Speed up DoFAccessorImplementation::get_dof_indices

[kronbichler]

Part of #2000.

This PR currently builds on #14063, I will rebase once that PR is reviewed and merged. Edit: rebased

This PR extracts the fast access to line indices initially written in #13924 and puts it to the appropriate place in internal::TriaAccessorImplementation::Implementation. I also added a similar function for the line orientations. With these changes, I can get the indices of all lines with twice the instruction count it took to get a single index/orientation previously - in 3D this is a 6x improvement. This is the first new commit on top of #14063.

The second commit then applies the new function to the extraction of dof_indices in DoFAccessorImplementation. With this commit, we're further closing the gap to the cell_dof_indices_cache, and in fact, once this PR is merged, we should be able to delete the cache because the performance is now good enough.

There is one final step I still see on the performance side, the case when the faces/lines are not in standard orientation. We then call FiniteElement::adjust_quad_dof_index_for_face_orientation, which extracts bits for the orientation/rotation/flip, only to then again put them together in a similar way. We should create an overload of that function in a follow-up PR that directly picks up the raw face orientation that we store nowadays.

[peterrum]

I guess this will be forever slow :(

[kronbichler]

It is not really difficult to apply a similar scheme also for the other shapes. Essentially, one needs to unroll the decision in

dealii/include/deal.II/grid/reference_cell.h

Lines 1381 to 1412 in 01e34f3

	{
	static const std::array<unsigned int, 2> table[6] = {
	{{0, 0}}, {{0, 1}}, {{0, 2}}, {{1, 1}}, {{1, 2}}, {{2, 1}}};
	return table[line];
	}
	else if (*this == ReferenceCells::Pyramid)
	{
	static const std::array<unsigned int, 2> table[8] = {{{0, 0}},
	{{0, 1}},
	{{0, 2}},
	{{0, 3}},
	{{1, 2}},
	{{2, 1}},
	{{1, 1}},
	{{2, 2}}};
	return table[line];
	}
	else if (*this == ReferenceCells::Wedge)
	{
	static const std::array<unsigned int, 2> table[9] = {{{0, 0}},
	{{0, 2}},
	{{0, 1}},
	{{1, 0}},
	{{1, 1}},
	{{1, 2}},
	{{2, 0}},
	{{2, 1}},
	{{3, 1}}};
	return table[line];

to the code here, so go through three or four faces and pick the lines there. All the rest will be similar to the hexahedral case. In case we have good tests, this should be easy to try out and get running (< 1 hour of work).

[kronbichler]

Should we tackle this as part of #14068?

[peterrum]

Should we tackle this as part of #14068?

If we see a significant slow down, yes.

[peterrum]

What happened with fe_index?

[peterrum]

OK. This is the MG path. Wouldn't it make sense to add an assert that fe_index is ineed 0 or default?

[kronbichler]

Yes, that makes sense.

[kronbichler]

Note that I added the check in line 1344 below, not here, as I do not want to pick up the index here again.