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.

diff --git a/doc/doxygen/images/truncated_cone_2d.png b/doc/doxygen/images/truncated_cone_2d.png
new file mode 100644 (file)
index 0000000..da4e05e
Binary files /dev/null and b/doc/doxygen/images/truncated_cone_2d.png differ

diff --git a/doc/doxygen/images/truncated_cone_3d.png b/doc/doxygen/images/truncated_cone_3d.png
new file mode 100644 (file)
index 0000000..59fd9ee
Binary files /dev/null and b/doc/doxygen/images/truncated_cone_3d.png differ

diff --git a/doc/news/changes/minor/20181103DavidWells b/doc/news/changes/minor/20181103DavidWells
new file mode 100644 (file)
index 0000000..3352b1f
--- /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 5c61e0faaa993ae9ffeb492f9020e0b844856713..9c055994f56f69ecbcf4dfb71139c41063c04625 100644 (file)
--- 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 4c23ad354bd3444de4dc06f68188fb0bd0dd7c26..44e8a50ed0b19a4ed42d739c65d4b412ac8691bf 100644 (file)
--- 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 7f0e8a739d40f036d49969faafa738f8ca83c84d..a6f407745927fff3213250ceaa1d5e82812ce3c5 100644 (file)
--- 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 4b0c4782a03ae2f4e9511755c3924bd6f5976e7f..2aa4e384c8a9a4e5dc74bd804339249f3541145e 100644 (file)
--- 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
-
--1.00000 -0.382683 -0.923880 2 0
--1.00000 0.00000 -0.673880 2 0
--0.500000 0.00000 -0.589645 2 0
--0.500000 -0.334848 -0.808395 2 0
--1.00000 -0.382683 -0.923880 2 0
-
--1.00000 0.00000 -1.00000 2 0
--1.00000 -0.382683 -0.923880 2 0
+-1.00000 -0.707107 0.707107 1 0
+-1.00000 -1.00000 2.22045e-16 1 0
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+-1.00000 -0.707107 0.707107 1 0
+
+-1.00000 -0.500000 0.500000 1 0
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+-1.00000 -0.500000 0.500000 1 0
+
+-1.00000 -0.707107 0.707107 1 0
+-1.00000 -0.500000 0.500000 1 0
 
--1.00000 0.382683 -0.923880 2 0
--1.00000 0.00000 -0.673880 2 0
+-1.00000 -1.00000 2.22045e-16 1 0
+-1.00000 -0.646447 1.11022e-16 1 0
 
--0.500000 0.334848 -0.808395 2 0
--0.500000 0.00000 -0.589645 2 0
+0.00000 -0.750000 8.32667e-16 1 0
+0.00000 -0.484835 4.44089e-16 1 0
 
--0.500000 0.00000 -0.875000 2 0
--0.500000 -0.334848 -0.808395 2 0
-
--1.00000 0.382683 -0.923880 2 0
--1.00000 0.707107 -0.707107 2 0
--0.500000 0.618718 -0.618718 2 0
--0.500000 0.334848 -0.808395 2 0
--1.00000 0.382683 -0.923880 2 0
-
--1.00000 0.00000 -0.673880 2 0
--1.00000 0.353553 -0.353553 2 0
--0.500000 0.309359 -0.309359 2 0
--0.500000 0.00000 -0.589645 2 0
--1.00000 0.00000 -0.673880 2 0
-
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--1.00000 0.00000 -0.673880 2 0
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+
+-1.00000 -1.00000 2.22045e-16 1 0
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--1.00000 0.707107 -0.707107 2 0
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+-1.00000 -0.707107 -0.707107 1 0
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--0.500000 0.334848 -0.808395 2 0
--0.500000 0.00000 -0.589645 2 0
-
--1.00000 -0.382683 -0.923880 2 0
--1.00000 0.00000 -0.673880 2 0
--0.500000 0.00000 -0.589645 2 0
--0.500000 -0.334848 -0.808395 2 0
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-
--1.00000 -0.707107 -0.707107 2 0
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--0.500000 -0.309359 -0.309359 2 0
--0.500000 -0.618718 -0.618718 2 0
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diff --git a/tests/bits/cone_02.cc b/tests/bits/cone_02.cc
index 2803ca79b034e55eb3ac53bd3c45ed65249a0397..a2c25dfb621272460d379ed0029b4ff0927ff711 100644 (file)
--- 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 2b215c4e3b5f1f46b596a574426ffeac81066756..8473a432e93bb4181c115f848f19d5f09a3484c7 100644 (file)
--- 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
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+-0.250000 -0.250000 0.250000 1 0
+
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+-0.250000 -0.250000 0.250000 1 0
 
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--0.250000 0.00000 -0.336940 2 0
+-0.250000 -0.500000 1.11022e-16 1 0
+-0.250000 -0.323223 5.55112e-17 1 0
 
--0.125000 0.239177 -0.577425 2 0
--0.125000 0.00000 -0.421175 2 0
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+0.00000 -0.484835 4.85723e-16 1 0
 
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+
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+-0.250000 -0.323223 5.55112e-17 1 0
 
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--0.250000 0.176777 -0.176777 2 0
+-0.250000 -0.353553 -0.353553 1 0
+-0.250000 -0.250000 -0.250000 1 0
 
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-0.125000 -0.618718 0.618718 2 0
-
-0.125000 -0.309359 0.309359 2 0
-0.125000 -0.618718 0.618718 2 0
-
-0.125000 -4.16334e-17 0.589645 2 0
-0.125000 -0.334848 0.808395 2 0
-
-0.250000 0.00000 0.673880 2 0
-0.250000 -0.382683 0.923880 2 0
-
-0.250000 -0.353553 0.353553 2 0
-0.250000 -0.707107 0.707107 2 0
-
-0.125000 -4.16334e-17 0.589645 2 0
-0.125000 0.334848 0.808395 2 0
-0.250000 0.382683 0.923880 2 0
-0.250000 0.00000 0.673880 2 0
-0.125000 -4.16334e-17 0.589645 2 0
-
-0.125000 -0.334848 0.808395 2 0
-0.125000 0.00000 0.875000 2 0
-0.250000 0.00000 1.00000 2 0
-0.250000 -0.382683 0.923880 2 0
-0.125000 -0.334848 0.808395 2 0
-
-0.125000 -4.16334e-17 0.589645 2 0
-0.125000 -0.334848 0.808395 2 0
-
-0.125000 0.334848 0.808395 2 0
-0.125000 0.00000 0.875000 2 0
-
-0.250000 0.382683 0.923880 2 0
-0.250000 0.00000 1.00000 2 0
-
-0.250000 0.00000 0.673880 2 0
-0.250000 -0.382683 0.923880 2 0
+0.250000 0.646447 0.00000 1 0
+0.250000 0.500000 -0.500000 1 0
 

diff --git a/tests/bits/cone_03.output b/tests/bits/cone_03.output
index 3a7d634b62a1f4cb0de641684fd32e7ceaf642a5..ff91bde7f59aa1aaae4100703ee3fd7c7a1c1fbc 100644 (file)
--- a/tests/bits/cone_03.output
+++ b/tests/bits/cone_03.output
@@ -6,17 +6,12 @@ DEAL::0
 DEAL::-1.00000 -1.00000: 0.125000 -0.500000
 DEAL::-0.500000 -0.875000: 0.125000 -0.500000
 DEAL::0
-DEAL::-1.00000 0.00000 -1.00000: -0.242536 3.81982e-16 0.970143
-DEAL::-1.00000 -0.382683 -0.923880: -0.242536 0.371257 0.896295
-DEAL::-0.500000 -5.55112e-17 -0.875000: -0.242536 3.81982e-16 0.970143
-DEAL::-0.500000 -0.334848 -0.808395: -0.242536 0.371257 0.896295
-DEAL::0
-DEAL::-1.00000 0.00000 -1.00000: -0.242536 -1.66567e-16 0.970143
-DEAL::-0.500000 -5.55112e-17 -0.875000: -0.242536 -7.15117e-16 0.970143
-DEAL::-1.00000 0.382683 -0.923880: -0.242536 -0.371257 0.896295
-DEAL::-0.500000 0.334848 -0.808395: -0.242536 -0.371257 0.896295
+DEAL::-1.00000 -0.707107 0.707107: -0.242536 0.685994 -0.685994
+DEAL::-0.500000 -0.618718 0.618718: -0.242536 0.685994 -0.685994
+DEAL::-1.00000 -0.923880 0.382683: -0.242536 0.896295 -0.371257
+DEAL::-0.500000 -0.808395 0.334848: -0.242536 0.896295 -0.371257
 DEAL::1
-DEAL::-1.00000 0.00000 -1.00000: 1.00000 0.00000 0.00000
-DEAL::-1.00000 0.382683 -0.923880: 1.00000 0.00000 0.00000
-DEAL::-1.00000 -0.382683 -0.923880: 1.00000 0.00000 0.00000
-DEAL::-1.00000 0.00000 -0.673880: 1.00000 0.00000 0.00000
+DEAL::-1.00000 -0.707107 0.707107: 1.00000 0.00000 0.00000
+DEAL::-1.00000 -0.923880 0.382683: 1.00000 0.00000 0.00000
+DEAL::-1.00000 -0.603553 0.603553: 1.00000 0.00000 0.00000
+DEAL::-1.00000 -0.748551 0.316342: 1.00000 0.00000 0.00000