Compute Quadrature formula over a general poly #13807
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fdrmrc
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This looks really nice. I must admit that I do not exactly understand the underlying algorithms in CGAL, but the overall workflow seems nice and convincing, so I agree with this one here. (It was a good opportunity for me to learn about the underlying assumptions in the CGAL part, like C++17 and similar.)
include/deal.II/cgal/utilities.h
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| * the polyhedral. | ||
| * @return A global Quadrature rule that allows to integrate over the polyhedron. | ||
| */ | ||
| template <typename Tr> |
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I did not read all of the CGAL code, but wouldn't
| template <typename Tr> | |
| template <typename CGALTriangulationType> |
be a more expressive name for the template type?
include/deal.II/cgal/utilities.h
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| /** | ||
| * Compute a Quadrature formula over the polygonal/polyhedral region described | ||
| * by a BooleanOperation between two deal.II cell_iterator. The degree of the |
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| * by a BooleanOperation between two deal.II cell_iterator. The degree of the | |
| * by a BooleanOperation between two deal.II cell_iterator objects. The degree of the |
| const Mapping<dim1, spacedim> &mapping1 = | ||
| (dealii::ReferenceCells::get_hypercube<dim1>() | ||
| .template get_default_linear_mapping<dim1, spacedim>())); | ||
| /** |
include/deal.II/cgal/utilities.h
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| * intersection. The rationale behind this specialization is that deal.II | ||
| * cells are convex sets, and as the intersection of convex sets is itself |
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Is this always true? As soon as cells are non-affine, convexity is lost, isn't it? I have too little insight into the algorithms, so this comment might or might not be restriction, but it might be good if you try to reflect the actual behavior in the description here.
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You're correct. This should definitely be called for affine-cells only. I'll fix this within the day.
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Sorry for being late here. I've just document what really the code is doing, thanks for pointing that out.
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| # include <deal.II/grid/tria.h> | ||
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| # include <boost/hana.hpp> |
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We will need to record this as another external boost dependency - we don't rely on hana anywhere else.
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Sorry, I wasn't aware of this. Actually, this has been used also in #13661
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Since this is not ready yet for all possible dim-spacedim dimensions, I think we can postpone this to 9.5, together with #13814 |
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The test failures are unrelated. |
…ure_over_region Compute Quadrature formula over a general poly
Given two deal.II cells, these two functions allow to compute a Quadrature rule over the region described by a given boolean operation between these two. Internally, the polyhedron is split into simplices and
compute_affine_transformation()is exploited in order to get a rule on each one of them.These will be used inside the
NonMatchingnamespace to provide exact quadratures during the assembly of coupling matrices (like the one in step-60). In particular, an exact version ofNonMatching::create_coupling_mass_matrix(https://www.dealii.org/developer/doxygen/deal.II/namespaceNonMatching.html#abe338fc879922cc67627b5ca039fc663) will be available.Currently, this works in 3D and codimension 0, but I have working versions for 2D-2D, 1D-2D and 2D-3D.