--- /dev/null
+New: Added a GridTools::regularize_corner_cells function that
+detects if the boundary cells of a mesh at corner positions
+(with dim adjacent faces on the boundary) need to be split into
+cells with smaller angles.
+<br> (Luca Heltai, Martin Kronbichler, 2017/05/18)
const double max_ratio = 1.6180339887,
const unsigned int max_iterations = 5);
+ /**
+ * Analyze the boundary cells of a mesh, and if one cell is found at
+ * a corner position (with dim adjacent faces on the boundary), and its
+ * dim-dimensional angle fraction exceeds @p limit_angle_fraction,
+ * refine globally once, and replace the children of such cell
+ * with children where the corner is no longer offending the given angle
+ * fraction.
+ *
+ * If no boundary cells exist with two adjacent faces on the boundary, then
+ * the triangulation is left untouched. If instead we do have cells with dim
+ * adjacent faces on the boundary, then the fraction between the dim-dimensional
+ * solid angle and dim*pi/2 is checked against the parameter @p limit_angle_fraction.
+ * If it is higher, the grid is refined once, and the children of the
+ * offending cell are replaced with some cells that instead respect the limit. After
+ * this process the triangulation is flattened, and all Manifold objects are restored
+ * as they were in the original triangulation.
+ *
+ * An example is given by the following mesh, obtained by attaching a SphericalManifold
+ * to a mesh generated using GridGenerator::hyper_cube:
+ *
+ * @code
+ * const SphericalManifold<dim> m0;
+ * Triangulation<dim> tria;
+ * GridGenerator::hyper_cube(tria,-1,1);
+ * tria.set_all_manifold_ids_on_boundary(0);
+ * tria.set_manifold(0, m0);
+ * tria.refine_global(4);
+ * @endcode
+ *
+ * <p ALIGN="center">
+ * @image html regularize_mesh_01.png
+ * </p>
+ *
+ * The four cells that were originally the corners of a square will give you some troubles
+ * during computations, as the jacobian of the transformation from the reference cell to
+ * those cells will go to zero, affecting the error constants of the finite element estimates.
+ *
+ * Those cells have a corner with an angle that is very close to 180 degrees, i.e., an angle
+ * fraction very close to one.
+ *
+ * The same code, adding a call to regularize_corner_cells:
+ * @code
+ * const SphericalManifold<dim> m0;
+ * Triangulation<dim> tria;
+ * GridGenerator::hyper_cube(tria,-1,1);
+ * tria.set_all_manifold_ids_on_boundary(0);
+ * tria.set_manifold(0, m0);
+ * GridTools::regularize_corner_cells(tria);
+ * tria.refine_global(2);
+ * @endcode
+ * generates a mesh that has a much better behaviour w.r.t. the jacobian of the Mapping:
+ *
+ * <p ALIGN="center">
+ * @image html regularize_mesh_02.png
+ * </p>
+ *
+ * This mesh is very similar to the one obtained by GridGenerator::hyper_ball. However, using
+ * GridTools::regularize_corner_cells one has the freedom to choose when to apply the
+ * regularization, i.e., one could in principle first refine a few times, and then call the
+ * regularize_corner_cells function:
+ *
+ * @code
+ * const SphericalManifold<dim> m0;
+ * Triangulation<dim> tria;
+ * GridGenerator::hyper_cube(tria,-1,1);
+ * tria.set_all_manifold_ids_on_boundary(0);
+ * tria.set_manifold(0, m0);
+ * tria.refine_global(2);
+ * GridTools::regularize_corner_cells(tria);
+ * tria.refine_global(1);
+ * @endcode
+ *
+ * This generates the following mesh:
+ *
+ * <p ALIGN="center">
+ * @image html regularize_mesh_03.png
+ * </p>
+ *
+ * The function is currently implemented only for dim = 2 and
+ * will throw an exception if called with dim = 3.
+ *
+ * @param[in,out] tria Triangulation to regularize.
+ *
+ * @param[in] limit_angle_fraction Maximum ratio of angle or solid
+ * angle that is allowed for a corner element in the mesh.
+ *
+ * @author Luca Heltai, Martin Kronbichler, 2017
+ */
+ template <int dim, int spacedim>
+ void
+ regularize_corner_cells(Triangulation<dim,spacedim> &tria,
+ const double limit_angle_fraction=.75);
+
/*@}*/
/**
* @name Finding cells and vertices of a triangulation
#include <deal.II/grid/tria_boundary.h>
#include <deal.II/grid/grid_generator.h>
#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/grid_reordering.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/dofs/dof_tools.h>
}
}
+
+ template<int dim, int spacedim>
+ void regularize_corner_cells (Triangulation<dim,spacedim> &tria,
+ const double limit_angle_fraction)
+ {
+ if (dim == 1)
+ return; // Nothing to do
+
+ // Check that we don't have hanging nodes
+ AssertThrow(!tria.has_hanging_nodes(), ExcMessage("The input Triangulation cannot "
+ "have hanging nodes."));
+
+
+ bool has_cells_with_more_than_dim_faces_on_boundary = true;
+ bool has_cells_with_dim_faces_on_boundary = false;
+
+ unsigned int refinement_cycles = 0;
+
+ while (has_cells_with_more_than_dim_faces_on_boundary)
+ {
+ has_cells_with_more_than_dim_faces_on_boundary = false;
+
+ for (auto cell: tria.active_cell_iterators())
+ {
+ unsigned int boundary_face_counter = 0;
+ for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
+ if (cell->face(f)->at_boundary())
+ boundary_face_counter++;
+ if (boundary_face_counter > dim)
+ {
+ has_cells_with_more_than_dim_faces_on_boundary = true;
+ break;
+ }
+ else if (boundary_face_counter == dim)
+ has_cells_with_dim_faces_on_boundary = true;
+ }
+ if (has_cells_with_more_than_dim_faces_on_boundary)
+ {
+ tria.refine_global(1);
+ refinement_cycles++;
+ }
+ }
+
+ if (has_cells_with_dim_faces_on_boundary)
+ {
+ tria.refine_global(1);
+ refinement_cycles++;
+ }
+ else
+ {
+ while (refinement_cycles>0)
+ {
+ for (auto cell: tria.active_cell_iterators())
+ cell->set_coarsen_flag();
+ tria.execute_coarsening_and_refinement();
+ refinement_cycles--;
+ }
+ return;
+ }
+
+ std::vector<bool> cells_to_remove(tria.n_active_cells(), false);
+ std::vector<Point<spacedim> > vertices = tria.get_vertices();
+
+ std::vector<bool> faces_to_remove(tria.n_raw_faces(),false);
+
+ std::vector<CellData<dim> > cells_to_add;
+ SubCellData subcelldata_to_add;
+
+ // Trick compiler for dimension independent things
+ const unsigned int
+ v0 = 0, v1 = 1,
+ v2 = (dim > 1 ? 2:0), v3 = (dim > 1 ? 3:0),
+ v4 = (dim > 2 ? 4:0), v5 = (dim > 2 ? 5:0),
+ v6 = (dim > 2 ? 6:0), v7 = (dim > 2 ? 7:0);
+
+ for (auto cell : tria.active_cell_iterators())
+ {
+ double angle_fraction = 0;
+ unsigned int vertex_at_corner = numbers::invalid_unsigned_int;
+
+ if (dim == 2)
+ {
+ Tensor<1,spacedim> p0;
+ p0[spacedim > 1 ? 1 : 0] = 1;
+ Tensor<1,spacedim> p1;
+ p1[0] = 1;
+
+ if (cell->face(v0)->at_boundary() && cell->face(v3)->at_boundary())
+ {
+ p0 = cell->vertex(v0) - cell->vertex(v2);
+ p1 = cell->vertex(v3) - cell->vertex(v2);
+ vertex_at_corner = v2;
+ }
+ else if (cell->face(v3)->at_boundary() && cell->face(v1)->at_boundary())
+ {
+ p0 = cell->vertex(v2) - cell->vertex(v3);
+ p1 = cell->vertex(v1) - cell->vertex(v3);
+ vertex_at_corner = v3;
+ }
+ else if (cell->face(1)->at_boundary() && cell->face(2)->at_boundary())
+ {
+ p0 = cell->vertex(v0) - cell->vertex(v1);
+ p1 = cell->vertex(v3) - cell->vertex(v1);
+ vertex_at_corner = v1;
+ }
+ else if (cell->face(2)->at_boundary() && cell->face(0)->at_boundary())
+ {
+ p0 = cell->vertex(v2) - cell->vertex(v0);
+ p1 = cell->vertex(v1) - cell->vertex(v0);
+ vertex_at_corner = v0;
+ }
+ p0 /= p0.norm();
+ p1 /= p1.norm();
+ angle_fraction = std::acos(p0*p1)/numbers::PI;
+
+ }
+ else
+ {
+ Assert(false, ExcNotImplemented());
+ }
+
+ if (angle_fraction > limit_angle_fraction)
+ {
+
+ auto flags_removal = [&](unsigned int f1, unsigned int f2,
+ unsigned int n1, unsigned int n2) -> void
+ {
+ cells_to_remove[cell->active_cell_index()] = true;
+ cells_to_remove[cell->neighbor(n1)->active_cell_index()] = true;
+ cells_to_remove[cell->neighbor(n2)->active_cell_index()] = true;
+
+ faces_to_remove[cell->face(f1)->index()] = true;
+ faces_to_remove[cell->face(f2)->index()] = true;
+
+ faces_to_remove[cell->neighbor(n1)->face(f1)->index()] = true;
+ faces_to_remove[cell->neighbor(n2)->face(f2)->index()] = true;
+ };
+
+ auto cell_creation = [&](
+ const unsigned int vv0,
+ const unsigned int vv1,
+ const unsigned int f0,
+ const unsigned int f1,
+
+ const unsigned int n0,
+ const unsigned int v0n0,
+ const unsigned int v1n0,
+
+ const unsigned int n1,
+ const unsigned int v0n1,
+ const unsigned int v1n1)
+ {
+ CellData<dim> c1, c2;
+ CellData<1> l1, l2;
+
+ c1.vertices[v0] = cell->vertex_index(vv0);
+ c1.vertices[v1] = cell->vertex_index(vv1);
+ c1.vertices[v2] = cell->neighbor(n0)->vertex_index(v0n0);
+ c1.vertices[v3] = cell->neighbor(n0)->vertex_index(v1n0);
+
+ c1.manifold_id = cell->manifold_id();
+ c1.material_id = cell->material_id();
+
+ c2.vertices[v0] = cell->vertex_index(vv0);
+ c2.vertices[v1] = cell->neighbor(n1)->vertex_index(v0n1);
+ c2.vertices[v2] = cell->vertex_index(vv1);
+ c2.vertices[v3] = cell->neighbor(n1)->vertex_index(v1n1);
+
+ c2.manifold_id = cell->manifold_id();
+ c2.material_id = cell->material_id();
+
+ l1.vertices[0] = cell->vertex_index(vv0);
+ l1.vertices[1] = cell->neighbor(n0)->vertex_index(v0n0);
+
+ l1.boundary_id = cell->line(f0)->boundary_id();
+ l1.manifold_id = cell->line(f0)->manifold_id();
+ subcelldata_to_add.boundary_lines.push_back(l1);
+
+ l2.vertices[0] = cell->vertex_index(vv0);
+ l2.vertices[1] = cell->neighbor(n1)->vertex_index(v0n1);
+
+ l2.boundary_id = cell->line(f1)->boundary_id();
+ l2.manifold_id = cell->line(f1)->manifold_id();
+ subcelldata_to_add.boundary_lines.push_back(l2);
+
+ cells_to_add.push_back(c1);
+ cells_to_add.push_back(c2);
+ };
+
+ if (dim == 2)
+ {
+ switch (vertex_at_corner)
+ {
+ case 0:
+ flags_removal(0,2,3,1);
+ cell_creation(0,3, 0,2, 3,2,3, 1,1,3);
+ break;
+ case 1:
+ flags_removal(1,2,3,0);
+ cell_creation(1,2, 2,1, 0,0,2, 3,3,2);
+ break;
+ case 2:
+ flags_removal(3,0,1,2);
+ cell_creation(2,1, 3,0, 1,3,1, 2,0,1);
+ break;
+ case 3:
+ flags_removal(3,1,0,2);
+ cell_creation(3,0, 1,3, 2,1,0, 0,2,0);
+ break;
+ }
+ }
+ else
+ {
+ Assert(false, ExcNotImplemented());
+ }
+ }
+ }
+
+ // if no cells need to be added, then no regularization is necessary. Restore things
+ // as they were before this function was called.
+ if (cells_to_add.size() == 0)
+ {
+ while (refinement_cycles>0)
+ {
+ for (auto cell: tria.active_cell_iterators())
+ cell->set_coarsen_flag();
+ tria.execute_coarsening_and_refinement();
+ refinement_cycles--;
+ }
+ return;
+ }
+
+ // add the cells that were not marked as skipped
+ for (auto cell : tria.active_cell_iterators())
+ {
+ if (cells_to_remove[cell->active_cell_index()] == false)
+ {
+ CellData<dim> c;
+ for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_cell; ++v)
+ c.vertices[v] = cell->vertex_index(v);
+ c.manifold_id = cell->manifold_id();
+ c.material_id = cell->material_id();
+ cells_to_add.push_back(c);
+ }
+ }
+
+ // Face counter for both dim == 2 and dim == 3
+ typename Triangulation<dim,spacedim>::active_face_iterator
+ face = tria.begin_active_face(),
+ endf = tria.end_face();
+ for (; face != endf; ++face)
+ if ( (face->at_boundary() || face->manifold_id() != numbers::invalid_manifold_id)
+ && faces_to_remove[face->index()] == false)
+ {
+ for (unsigned int l=0; l<GeometryInfo<dim>::lines_per_face; ++l)
+ {
+ CellData<1> line;
+ if (dim == 2)
+ {
+ for (unsigned int v=0; v<GeometryInfo<1>::vertices_per_cell; ++v)
+ line.vertices[v] = face->vertex_index(v);
+ line.boundary_id = face->boundary_id();
+ line.manifold_id = face->manifold_id();
+ }
+ else
+ {
+ for (unsigned int v=0; v<GeometryInfo<1>::vertices_per_cell; ++v)
+ line.vertices[v] = face->line(l)->vertex_index(v);
+ line.boundary_id = face->line(l)->boundary_id();
+ line.manifold_id = face->line(l)->manifold_id();
+ }
+ subcelldata_to_add.boundary_lines.push_back(line);
+ }
+ if (dim == 3)
+ {
+ CellData<2> quad;
+ for (unsigned int v=0; v<GeometryInfo<2>::vertices_per_cell; ++v)
+ quad.vertices[v] = face->vertex_index(v);
+ quad.boundary_id = face->boundary_id();
+ quad.manifold_id = face->manifold_id();
+ subcelldata_to_add.boundary_quads.push_back(quad);
+ }
+ }
+ GridTools::delete_unused_vertices(vertices, cells_to_add, subcelldata_to_add);
+ GridReordering<dim,spacedim>::reorder_cells(cells_to_add, true);
+
+ // Save manifolds
+ auto manifold_ids = tria.get_manifold_ids();
+ std::map<types::manifold_id, const Manifold<dim,spacedim>*> manifolds;
+ // Set manifolds in new Triangulation
+ for (auto manifold_id: manifold_ids)
+ if (manifold_id != numbers::invalid_manifold_id)
+ manifolds[manifold_id] = &tria.get_manifold(manifold_id);
+
+ tria.clear();
+
+ tria.create_triangulation(vertices, cells_to_add, subcelldata_to_add);
+
+ // Restore manifolds
+ for (auto manifold_id: manifold_ids)
+ if (manifold_id != numbers::invalid_manifold_id)
+ tria.set_manifold(manifold_id, *manifolds[manifold_id]);
+ }
+
+
+
} /* namespace GridTools */
template void copy_material_to_manifold_id<deal_II_dimension, deal_II_space_dimension>
(Triangulation<deal_II_dimension, deal_II_space_dimension> &, const bool);
+ template
+ void regularize_corner_cells
+ (Triangulation<deal_II_dimension,deal_II_space_dimension> &, double);
\}
#endif
}
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2001 - 2015 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// GridTools::regularize_corner_cells
+
+#include "../tests.h"
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/grid_out.h>
+
+template <int dim>
+void test ()
+{
+ const SphericalManifold<dim> m0;
+ Triangulation<dim> tria;
+ GridGenerator::hyper_cube(tria,-1,1);
+ tria.set_all_manifold_ids_on_boundary(0);
+ tria.set_manifold(0, m0);
+
+ GridTools::regularize_corner_cells (tria);
+
+ GridOut grid_out;
+ grid_out.write_msh (tria, deallog.get_file_stream());
+}
+
+
+
+int main ()
+{
+ initlog();
+
+ test<2> ();
+
+ return 0;
+}
+
--- /dev/null
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+$ENDELM
--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2001 - 2015 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// GridTools::regularize_corner_cells on more complicated mesh
+
+#include "../tests.h"
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/grid_out.h>
+
+int main()
+{
+ initlog();
+
+ Point<2> p0(0,0), p1(4,1);
+ Point<2> c0(.1, .5), c1(3.9,.5);
+
+ SphericalManifold<2> m0(c0);
+ SphericalManifold<2> m1(c1);
+
+ Triangulation<2> tria;
+ std::vector<unsigned int> subdivisions(2);
+ subdivisions[0] = 4;
+ subdivisions[1] = 1;
+ GridGenerator::subdivided_hyper_rectangle(tria,subdivisions, p0,p1,true);
+
+ GridTools::copy_boundary_to_manifold_id(tria);
+
+ tria.set_manifold(0, m0);
+ tria.set_manifold(1, m1);
+
+ GridTools::regularize_corner_cells (tria);
+ tria.refine_global(1);
+
+ GridOut grid_out;
+ grid_out.write_msh (tria, deallog.get_file_stream());
+
+ return 0;
+}
+
+
--- /dev/null
+
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projects / dealii.git / commitdiff
