From 7b4c90cc3d8994095a164994792f2aa7562ddb61 Mon Sep 17 00:00:00 2001 From: David Wells <drwells@email.unc.edu> Date: Sat, 3 Nov 2018 15:09:06 -0400 Subject: [PATCH] Update GridGenerator::truncated_cone. The 3D grid currently uses 4 coarse level cells on circular slices: this is poorly conditioned since, when refined, some cells will converge to triangles. This commit uses the five-square (implemented by GridGenerator::hyper_ball<2>) to get a much better coarse grid. --- doc/doxygen/images/truncated_cone_2d.png | Bin 0 -> 64742 bytes doc/doxygen/images/truncated_cone_3d.png | Bin 0 -> 191918 bytes doc/news/changes/minor/20181103DavidWells | 4 + include/deal.II/grid/grid_generator.h | 5 + source/grid/grid_generator.cc | 114 +- tests/bits/cone_01.cc | 2 +- tests/bits/cone_01.output | 2104 ++++++++------------- tests/bits/cone_02.cc | 2 +- tests/bits/cone_02.output | 2104 ++++++++------------- tests/bits/cone_03.output | 21 +- 10 files changed, 1586 insertions(+), 2770 deletions(-) create mode 100644 doc/doxygen/images/truncated_cone_2d.png create mode 100644 doc/doxygen/images/truncated_cone_3d.png create mode 100644 doc/news/changes/minor/20181103DavidWells diff --git a/doc/doxygen/images/truncated_cone_2d.png b/doc/doxygen/images/truncated_cone_2d.png new file mode 100644 index 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0000000000..3352b1f360 --- /dev/null +++ b/doc/news/changes/minor/20181103DavidWells @@ -0,0 +1,4 @@ +Fixed: The grid generated by GridGenerator::truncated_cone now uses more level 0 +cells to improve conditioning of cells when they are refined. +<br> +(David Wells, 2018/11/03) diff --git a/include/deal.II/grid/grid_generator.h b/include/deal.II/grid/grid_generator.h index 5c61e0faaa..9c055994f5 100644 --- a/include/deal.II/grid/grid_generator.h +++ b/include/deal.II/grid/grid_generator.h @@ -764,6 +764,11 @@ namespace GridGenerator * In three dimensions, the manifold id of the hull is set to zero, and a * CylindricalManifold is attached to it. * + * Here are the grids in 2D and 3D after two mesh refinements: + * + * @image html truncated_cone_2d.png + * @image html truncated_cone_3d.png + * * @note The triangulation passed as argument needs to be empty when calling this function. * * @author Markus Bürg, 2009 diff --git a/source/grid/grid_generator.cc b/source/grid/grid_generator.cc index 4c23ad354b..44e8a50ed0 100644 --- a/source/grid/grid_generator.cc +++ b/source/grid/grid_generator.cc @@ -3381,82 +3381,46 @@ namespace GridGenerator const double radius_1, const double half_length) { - // Determine number of cells and vertices - const unsigned int n_cells = static_cast<unsigned int>( - std::ceil(half_length / std::max(radius_0, radius_1))); - const unsigned int n_vertices = 4 * (n_cells + 1); - std::vector<Point<3>> vertices_tmp(n_vertices); - - vertices_tmp[0] = Point<3>(-half_length, 0, -radius_0); - vertices_tmp[1] = Point<3>(-half_length, radius_0, 0); - vertices_tmp[2] = Point<3>(-half_length, -radius_0, 0); - vertices_tmp[3] = Point<3>(-half_length, 0, radius_0); - - const double dx = 2 * half_length / n_cells; - - for (unsigned int i = 0; i < n_cells; ++i) - { - vertices_tmp[4 * (i + 1)] = - vertices_tmp[4 * i] + - Point<3>(dx, 0, 0.5 * (radius_0 - radius_1) * dx / half_length); - vertices_tmp[4 * i + 5] = - vertices_tmp[4 * i + 1] + - Point<3>(dx, 0.5 * (radius_1 - radius_0) * dx / half_length, 0); - vertices_tmp[4 * i + 6] = - vertices_tmp[4 * i + 2] + - Point<3>(dx, 0.5 * (radius_0 - radius_1) * dx / half_length, 0); - vertices_tmp[4 * i + 7] = - vertices_tmp[4 * i + 3] + - Point<3>(dx, 0, 0.5 * (radius_1 - radius_0) * dx / half_length); - } - - const std::vector<Point<3>> vertices(vertices_tmp.begin(), - vertices_tmp.end()); - Table<2, unsigned int> cell_vertices(n_cells, - GeometryInfo<3>::vertices_per_cell); - - for (unsigned int i = 0; i < n_cells; ++i) - for (unsigned int j = 0; j < GeometryInfo<3>::vertices_per_cell; ++j) - cell_vertices[i][j] = 4 * i + j; - - std::vector<CellData<3>> cells(n_cells, CellData<3>()); - - for (unsigned int i = 0; i < n_cells; ++i) - { - for (unsigned int j = 0; j < GeometryInfo<3>::vertices_per_cell; ++j) - cells[i].vertices[j] = cell_vertices[i][j]; - - cells[i].material_id = 0; - } - - triangulation.create_triangulation(vertices, cells, SubCellData()); - triangulation.set_all_manifold_ids_on_boundary(0); - - for (Triangulation<3>::cell_iterator cell = triangulation.begin(); - cell != triangulation.end(); - ++cell) - { - if (cell->vertex(0)(0) == -half_length) - { - cell->face(4)->set_boundary_id(1); - cell->face(4)->set_manifold_id(numbers::flat_manifold_id); - - for (unsigned int i = 0; i < 4; ++i) - cell->line(i)->set_boundary_id(0); - } - - if (cell->vertex(4)(0) == half_length) - { - cell->face(5)->set_boundary_id(2); - cell->face(5)->set_manifold_id(numbers::flat_manifold_id); - - for (unsigned int i = 4; i < 8; ++i) - cell->line(i)->set_boundary_id(0); - } + Assert(triangulation.n_cells() == 0, + ExcMessage("The output triangulation object needs to be empty.")); + Assert(0 < radius_0, ExcMessage("The radii must be positive.")); + Assert(0 < radius_1, ExcMessage("The radii must be positive.")); + Assert(0 < half_length, ExcMessage("The half length must be positive.")); + + const auto n_slices = 1 + static_cast<unsigned int>(std::ceil( + half_length / std::max(radius_0, radius_1))); + + Triangulation<2> triangulation_2; + GridGenerator::hyper_ball(triangulation_2, Point<2>(), radius_0); + GridGenerator::extrude_triangulation(triangulation_2, + n_slices, + 2 * half_length, + triangulation); + GridTools::rotate(numbers::PI / 2, 1, triangulation); + GridTools::shift(Tensor<1, 3>({-half_length, 0.0, 0.0}), triangulation); + // At this point we have a cylinder. Multiply the y and z coordinates by a + // factor that scales (with x) linearly between radius_0 and radius_1 to fix + // the circle radii and interior points: + auto shift_radii = [=](const Point<3> &p) { + const double slope = (radius_1 / radius_0 - 1.0) / (2.0 * half_length); + const double factor = slope * (p[0] - -half_length) + 1.0; + return Point<3>(p[0], factor * p[1], factor * p[2]); + }; + GridTools::transform(shift_radii, triangulation); - for (unsigned int i = 0; i < 4; ++i) - cell->face(i)->set_boundary_id(0); - } + // Set boundary ids at -half_length to 1 and at half_length to 2. Set the + // manifold id on hull faces (i.e., faces not on either end) to 0. + for (auto face : triangulation.active_face_iterators()) + if (face->at_boundary()) + { + if (std::abs(face->center()[0] - -half_length) < 1e-8 * half_length) + face->set_boundary_id(1); + else if (std::abs(face->center()[0] - half_length) < + 1e-8 * half_length) + face->set_boundary_id(2); + else + face->set_all_manifold_ids(0); + } triangulation.set_manifold(0, CylindricalManifold<3>()); } diff --git a/tests/bits/cone_01.cc b/tests/bits/cone_01.cc index 7f0e8a739d..a6f4077459 100644 --- a/tests/bits/cone_01.cc +++ b/tests/bits/cone_01.cc @@ -66,7 +66,7 @@ check<3>() static const CylindricalManifold<dim> boundary; triangulation.set_manifold(0, boundary); - triangulation.refine_global(2); + triangulation.refine_global(1); GridOut().write_gnuplot(triangulation, deallog.get_file_stream()); } diff --git a/tests/bits/cone_01.output b/tests/bits/cone_01.output index 4b0c4782a0..2aa4e384c8 100644 --- a/tests/bits/cone_01.output +++ b/tests/bits/cone_01.output @@ -111,1539 +111,963 @@ 0.500000 0.312500 2 0 --1.00000 0.00000 -1.00000 2 0 --1.00000 0.382683 -0.923880 2 0 --0.500000 0.334848 -0.808395 2 0 --0.500000 0.00000 -0.875000 2 0 --1.00000 0.00000 -1.00000 2 0 - 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-0.500000 -0.239177 0.577425 2 0 -0.500000 0.00000 0.625000 2 0 -1.00000 0.00000 0.500000 2 0 -1.00000 -0.191342 0.461940 2 0 -0.500000 -0.239177 0.577425 2 0 - -0.500000 0.00000 0.421175 2 0 -0.500000 -0.239177 0.577425 2 0 - -0.500000 0.239177 0.577425 2 0 -0.500000 0.00000 0.625000 2 0 - -1.00000 0.191342 0.461940 2 0 -1.00000 0.00000 0.500000 2 0 - -1.00000 0.00000 0.336940 2 0 -1.00000 -0.191342 0.461940 2 0 +1.00000 0.323223 0.00000 1 0 +1.00000 0.250000 -0.250000 1 0 diff --git a/tests/bits/cone_02.cc b/tests/bits/cone_02.cc index 2803ca79b0..a2c25dfb62 100644 --- a/tests/bits/cone_02.cc +++ b/tests/bits/cone_02.cc @@ -72,7 +72,7 @@ check<3>() static const CylindricalManifold<dim> boundary; triangulation.set_manifold(0, boundary); - triangulation.refine_global(2); + triangulation.refine_global(1); GridOut().write_gnuplot(triangulation, deallog.get_file_stream()); } diff --git a/tests/bits/cone_02.output b/tests/bits/cone_02.output index 2b215c4e3b..8473a432e9 100644 --- a/tests/bits/cone_02.output +++ b/tests/bits/cone_02.output @@ -113,1539 +113,963 @@ DEAL::dim=2 DEAL::dim=3 --0.250000 0.00000 -0.500000 2 0 --0.250000 0.191342 -0.461940 2 0 --0.125000 0.239177 -0.577425 2 0 --0.125000 0.00000 -0.625000 2 0 --0.250000 0.00000 -0.500000 2 0 - 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