_index_pair.first.first)
	.n_dofs_per_cell());
	for (unsigned int i = 0;
	i <
	lexicographic_numbering_fine[fe_index_pair.second].size();
	++i)
	lexicographic_numbering_fine[fe_index_pair.second][i] = i;
	for (unsigned int i = 0;
	i < lexicographic_numbering_coarse[fe_index_pair.second]
	.size();
	++i)
	lexicographic_numbering_coarse[fe_index_pair.second][i] = i;
	}
	}

dealii/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h

Lines 2130 to 2170 in 468444d

	{
	transfer.n_components = 1;
	const auto &fe_fine =
	dof_handler_fine.get_fe(fe_index_pair.second);
	const auto &fe_coarse =
	dof_handler_coarse.get_fe(fe_index_pair.first);
	{
	FullMatrix<double> matrix(fe_fine.n_dofs_per_cell(),
	fe_coarse.n_dofs_per_cell());
	FETools::get_projection_matrix(fe_coarse, fe_fine, matrix);
	transfer.schemes[fe_index_no].prolongation_matrix.resize(
	fe_fine.n_dofs_per_cell() * fe_coarse.n_dofs_per_cell());
	for (unsigned int i = 0, k = 0;
	i < fe_coarse.n_dofs_per_cell();
	++i)
	for (unsigned int j = 0; j < fe_fine.n_dofs_per_cell();
	++j, ++k)
	transfer.schemes[fe_index_no].prolongation_matrix[k] =
	matrix(j, i);
	}
	{
	FullMatrix<double> matrix(fe_coarse.n_dofs_per_cell(),
	fe_fine.n_dofs_per_cell());
	FETools::get_projection_matrix(fe_fine, fe_coarse, matrix);
	transfer.schemes[fe_index_no].restriction_matrix.resize(
	fe_fine.n_dofs_per_cell() * fe_coarse.n_dofs_per_cell());
	for (unsigned int i = 0, k = 0;
	i < fe_coarse.n_dofs_per_cell();
	++i)
	for (unsigned int j = 0; j < fe_fine.n_dofs_per_cell();
	++j, ++k)
	transfer.schemes[fe_index_no].restriction_matrix[k] =
	matrix(i, j);
	}
	}

depends on #12923

[kronbichler]

Looks like a good extension to me, but there are some questions I have regarding vector-valued cases (did we support them before)? See below.

[kronbichler]

Is there an assumption about a single component somewhere else or are you now restricting to a smaller class of finite elements in the hypercube case? The original code of ShapeInfo allowed multiple components, but you ask for n_components()==1 now, which is more restrictive than fe.n_base_elements()==1 I found as assertions elsewhere.

[kronbichler]

I know this is pre-existing, but isn't this the regular hierarchic-to-lexicographic renumbering you would get from ShapeInfo::lexicographic_numbering or maybe the inverse? I know it is a bit of a hammer to call that function, but this is not performance-critical code and 1D anyway, and I find it more documenting, and is what we do below.

[kronbichler]

I don't see how this else clause differs from the other places, except that it uses a different dummy quadrature. But we never use anything from the quadrature (as it is a dummy), so I don't see why we can't use the one from the if clause also for non-hypercubes. Again, not the change in question here, but maybe we can fix it. If not, I would prefer to only set the quadrature formula in an if/else setup.

[kronbichler]

@peterrum what should we do about this PR? I suggest we move the target milestone, it seems like too much work the release now.

[peterrum]

@kronbichler I have removed the label.

[adamqc]

Hi @peterrum, I have reviewed this PR, however, given my limited familiarity with MGTransfers, I'm uncertain about the next steps. Could you please provide some guidance on how to proceed and complete it?