Interestingly, mesh refinement of surfaces in higher spaces produced the wrong result...

git-svn-id: https://svn.dealii.org/trunk@22811 0785d39b-7218-0410-832d-ea1e28bc413d

diff --git a/deal.II/doc/news/changes.h b/deal.II/doc/news/changes.h
index 642e959a304e70c356ab50a850dc2f17fd178bf1..2be99ffac4407413d8c6a8d41466310f44dd3f00 100644 (file)
--- a/deal.II/doc/news/changes.h
+++ b/deal.II/doc/news/changes.h
@@ -379,6 +379,14 @@ independent of the dimension.
 <h3>deal.II</h3>
 
 <ol>
+  <li><p>Fixed: Triangulation::execute_coarsening_and_refinement misplaced
+  the new central vertex of a quad in a two-dimensional mesh embedded into
+  higher dimensional space if said quad was at the boundary of the surface
+  described by this triangulation. This is now fixed.
+  <br>
+  (WB, 2010/11/18)
+  </p></li>
+
   <li><p>New: The GridTools::extract_boundary_mesh function can be used to
   generate a surface mesh from the boundary of a volume mesh.
   <br>

diff --git a/deal.II/source/grid/tria.cc b/deal.II/source/grid/tria.cc
index cec3bde55fd02f840473a865fdf2852747bdeb89..c5783dadb17200a1e570c97871645681cddafb0f 100644 (file)
--- a/deal.II/source/grid/tria.cc
+++ b/deal.II/source/grid/tria.cc
@@ -1407,6 +1407,9 @@ namespace internal
                              const SubCellData                   &/*subcelldata*/,
                              Triangulation<1,spacedim>           &triangulation)
          {
+           AssertThrow (v.size() > 0, ExcMessage ("No vertices given"));
+           AssertThrow (cells.size() > 0, ExcMessage ("No cells given"));
+
                                             // note: since no boundary
                                             // information can be given in one
                                             // dimension, the @p{subcelldata}
@@ -1544,6 +1547,9 @@ namespace internal
                              const SubCellData                   &subcelldata,
                              Triangulation<2,spacedim>           &triangulation)
          {
+           AssertThrow (v.size() > 0, ExcMessage ("No vertices given"));
+           AssertThrow (cells.size() > 0, ExcMessage ("No cells given"));
+
            const unsigned int dim=2;
 
                                             // copy vertices
@@ -1847,6 +1853,9 @@ namespace internal
                              const SubCellData                   &subcelldata,
                              Triangulation<3,spacedim>           &triangulation)
          {
+           AssertThrow (v.size() > 0, ExcMessage ("No vertices given"));
+           AssertThrow (cells.size() > 0, ExcMessage ("No cells given"));
+
            const unsigned int dim=3;
 
                                             // copy vertices
@@ -3812,11 +3821,25 @@ namespace internal
    .--.--.
 */
 
-                                            // collect the indices
-                                            // all vertices
+                                            // find the next
+                                            // unused vertex and
+                                            // allocate it for
+                                            // the new vertex we
+                                            // need here
+           while (triangulation.vertices_used[next_unused_vertex] == true)
+             ++next_unused_vertex;
+           Assert (next_unused_vertex < triangulation.vertices.size(),
+                   ExcTooFewVerticesAllocated());
+           triangulation.vertices_used[next_unused_vertex] = true;
+
+                                            // collect the
+                                            // indices of the
+                                            // eight
+                                            // surrounding
+                                            // vertices
                                             //   2--7--3
                                             //   |  |  |
-                                            //   4--8--5
+                                            //   4--9--5
                                             //   |  |  |
                                             //   0--6--1
            int new_vertices[9];
@@ -3825,94 +3848,120 @@ namespace internal
            for (unsigned int line_no=0; line_no<4; ++line_no)
              if (cell->line(line_no)->has_children())
                new_vertices[4+line_no]=cell->line(line_no)->child(0)->vertex_index(1);
+           new_vertices[8] = next_unused_vertex;
 
            if (ref_case==RefinementCase<dim>::cut_xy)
              {
-                                                // find the next
-                                                // unused vertex and
-                                                // set it
-                                                // appropriately
-               while (triangulation.vertices_used[next_unused_vertex] == true)
-                 ++next_unused_vertex;
-               Assert (next_unused_vertex < triangulation.vertices.size(),
-                       ExcTooFewVerticesAllocated());
-               triangulation.vertices_used[next_unused_vertex] = true;
-
-               new_vertices[8]=next_unused_vertex;
-
-               Point<spacedim> new_point;
+                                                // if this quad lives
+                                                // in 2d, then we can
+                                                // compute the new
+                                                // central vertex
+                                                // location just from
+                                                // the surrounding
+                                                // ones. If this is
+                                                // not the case, then
+                                                // we need to ask a
+                                                // boundary object
                if (dim == spacedim)
                  {
+                                                    // in a first
+                                                    // step, compute
+                                                    // the location
+                                                    // of central
+                                                    // vertex as the
+                                                    // average of the
+                                                    // 8 surrounding
+                                                    // vertices
+                   Point<spacedim> new_point;
                    for (unsigned int i=0; i<8; ++i)
                      new_point += triangulation.vertices[new_vertices[i]];
                    new_point /= 8.0;
+
+                   triangulation.vertices[next_unused_vertex] = new_point;
+
+                                                    // if the user_flag is set, i.e. if the
+                                                    // cell is at the boundary, use a
+                                                    // different calculation of the middle
+                                                    // vertex here. this is of advantage, if
+                                                    // the boundary is strongly curved and
+                                                    // the cell has a high aspect ratio. this
+                                                    // can happen for example, if it was
+                                                    // refined anisotropically before.
+                   if (cell->user_flag_set())
+                     {
+                                                        // first reset the user_flag
+                       cell->clear_user_flag();
+                                                        // the user flag indicates: at least
+                                                        // one face is at the boundary. if it
+                                                        // is only one, set the new middle
+                                                        // vertex in a different way to avoid
+                                                        // some mis-shaped elements if the
+                                                        // new point on the boundary is not
+                                                        // where we expect it, especially if
+                                                        // it is to far inside the current
+                                                        // cell
+                       unsigned int boundary_face=GeometryInfo<dim>::faces_per_cell;
+                       for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+                         if (cell->face(face)->at_boundary())
+                           {
+                             if (boundary_face == GeometryInfo<dim>::faces_per_cell)
+                                                                // no boundary face found so
+                                                                // far, so set it now
+                               boundary_face=face;
+                             else
+                                                                // there is another boundary
+                                                                // face, so reset boundary_face to
+                                                                // invalid value as a flag to
+                                                                // do nothing in the following
+                               boundary_face=GeometryInfo<dim>::faces_per_cell+1;
+                           }
+
+                       if (boundary_face<GeometryInfo<dim>::faces_per_cell)
+                                                          // reset the cell's middle vertex
+                                                          // to the middle of the straight
+                                                          // connection between the new
+                                                          // points on this face and on the
+                                                          // opposite face
+                         triangulation.vertices[next_unused_vertex]
+                           = 0.5*(cell->face(boundary_face)
+                                  ->child(0)->vertex(1)+
+                                  cell->face(GeometryInfo<dim>
+                                             ::opposite_face[boundary_face])
+                                  ->child(0)->vertex(1));
+                     }
                  }
                else
                  {
+                                                    // if this quad
+                                                    // lives in a
+                                                    // higher
+                                                    // dimensional
+                                                    // space then we
+                                                    // don't need to
+                                                    // worry if it is
+                                                    // at the
+                                                    // boundary of
+                                                    // the manifold
+                                                    // -- we always
+                                                    // have to use
+                                                    // the boundary
+                                                    // object anyway;
+                                                    // so ignore
+                                                    // whether the
+                                                    // user flag is
+                                                    // set or not
+                   cell->clear_user_flag();
+
                                                     // new vertex is
                                                     // placed on the
                                                     // surface according
                                                     // to the information
                                                     // stored in the
                                                     // boundary class
-                   new_point =
+                   triangulation.vertices[next_unused_vertex] =
                      triangulation.boundary[cell->material_id()]
                      ->get_new_point_on_quad (cell);
                  }
-
-               triangulation.vertices[new_vertices[8]] = new_point;
-
-
-                                                // if the user_flag is set, i.e. if the
-                                                // cell is at the boundary, use a
-                                                // different calculation of the middle
-                                                // vertex here. this is of advantage, if
-                                                // the boundary is strongly curved and
-                                                // the cell has a high aspect ratio. this
-                                                // can happen for example, if it was
-                                                // refined anisotropically before.
-               if (cell->user_flag_set())
-                 {
-                                                    // first reset the user_flag
-                   cell->clear_user_flag();
-                                                    // the user flag indicates: at least
-                                                    // one face is at the boundary. if it
-                                                    // is only one, set the new middle
-                                                    // vertex in a different way to avoid
-                                                    // some mis-shaped elements if the
-                                                    // new point on the boundary is not
-                                                    // where we expect it, especially if
-                                                    // it is to far inside the current
-                                                    // cell
-                   unsigned int bound_face=GeometryInfo<dim>::faces_per_cell;
-                   for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
-                     if (cell->face(face)->at_boundary())
-                       {
-                         if (bound_face == GeometryInfo<dim>::faces_per_cell)
-                                                            // no boundary face found so
-                                                            // far, so set it now
-                           bound_face=face;
-                         else
-                                                            // there is another boundary
-                                                            // face, so reset bound_face to
-                                                            // invalid value as a flag to
-                                                            // do nothing in the following
-                           bound_face=GeometryInfo<dim>::faces_per_cell+1;
-                       }
-
-                   if (bound_face<GeometryInfo<dim>::faces_per_cell)
-                                                      // reset the cell's middle vertex
-                                                      // to the middle of the straight
-                                                      // connection between the new
-                                                      // points on this face and on the
-                                                      // opposite face
-                     triangulation.vertices[new_vertices[8]]
-                       = 0.5*(cell->face(bound_face)
-                              ->child(0)->vertex(1)+
-                              cell->face(GeometryInfo<dim>
-                                         ::opposite_face[bound_face])
-                              ->child(0)->vertex(1));
-                 }
              }
 
 

diff --git a/tests/codim_one/extract_boundary_mesh_04.cc b/tests/codim_one/extract_boundary_mesh_04.cc
index 6a034703132dbdacdb8c0eb21af60e36bd9254fa..2bac4696be19c407dbfe195a81ff3c89d3271ca3 100644 (file)
--- a/tests/codim_one/extract_boundary_mesh_04.cc
+++ b/tests/codim_one/extract_boundary_mesh_04.cc
@@ -107,30 +107,29 @@ int main ()
       for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
        if (cell->at_boundary(f) && (cell->center()[dim-1]>0))
          cell->face(f)->set_all_boundary_indicators (1);
-    
+
     volume_mesh.set_boundary (1, boundary_description);
     volume_mesh.set_boundary (0, boundary_description);
-    volume_mesh.refine_global (3);
+    volume_mesh.refine_global (1);
 
     const HyperBallBoundary<dim-1,dim> surface_description;
     Triangulation<dim-1,dim> boundary_mesh;
     boundary_mesh.set_boundary (1, surface_description);
     boundary_mesh.set_boundary (0, surface_description);
-   
+
     set<unsigned char> boundary_ids;
     boundary_ids.insert(1);
-    
+
     GridTools::extract_boundary_mesh (volume_mesh, boundary_mesh,
                                      surface_to_volume_mapping,
                                      boundary_ids);
 
     deallog << volume_mesh.n_active_cells () << std::endl;
     deallog << boundary_mesh.n_active_cells () << std::endl;
-    //save_mesh(boundary_mesh);
-
+    deallog << "Surface mesh:" << std::endl;
+    save_mesh(boundary_mesh);
 
     test_vertices_orientation(boundary_mesh, surface_to_volume_mapping);
-    //save_mesh(boundary_mesh);
   }
 
 

diff --git a/tests/codim_one/extract_boundary_mesh_04/cmp/generic b/tests/codim_one/extract_boundary_mesh_04/cmp/generic
new file mode 100644 (file)
index 0000000..6c7fcad
--- /dev/null
+++ b/tests/codim_one/extract_boundary_mesh_04/cmp/generic
@@ -0,0 +1,345 @@
+
+DEAL::Testing hyper_cube in dim: 3...
+DEAL::56
+DEAL::20
+DEAL::Surface mesh:
+0.577350 -0.577350 -0.577350 1 1
+0.707107 -0.707107 0.00000 1 1
+1.00000 0.00000 0.00000 1 1
+0.707107 0.00000 -0.707107 1 1
+0.577350 -0.577350 -0.577350 1 1
+
+
+0.707107 -0.707107 0.00000 1 1
+0.577350 -0.577350 0.577350 1 1
+0.707107 0.00000 0.707107 1 1
+1.00000 0.00000 0.00000 1 1
+0.707107 -0.707107 0.00000 1 1
+
+
+0.707107 0.00000 -0.707107 1 1
+1.00000 0.00000 0.00000 1 1
+0.707107 0.707107 0.00000 1 1
+0.577350 0.577350 -0.577350 1 1
+0.707107 0.00000 -0.707107 1 1
+
+
+1.00000 0.00000 0.00000 1 1
+0.707107 0.00000 0.707107 1 1
+0.577350 0.577350 0.577350 1 1
+0.707107 0.707107 0.00000 1 1
+1.00000 0.00000 0.00000 1 1
+
+
+-0.577350 -0.577350 0.577350 1 1
+-0.707107 0.00000 0.707107 1 1
+0.00000 0.00000 1.00000 1 1
+0.00000 -0.707107 0.707107 1 1
+-0.577350 -0.577350 0.577350 1 1
+
+
+-0.707107 0.00000 0.707107 1 1
+-0.577350 0.577350 0.577350 1 1
+0.00000 0.707107 0.707107 1 1
+0.00000 0.00000 1.00000 1 1
+-0.707107 0.00000 0.707107 1 1
+
+
+0.00000 -0.707107 0.707107 1 1
+0.00000 0.00000 1.00000 1 1
+0.707107 0.00000 0.707107 1 1
+0.577350 -0.577350 0.577350 1 1
+0.00000 -0.707107 0.707107 1 1
+
+
+0.00000 0.00000 1.00000 1 1
+0.00000 0.707107 0.707107 1 1
+0.577350 0.577350 0.577350 1 1
+0.707107 0.00000 0.707107 1 1
+0.00000 0.00000 1.00000 1 1
+
+
+-0.577350 -0.577350 -0.577350 1 1
+-0.707107 0.00000 -0.707107 1 1
+-1.00000 0.00000 0.00000 1 1
+-0.707107 -0.707107 0.00000 1 1
+-0.577350 -0.577350 -0.577350 1 1
+
+
+-0.707107 0.00000 -0.707107 1 1
+-0.577350 0.577350 -0.577350 1 1
+-0.707107 0.707107 0.00000 1 1
+-1.00000 0.00000 0.00000 1 1
+-0.707107 0.00000 -0.707107 1 1
+
+
+-0.707107 -0.707107 0.00000 1 1
+-1.00000 0.00000 0.00000 1 1
+-0.707107 0.00000 0.707107 1 1
+-0.577350 -0.577350 0.577350 1 1
+-0.707107 -0.707107 0.00000 1 1
+
+
+-1.00000 0.00000 0.00000 1 1
+-0.707107 0.707107 0.00000 1 1
+-0.577350 0.577350 0.577350 1 1
+-0.707107 0.00000 0.707107 1 1
+-1.00000 0.00000 0.00000 1 1
+
+
+-0.577350 -0.577350 -0.577350 1 1
+-0.707107 -0.707107 0.00000 1 1
+0.00000 -1.00000 0.00000 1 1
+0.00000 -0.707107 -0.707107 1 1
+-0.577350 -0.577350 -0.577350 1 1
+
+
+-0.707107 -0.707107 0.00000 1 1
+-0.577350 -0.577350 0.577350 1 1
+0.00000 -0.707107 0.707107 1 1
+0.00000 -1.00000 0.00000 1 1
+-0.707107 -0.707107 0.00000 1 1
+
+
+0.00000 -0.707107 -0.707107 1 1
+0.00000 -1.00000 0.00000 1 1
+0.707107 -0.707107 0.00000 1 1
+0.577350 -0.577350 -0.577350 1 1
+0.00000 -0.707107 -0.707107 1 1
+
+
+0.00000 -1.00000 0.00000 1 1
+0.00000 -0.707107 0.707107 1 1
+0.577350 -0.577350 0.577350 1 1
+0.707107 -0.707107 0.00000 1 1
+0.00000 -1.00000 0.00000 1 1
+
+
+-0.577350 0.577350 -0.577350 1 1
+0.00000 0.707107 -0.707107 1 1
+0.00000 1.00000 0.00000 1 1
+-0.707107 0.707107 0.00000 1 1
+-0.577350 0.577350 -0.577350 1 1
+
+
+0.00000 0.707107 -0.707107 1 1
+0.577350 0.577350 -0.577350 1 1
+0.707107 0.707107 0.00000 1 1
+0.00000 1.00000 0.00000 1 1
+0.00000 0.707107 -0.707107 1 1
+
+
+-0.707107 0.707107 0.00000 1 1
+0.00000 1.00000 0.00000 1 1
+0.00000 0.707107 0.707107 1 1
+-0.577350 0.577350 0.577350 1 1
+-0.707107 0.707107 0.00000 1 1
+
+
+0.00000 1.00000 0.00000 1 1
+0.707107 0.707107 0.00000 1 1
+0.577350 0.577350 0.577350 1 1
+0.00000 0.707107 0.707107 1 1
+0.00000 1.00000 0.00000 1 1
+
+
+DEAL::Surface cell: 1.0 with vertices:
+DEAL::  0.577350 -0.577350 -0.577350
+DEAL::  0.707107 -0.707107 0.00000
+DEAL::  0.707107 0.00000 -0.707107
+DEAL::  1.00000 0.00000 0.00000
+DEAL::Volume face: 80 with vertices:
+DEAL::  0.577350 -0.577350 -0.577350
+DEAL::  0.707107 -0.707107 0.00000
+DEAL::  0.707107 0.00000 -0.707107
+DEAL::  1.00000 0.00000 0.00000
+DEAL::Surface cell: 1.1 with vertices:
+DEAL::  0.707107 -0.707107 0.00000
+DEAL::  0.577350 -0.577350 0.577350
+DEAL::  1.00000 0.00000 0.00000
+DEAL::  0.707107 0.00000 0.707107
+DEAL::Volume face: 81 with vertices:
+DEAL::  0.707107 -0.707107 0.00000
+DEAL::  0.577350 -0.577350 0.577350
+DEAL::  1.00000 0.00000 0.00000
+DEAL::  0.707107 0.00000 0.707107
+DEAL::Surface cell: 1.2 with vertices:
+DEAL::  0.707107 0.00000 -0.707107
+DEAL::  1.00000 0.00000 0.00000
+DEAL::  0.577350 0.577350 -0.577350
+DEAL::  0.707107 0.707107 0.00000
+DEAL::Volume face: 82 with vertices:
+DEAL::  0.707107 0.00000 -0.707107
+DEAL::  1.00000 0.00000 0.00000
+DEAL::  0.577350 0.577350 -0.577350
+DEAL::  0.707107 0.707107 0.00000
+DEAL::Surface cell: 1.3 with vertices:
+DEAL::  1.00000 0.00000 0.00000
+DEAL::  0.707107 0.00000 0.707107
+DEAL::  0.707107 0.707107 0.00000
+DEAL::  0.577350 0.577350 0.577350
+DEAL::Volume face: 83 with vertices:
+DEAL::  1.00000 0.00000 0.00000
+DEAL::  0.707107 0.00000 0.707107
+DEAL::  0.707107 0.707107 0.00000
+DEAL::  0.577350 0.577350 0.577350
+DEAL::Surface cell: 1.4 with vertices:
+DEAL::  -0.577350 -0.577350 0.577350
+DEAL::  -0.707107 0.00000 0.707107
+DEAL::  0.00000 -0.707107 0.707107
+DEAL::  0.00000 0.00000 1.00000
+DEAL::Volume face: 92 with vertices:
+DEAL::  -0.577350 -0.577350 0.577350
+DEAL::  -0.707107 0.00000 0.707107
+DEAL::  0.00000 -0.707107 0.707107
+DEAL::  0.00000 0.00000 1.00000
+DEAL::Surface cell: 1.5 with vertices:
+DEAL::  -0.707107 0.00000 0.707107
+DEAL::  -0.577350 0.577350 0.577350
+DEAL::  0.00000 0.00000 1.00000
+DEAL::  0.00000 0.707107 0.707107
+DEAL::Volume face: 93 with vertices:
+DEAL::  -0.707107 0.00000 0.707107
+DEAL::  -0.577350 0.577350 0.577350
+DEAL::  0.00000 0.00000 1.00000
+DEAL::  0.00000 0.707107 0.707107
+DEAL::Surface cell: 1.6 with vertices:
+DEAL::  0.00000 -0.707107 0.707107
+DEAL::  0.00000 0.00000 1.00000
+DEAL::  0.577350 -0.577350 0.577350
+DEAL::  0.707107 0.00000 0.707107
+DEAL::Volume face: 94 with vertices:
+DEAL::  0.00000 -0.707107 0.707107
+DEAL::  0.00000 0.00000 1.00000
+DEAL::  0.577350 -0.577350 0.577350
+DEAL::  0.707107 0.00000 0.707107
+DEAL::Surface cell: 1.7 with vertices:
+DEAL::  0.00000 0.00000 1.00000
+DEAL::  0.00000 0.707107 0.707107
+DEAL::  0.707107 0.00000 0.707107
+DEAL::  0.577350 0.577350 0.577350
+DEAL::Volume face: 95 with vertices:
+DEAL::  0.00000 0.00000 1.00000
+DEAL::  0.00000 0.707107 0.707107
+DEAL::  0.707107 0.00000 0.707107
+DEAL::  0.577350 0.577350 0.577350
+DEAL::Surface cell: 1.8 with vertices:
+DEAL::  -0.577350 -0.577350 -0.577350
+DEAL::  -0.707107 0.00000 -0.707107
+DEAL::  -0.707107 -0.707107 0.00000
+DEAL::  -1.00000 0.00000 0.00000
+DEAL::Volume face: 64 with vertices:
+DEAL::  -0.577350 -0.577350 -0.577350
+DEAL::  -0.707107 0.00000 -0.707107
+DEAL::  -0.707107 -0.707107 0.00000
+DEAL::  -1.00000 0.00000 0.00000
+DEAL::Surface cell: 1.9 with vertices:
+DEAL::  -0.707107 0.00000 -0.707107
+DEAL::  -0.577350 0.577350 -0.577350
+DEAL::  -1.00000 0.00000 0.00000
+DEAL::  -0.707107 0.707107 0.00000
+DEAL::Volume face: 65 with vertices:
+DEAL::  -0.707107 0.00000 -0.707107
+DEAL::  -0.577350 0.577350 -0.577350
+DEAL::  -1.00000 0.00000 0.00000
+DEAL::  -0.707107 0.707107 0.00000
+DEAL::Surface cell: 1.10 with vertices:
+DEAL::  -0.707107 -0.707107 0.00000
+DEAL::  -1.00000 0.00000 0.00000
+DEAL::  -0.577350 -0.577350 0.577350
+DEAL::  -0.707107 0.00000 0.707107
+DEAL::Volume face: 66 with vertices:
+DEAL::  -0.707107 -0.707107 0.00000
+DEAL::  -1.00000 0.00000 0.00000
+DEAL::  -0.577350 -0.577350 0.577350
+DEAL::  -0.707107 0.00000 0.707107
+DEAL::Surface cell: 1.11 with vertices:
+DEAL::  -1.00000 0.00000 0.00000
+DEAL::  -0.707107 0.707107 0.00000
+DEAL::  -0.707107 0.00000 0.707107
+DEAL::  -0.577350 0.577350 0.577350
+DEAL::Volume face: 67 with vertices:
+DEAL::  -1.00000 0.00000 0.00000
+DEAL::  -0.707107 0.707107 0.00000
+DEAL::  -0.707107 0.00000 0.707107
+DEAL::  -0.577350 0.577350 0.577350
+DEAL::Surface cell: 1.12 with vertices:
+DEAL::  -0.577350 -0.577350 -0.577350
+DEAL::  -0.707107 -0.707107 0.00000
+DEAL::  0.00000 -0.707107 -0.707107
+DEAL::  0.00000 -1.00000 0.00000
+DEAL::Volume face: 60 with vertices:
+DEAL::  -0.577350 -0.577350 -0.577350
+DEAL::  -0.707107 -0.707107 0.00000
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+DEAL::  0.00000 -1.00000 0.00000
+DEAL::Surface cell: 1.13 with vertices:
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+DEAL::  0.00000 -1.00000 0.00000
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+DEAL::Volume face: 61 with vertices:
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+DEAL::  -0.577350 -0.577350 0.577350
+DEAL::  0.00000 -1.00000 0.00000
+DEAL::  0.00000 -0.707107 0.707107
+DEAL::Surface cell: 1.14 with vertices:
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+DEAL::  0.577350 -0.577350 -0.577350
+DEAL::  0.707107 -0.707107 0.00000
+DEAL::Volume face: 62 with vertices:
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+DEAL::  0.577350 -0.577350 -0.577350
+DEAL::  0.707107 -0.707107 0.00000
+DEAL::Surface cell: 1.15 with vertices:
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+DEAL::  0.707107 -0.707107 0.00000
+DEAL::  0.577350 -0.577350 0.577350
+DEAL::Volume face: 63 with vertices:
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+DEAL::  0.707107 -0.707107 0.00000
+DEAL::  0.577350 -0.577350 0.577350
+DEAL::Surface cell: 1.16 with vertices:
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+DEAL::  0.00000 0.707107 -0.707107
+DEAL::  -0.707107 0.707107 0.00000
+DEAL::  0.00000 1.00000 0.00000
+DEAL::Volume face: 108 with vertices:
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+DEAL::  0.00000 0.707107 -0.707107
+DEAL::  -0.707107 0.707107 0.00000
+DEAL::  0.00000 1.00000 0.00000
+DEAL::Surface cell: 1.17 with vertices:
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+DEAL::  0.00000 1.00000 0.00000
+DEAL::  0.707107 0.707107 0.00000
+DEAL::Volume face: 109 with vertices:
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+DEAL::  0.00000 1.00000 0.00000
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+DEAL::  -0.577350 0.577350 0.577350
+DEAL::  0.00000 0.707107 0.707107
+DEAL::Volume face: 110 with vertices:
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+DEAL::  -0.577350 0.577350 0.577350
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