From: Martin Kronbichler <kronbichler@lnm.mw.tum.de>
Date: Thu, 16 May 2019 13:59:46 +0000 (+0200)
Subject: Update the torus grid and its test case
X-Git-Tag: v9.2.0-rc1~1441^2~4
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=f2432fbc0e06b10cb424aeeb52cdca60350b3614;p=dealii.git

Update the torus grid and its test case
---

diff --git a/include/deal.II/grid/grid_generator.h b/include/deal.II/grid/grid_generator.h
index a3210b3a69..3d7c616c78 100644
--- a/include/deal.II/grid/grid_generator.h
+++ b/include/deal.II/grid/grid_generator.h
@@ -1047,9 +1047,15 @@ namespace GridGenerator
    * Produce the volume or surface mesh of a torus. The axis of the torus is
    * the $y$-axis while the plane of the torus is the $x$-$z$ plane.
    *
-   * If @p dim is 3, the mesh will be the volume of the torus and this
-   * function attaches a TorusManifold to all boundary cells and faces (which
-   * are marked with a manifold id of 0).
+   * If @p dim is 3, the mesh will be the volume of the torus, using a mesh
+   * equivalent to the circle in the poloidal coordinates with 5 cells on the
+   * cross section. This function attaches a TorusManifold to all boundary
+   * faces which are marked with a manifold id of 0, a CylindricalManifold to
+   * the interior cells and all their faces which are marked with a manifold
+   * id of 2 (representing a flat state within the poloidal coordinates), and
+   * a TransfiniteInterpolationManifold to the cells between the TorusManifold
+   * on the surface and the ToroidalManifold in the center, with cells marked
+   * with manifold id 1.
    *
    * If @p dim is 2, the mesh will describe the surface of the torus and this
    * function attaches a TorusManifold to all cells and faces (which are
@@ -1062,11 +1068,17 @@ namespace GridGenerator
    *
    * @param r The inner radius of the torus.
    *
+   * @param n_cells_toroidal Optional argument to set the number of cell
+   * layers in toroidal direction. The default is 6 cell layers.
+   *
    * @note Implemented for Triangulation<2,3> and Triangulation<3,3>.
    */
   template <int dim, int spacedim>
   void
-  torus(Triangulation<dim, spacedim> &tria, const double R, const double r);
+  torus(Triangulation<dim, spacedim> &tria,
+        const double                  R,
+        const double                  r,
+        const unsigned int            n_cells_toroidal = 6);
 
   /**
    * This function produces a square in the <i>xy</i>-plane with a cylindrical
diff --git a/source/grid/grid_generator.cc b/source/grid/grid_generator.cc
index 59f1339eff..91afef6700 100644
--- a/source/grid/grid_generator.cc
+++ b/source/grid/grid_generator.cc
@@ -589,7 +589,10 @@ namespace GridGenerator
 
 
   template <>
-  void torus<2, 3>(Triangulation<2, 3> &tria, const double R, const double r)
+  void torus<2, 3>(Triangulation<2, 3> &tria,
+                   const double         R,
+                   const double         r,
+                   const unsigned int)
   {
     Assert(R > r,
            ExcMessage("Outer radius R must be greater than the inner "
@@ -725,26 +728,111 @@ namespace GridGenerator
     tria.set_manifold(0, TorusManifold<2>(R, r));
   }
 
+
+
   template <>
-  void torus<3, 3>(Triangulation<3, 3> &tria, const double R, const double r)
+  void torus<3, 3>(Triangulation<3, 3> &tria,
+                   const double         R,
+                   const double         r,
+                   const unsigned int   n_cells_toroidal)
   {
     Assert(R > r,
            ExcMessage("Outer radius R must be greater than the inner "
                       "radius r."));
     Assert(r > 0.0, ExcMessage("The inner radius r must be positive."));
+    Assert(n_cells_toroidal > 2,
+           ExcMessage("Number of cells in toroidal direction has "
+                      "to be at least 3."));
+
+    // the first 8 vertices are in the x-y-plane
+    Point<3> const        p = Point<3>(R, 0.0, 0.0);
+    double const          a = 1. / (1 + std::sqrt(2.0));
+    std::vector<Point<3>> vertices(8 * n_cells_toroidal);
+    vertices[0] = p + Point<3>(-1, -1, 0) * (r / std::sqrt(2.0)),
+    vertices[1] = p + Point<3>(+1, -1, 0) * (r / std::sqrt(2.0)),
+    vertices[2] = p + Point<3>(-1, -1, 0) * (r / std::sqrt(2.0) * a),
+    vertices[3] = p + Point<3>(+1, -1, 0) * (r / std::sqrt(2.0) * a),
+    vertices[4] = p + Point<3>(-1, +1, 0) * (r / std::sqrt(2.0) * a),
+    vertices[5] = p + Point<3>(+1, +1, 0) * (r / std::sqrt(2.0) * a),
+    vertices[6] = p + Point<3>(-1, +1, 0) * (r / std::sqrt(2.0)),
+    vertices[7] = p + Point<3>(+1, +1, 0) * (r / std::sqrt(2.0));
+
+    // create remaining vertices by rotating around positive y-axis
+    double phi_cell = 2.0 * numbers::PI / n_cells_toroidal;
+    for (unsigned int c = 1; c < n_cells_toroidal; ++c)
+      {
+        for (unsigned int v = 0; v < 8; ++v)
+          {
+            double const r_2d      = vertices[v][0];
+            vertices[8 * c + v][0] = r_2d * std::cos(phi_cell * c);
+            vertices[8 * c + v][1] = vertices[v][1];
+            vertices[8 * c + v][2] = r_2d * std::sin(phi_cell * c);
+          }
+      }
 
-    // abuse the moebius function to generate a torus for us
-    GridGenerator::moebius(tria, 6 /*n_cells*/, 0 /*n_rotations*/, R, r);
+    // cell connectivity
+    std::vector<CellData<3>> cells(5 * n_cells_toroidal);
+    for (unsigned int c = 0; c < n_cells_toroidal; ++c)
+      {
+        for (unsigned int j = 0; j < 2; ++j)
+          {
+            unsigned int offset = (8 * (c + j)) % (8 * n_cells_toroidal);
+            // cell 0 in x-y-plane
+            cells[5 * c].vertices[0 + j * 4] = offset + 0;
+            cells[5 * c].vertices[1 + j * 4] = offset + 1;
+            cells[5 * c].vertices[2 + j * 4] = offset + 2;
+            cells[5 * c].vertices[3 + j * 4] = offset + 3;
+            // cell 1 in x-y-plane
+            cells[5 * c + 1].vertices[0 + j * 4] = offset + 2;
+            cells[5 * c + 1].vertices[1 + j * 4] = offset + 3;
+            cells[5 * c + 1].vertices[2 + j * 4] = offset + 4;
+            cells[5 * c + 1].vertices[3 + j * 4] = offset + 5;
+            // cell 2 in x-y-plane
+            cells[5 * c + 2].vertices[0 + j * 4] = offset + 4;
+            cells[5 * c + 2].vertices[1 + j * 4] = offset + 5;
+            cells[5 * c + 2].vertices[2 + j * 4] = offset + 6;
+            cells[5 * c + 2].vertices[3 + j * 4] = offset + 7;
+            // cell 3 in x-y-plane
+            cells[5 * c + 3].vertices[0 + j * 4] = offset + 0;
+            cells[5 * c + 3].vertices[1 + j * 4] = offset + 2;
+            cells[5 * c + 3].vertices[2 + j * 4] = offset + 6;
+            cells[5 * c + 3].vertices[3 + j * 4] = offset + 4;
+            // cell 4 in x-y-plane
+            cells[5 * c + 4].vertices[0 + j * 4] = offset + 3;
+            cells[5 * c + 4].vertices[1 + j * 4] = offset + 1;
+            cells[5 * c + 4].vertices[2 + j * 4] = offset + 5;
+            cells[5 * c + 4].vertices[3 + j * 4] = offset + 7;
+          }
 
-    // rotate by 90 degrees around the x axis to make the torus sit in the
-    // x-z plane instead of the x-y plane to be consistent with the other
-    // torus() function.
-    GridTools::rotate(numbers::PI / 2.0, 0, tria);
+        cells[5 * c].material_id     = 0;
+        cells[5 * c + 1].material_id = 0;
+        cells[5 * c + 2].material_id = 0;
+        cells[5 * c + 3].material_id = 0;
+        cells[5 * c + 4].material_id = 0;
+      }
 
-    // set manifolds as documented
-    tria.set_all_manifold_ids(1);
-    tria.set_all_manifold_ids_on_boundary(0);
-    tria.set_manifold(0, TorusManifold<3>(R, r));
+    tria.create_triangulation(vertices, cells, SubCellData());
+
+    tria.reset_all_manifolds();
+    tria.set_all_manifold_ids(0);
+
+    for (auto &cell : tria.cell_iterators())
+      {
+        bool cell_at_boundary = false;
+        for (unsigned int f = 0; f < GeometryInfo<3>::faces_per_cell; ++f)
+          if (cell->at_boundary(f))
+            cell_at_boundary = true;
+        if (cell_at_boundary == false)
+          cell->set_all_manifold_ids(2);
+      }
+    tria.set_all_manifold_ids_on_boundary(1);
+    tria.set_manifold(1, TorusManifold<3>(2, 0.5));
+    tria.set_manifold(2,
+                      CylindricalManifold<3>(Tensor<1, 3>({0., 1., 0.}),
+                                             Point<3>()));
+    TransfiniteInterpolationManifold<3> transfinite;
+    transfinite.initialize(tria);
+    tria.set_manifold(0, transfinite);
   }
 
 
diff --git a/tests/grid/torus_01.cc b/tests/grid/torus_01.cc
index 69b300d761..84fd25bebc 100644
--- a/tests/grid/torus_01.cc
+++ b/tests/grid/torus_01.cc
@@ -1,6 +1,6 @@
 // ---------------------------------------------------------------------
 //
-// Copyright (C) 2016 - 2018 by the deal.II authors
+// Copyright (C) 2016 - 2019 by the deal.II authors
 //
 // This file is part of the deal.II library.
 //
@@ -13,7 +13,9 @@
 //
 // ---------------------------------------------------------------------
 
-// test GridTools::torus() and TorusManifold, output visually checked
+// test GridTools::torus() the manifolds attached to the torus (TorusManifold,
+// ToriodalManifold, TransfiniteInterpolationManifold), output visually
+// checked
 
 #include <deal.II/grid/grid_generator.h>
 #include <deal.II/grid/grid_out.h>
@@ -38,7 +40,6 @@ test<3, 3>()
   Triangulation<dim, spacedim> triangulation;
 
   GridGenerator::torus(triangulation, 1.0, 0.4);
-  triangulation.set_manifold(1, SphericalManifold<3>());
 
   triangulation.begin_active()->set_refine_flag();
   triangulation.execute_coarsening_and_refinement();
diff --git a/tests/grid/torus_01.output b/tests/grid/torus_01.output
index 6f0ecd3680..86372b65c9 100644
--- a/tests/grid/torus_01.output
+++ b/tests/grid/torus_01.output
@@ -1,332 +1,916 @@
 
-set arrow from 1.40000, 0.00000, 0.00000 rto 1.77636e-16, 0.359039, 1.75929
-set arrow from 1.00000, 0.400000, -2.44929e-17 rto 0.269279, 1.91913e-16, 1.25664
-set arrow from 0.300000, -1.71686e-17, 0.519615 rto -0.108828, 0.897598, 0.0628319
-set arrow from -0.500000, -0.400000, 0.866025 rto 0.231841, -5.11243e-16, 1.27396
-set arrow from -1.40000, 1.04983e-32, 1.71451e-16 rto 1.45541e-16, 0.359039, 2.63894
-set arrow from -1.00000, 0.400000, 9.79717e-17 rto -0.269279, 1.91913e-16, 1.88496
-set arrow from -0.300000, -8.08031e-17, -0.519615 rto -1.52359, 0.897598, 0.879646
-set arrow from 0.500000, -0.400000, -0.866025 rto 2.48886, 6.04582e-17, 0.296840
-set arrow from 1.28284, -0.282843, 1.57103e-17 rto 0.476023, 0.476023, 1.61207
-set arrow from 0.717157, 0.282843, -1.75653e-16 rto 0.412553, 0.412553, 0.901206
+set arrow from 0.717157, -0.282843, 0.00000 rto -0.856842, 0.856842, 0.901206
+set arrow from 1.11716, -0.117157, 0.00000 rto 0.362861, 0.0314898, 1.40386
+set arrow from 0.717157, 0.282843, 0.00000 rto 0.412553, 0.412553, 0.901206
+set arrow from 0.641421, -0.282843, 1.11097 rto 0.00532966, 0.476023, 0.546587
+set arrow from 0.441421, 0.117157, 0.764564 rto -0.157530, 0.336571, 0.0969542
 set arrow from 0.641421, 0.282843, 1.11097 rto -0.248549, 0.0317349, 0.106856
-set arrow from 0.519615, 4.89859e-17, 0.300000 rto -0.219911, 0.897598, 0.380898
-set arrow from 1.04605, 2.90339e-17, -2.43399e-16 rto 0.353945, 0.0413389, 1.31451
-set arrow from 0.523027, 5.80677e-17, 0.905910 rto -0.0127609, 0.0413389, 0.416068
-set arrow from 0.905910, -5.58405e-17, 0.523027 rto -0.0768738, 0.0413389, 0.841039
+set arrow from -0.441421, -0.117157, 0.764564 rto 0.900820, 0.189230, -0.0810493
+set arrow from -0.558579, 0.117157, 0.967487 rto 0.734249, 0.178830, 0.600058
+set arrow from -0.717157, -0.282843, 8.78264e-17 rto 0.856842, 0.856842, 1.35181
+set arrow from -1.11716, -0.117157, 1.36812e-16 rto -0.362861, 0.0314898, 2.10579
+set arrow from -0.717157, 0.282843, 8.78264e-17 rto -0.412553, 0.412553, 1.35181
+set arrow from -0.641421, -0.282843, -1.11097 rto -3.49556, 0.476023, 1.46850
+set arrow from -0.441421, 0.117157, -0.764564 rto -2.24442, 0.336571, 1.28981
+set arrow from -0.641421, 0.282843, -1.11097 rto -3.24168, 0.0317349, 1.90823
+set arrow from 0.441421, -0.117157, -0.764564 rto 1.50113, 0.189230, 1.46782
+set arrow from 0.558579, 0.117157, -0.967487 rto 2.30520, 0.178830, 1.15477
+set arrow from 1.00314, -0.304367, 0.00000 rto 0.749141, -0.0878816, 1.26059
+set arrow from 1.20000, -0.200000, -8.81836e-16 rto 0.419442, 0.253757, 1.50796
+set arrow from 0.764564, -0.117157, 0.441421 rto -0.774432, 0.189230, 0.300154
+set arrow from 0.400000, -0.200000, 0.692820 rto -0.489465, 0.523036, -0.512674
+set arrow from 0.868749, -0.304367, 0.501572 rto 0.281103, -0.0878816, 1.01140
+set arrow from 1.03923, -0.200000, 0.600000 rto -0.0765756, 0.253757, 0.971517
+set arrow from 0.867387, -0.210762, 0.500786 rto 0.0833099, -0.185357, 0.895870
 set view equal xyz
 splot '-' w l
--0.700000 7.42403e-17 1.21244 0 0
--0.500000 0.400000 0.866025 0 0
--0.300000 -1.71686e-17 0.519615 0 0
--0.500000 -0.400000 0.866025 0 0
--0.700000 7.42403e-17 1.21244 0 0
-
-0.700000 7.42403e-17 1.21244 0 0
-0.500000 0.400000 0.866025 0 0
-0.300000 -1.71686e-17 0.519615 0 0
-0.500000 -0.400000 0.866025 0 0
-0.700000 7.42403e-17 1.21244 0 0
-
--0.700000 7.42403e-17 1.21244 0 0
-0.700000 7.42403e-17 1.21244 0 0
+0.882843 -0.117157 0.00000 0 0
+1.11716 -0.117157 0.00000 0 0
+0.558579 -0.117157 0.967487 0 0
+0.441421 -0.117157 0.764564 0 0
+0.882843 -0.117157 0.00000 0 0
+
+0.882843 0.117157 0.00000 0 0
+1.11716 0.117157 0.00000 0 0
+0.558579 0.117157 0.967487 0 0
+0.441421 0.117157 0.764564 0 0
+0.882843 0.117157 0.00000 0 0
+
+0.882843 -0.117157 0.00000 0 0
+0.882843 0.117157 0.00000 0 0
 
--0.500000 0.400000 0.866025 0 0
-0.500000 0.400000 0.866025 0 0
+1.11716 -0.117157 0.00000 0 0
+1.11716 0.117157 0.00000 0 0
 
--0.300000 -1.71686e-17 0.519615 0 0
-0.300000 -1.71686e-17 0.519615 0 0
+0.558579 -0.117157 0.967487 0 0
+0.558579 0.117157 0.967487 0 0
 
--0.500000 -0.400000 0.866025 0 0
-0.500000 -0.400000 0.866025 0 0
+0.441421 -0.117157 0.764564 0 0
+0.441421 0.117157 0.764564 0 0
+
+0.882843 0.117157 0.00000 0 0
+1.11716 0.117157 0.00000 0 0
+0.558579 0.117157 0.967487 0 0
+0.441421 0.117157 0.764564 0 0
+0.882843 0.117157 0.00000 0 0
+
+0.717157 0.282843 0.00000 0 0
+1.28284 0.282843 0.00000 0 0
+0.641421 0.282843 1.11097 0 0
+0.358579 0.282843 0.621076 0 0
+0.717157 0.282843 0.00000 0 0
+
+0.882843 0.117157 0.00000 0 0
+0.717157 0.282843 0.00000 0 0
 
--1.40000 1.04983e-32 1.71451e-16 0 0
--1.00000 0.400000 9.79717e-17 0 0
--0.600000 -4.89859e-17 7.34788e-17 0 0
--1.00000 -0.400000 1.46958e-16 0 0
--1.40000 1.04983e-32 1.71451e-16 0 0
+1.11716 0.117157 0.00000 0 0
+1.28284 0.282843 0.00000 0 0
 
--0.700000 7.42403e-17 1.21244 0 0
--0.500000 0.400000 0.866025 0 0
--0.300000 -1.71686e-17 0.519615 0 0
--0.500000 -0.400000 0.866025 0 0
--0.700000 7.42403e-17 1.21244 0 0
+0.558579 0.117157 0.967487 0 0
+0.641421 0.282843 1.11097 0 0
 
--1.40000 1.04983e-32 1.71451e-16 0 0
--0.700000 7.42403e-17 1.21244 0 0
+0.441421 0.117157 0.764564 0 0
+0.358579 0.282843 0.621076 0 0
+
+0.717157 -0.282843 0.00000 0 0
+0.882843 -0.117157 0.00000 0 0
+0.441421 -0.117157 0.764564 0 0
+0.358579 -0.282843 0.621076 0 0
+0.717157 -0.282843 0.00000 0 0
+
+0.717157 0.282843 0.00000 0 0
+0.882843 0.117157 0.00000 0 0
+0.441421 0.117157 0.764564 0 0
+0.358579 0.282843 0.621076 0 0
+0.717157 0.282843 0.00000 0 0
+
+0.717157 -0.282843 0.00000 0 0
+0.717157 0.282843 0.00000 0 0
 
--1.00000 0.400000 9.79717e-17 0 0
--0.500000 0.400000 0.866025 0 0
+0.882843 -0.117157 0.00000 0 0
+0.882843 0.117157 0.00000 0 0
 
--0.600000 -4.89859e-17 7.34788e-17 0 0
--0.300000 -1.71686e-17 0.519615 0 0
+0.441421 -0.117157 0.764564 0 0
+0.441421 0.117157 0.764564 0 0
 
--1.00000 -0.400000 1.46958e-16 0 0
--0.500000 -0.400000 0.866025 0 0
+0.358579 -0.282843 0.621076 0 0
+0.358579 0.282843 0.621076 0 0
+
+1.11716 -0.117157 0.00000 0 0
+1.28284 -0.282843 0.00000 0 0
+0.641421 -0.282843 1.11097 0 0
+0.558579 -0.117157 0.967487 0 0
+1.11716 -0.117157 0.00000 0 0
+
+1.11716 0.117157 0.00000 0 0
+1.28284 0.282843 0.00000 0 0
+0.641421 0.282843 1.11097 0 0
+0.558579 0.117157 0.967487 0 0
+1.11716 0.117157 0.00000 0 0
+
+1.11716 -0.117157 0.00000 0 0
+1.11716 0.117157 0.00000 0 0
 
--0.700000 -7.42403e-17 -1.21244 0 0
--0.500000 0.400000 -0.866025 0 0
--0.300000 -8.08031e-17 -0.519615 0 0
--0.500000 -0.400000 -0.866025 0 0
--0.700000 -7.42403e-17 -1.21244 0 0
+1.28284 -0.282843 0.00000 0 0
+1.28284 0.282843 0.00000 0 0
 
--1.40000 1.04983e-32 1.71451e-16 0 0
--1.00000 0.400000 9.79717e-17 0 0
--0.600000 -4.89859e-17 7.34788e-17 0 0
--1.00000 -0.400000 1.46958e-16 0 0
--1.40000 1.04983e-32 1.71451e-16 0 0
+0.641421 -0.282843 1.11097 0 0
+0.641421 0.282843 1.11097 0 0
 
--0.700000 -7.42403e-17 -1.21244 0 0
--1.40000 1.04983e-32 1.71451e-16 0 0
+0.558579 -0.117157 0.967487 0 0
+0.558579 0.117157 0.967487 0 0
+
+0.358579 -0.282843 0.621076 0 0
+0.641421 -0.282843 1.11097 0 0
+-0.641421 -0.282843 1.11097 0 0
+-0.358579 -0.282843 0.621076 0 0
+0.358579 -0.282843 0.621076 0 0
+
+0.441421 -0.117157 0.764564 0 0
+0.558579 -0.117157 0.967487 0 0
+-0.558579 -0.117157 0.967487 0 0
+-0.441421 -0.117157 0.764564 0 0
+0.441421 -0.117157 0.764564 0 0
 
--0.500000 0.400000 -0.866025 0 0
--1.00000 0.400000 9.79717e-17 0 0
+0.358579 -0.282843 0.621076 0 0
+0.441421 -0.117157 0.764564 0 0
 
--0.300000 -8.08031e-17 -0.519615 0 0
--0.600000 -4.89859e-17 7.34788e-17 0 0
+0.641421 -0.282843 1.11097 0 0
+0.558579 -0.117157 0.967487 0 0
 
--0.500000 -0.400000 -0.866025 0 0
--1.00000 -0.400000 1.46958e-16 0 0
+-0.641421 -0.282843 1.11097 0 0
+-0.558579 -0.117157 0.967487 0 0
 
-0.700000 -7.42403e-17 -1.21244 0 0
-0.500000 0.400000 -0.866025 0 0
-0.300000 -8.08031e-17 -0.519615 0 0
-0.500000 -0.400000 -0.866025 0 0
-0.700000 -7.42403e-17 -1.21244 0 0
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