Made MappingQ compatible with Manifold.

diff --git a/doc/news/changes.h b/doc/news/changes.h
index 2c11a85ba43f53539497151d6ba2f6212595ead5..bb77d0f02a5151ecbdc08edac48f316ac298bd0f 100644 (file)
--- a/doc/news/changes.h
+++ b/doc/news/changes.h
@@ -111,7 +111,14 @@ inconvenience this causes.
 
 
 <ol>
-  
+
+  <li> New: Made MappingQ<dim,spacedim> aware of
+  Manifold<dim,spacedim>. Now we can use high order mappings that
+  actually follow the geometry also on the interior of codimension
+  zero meshes.
+  <br> (Luca Heltai, 2014/09/13) 
+  </li>
+
   <li> New: Added two optional parameters to TriaAccessor::center()
   and a new method TriaAccessor::intermediate_point(). 
   They allow to query for a 
@@ -122,18 +129,19 @@ inconvenience this causes.
   TriaAccessor::center() interface when querying for new points.
   <br>
   (Luca Heltai, 2014/09/13)
-
+  </li>
 
   <li> New: The new tutorial program step-52 explains how to use the 
   new time stepping methods.
   <br>
   (Bruno Turcksin, Damien Lebrun-Grandie, 2014/09/12)
-
+  </li>
 
   <li> New: The new tutorial program step-53 explains how to deal with
   complicated geometries.
   <br>
   (Wolfgang Bangerth, Luca Heltai, 2014/09/02)
+  </li>
 
   <li> Changed: Namespace std_cxx1x has been renamed to namespace
   std_cxx11 to match the fact that the corresponding C++ standard

diff --git a/include/deal.II/fe/mapping_q.h b/include/deal.II/fe/mapping_q.h
index 28e4aefcbf1e75d334bc88c11bcfc2198c4b87d2..02016110db734549286d71489167ed0c475d7749 100644 (file)
--- a/include/deal.II/fe/mapping_q.h
+++ b/include/deal.II/fe/mapping_q.h
@@ -22,6 +22,7 @@
 #include <deal.II/base/table.h>
 #include <deal.II/fe/mapping_q1.h>
 #include <deal.II/fe/fe_q.h>
+#include <deal.II/grid/manifold.h>
 
 DEAL_II_NAMESPACE_OPEN
 
@@ -265,7 +266,35 @@ protected:
   add_quad_support_points(const typename Triangulation<dim,spacedim>::cell_iterator &cell,
                           std::vector<Point<spacedim> > &a) const;
 
+
 private:
+  /**
+   * Ask the manifold descriptor to return intermediate points on
+   * lines or faces. The function needs to return one or multiple
+   * points (depending on the number of elements in the output vector
+   * @p points that lie inside a line, quad or hex). Whether it is a
+   * line, quad or hex doesn't really matter to this function but it
+   * can be inferred from the number of input points in the @p
+   * surrounding_points vector.
+   */
+  void get_intermediate_points(const Manifold<dim, spacedim> &manifold,
+                               const std::vector<Point<spacedim> > &surrounding_points,
+                               std::vector<Point<spacedim> > &points) const;
+
+
+  /**
+   * Ask the manifold descriptor to return intermediate points on the
+   * object pointed to by the TriaIterator @p iter. This function
+   * tries to be backward compatible with respect to the differences
+   * between Boundary<dim,spacedim> and Manifold<dim,spacedim>,
+   * querying the first whenever the passed @p manifold can be
+   * upgraded to a Boundary<dim,spacedim>.
+   */
+  template <class TriaIterator>
+  void get_intermediate_points_on_object(const Manifold<dim, spacedim> &manifold,
+                                         const TriaIterator &iter,
+                                         std::vector<Point<spacedim> > &points) const;
+
 
   virtual
   typename Mapping<dim,spacedim>::InternalDataBase *
@@ -434,6 +463,18 @@ private:
    */
   const FE_Q<dim> feq;
 
+
+  /*
+   * The default line support points. These are used when computing
+   * the location in real space of the support points on lines and
+   * quads, which are asked to the Manifold<dim,spacedim> class.
+   *
+   * The number of quadrature points depends on the degree of this
+   * class, and it matches the number of degrees of freedom of an
+   * FE_Q<1>(this->degree).
+   */
+  QGaussLobatto<1> line_support_points;
+
   /**
    * Declare other MappingQ classes friends.
    */
@@ -461,20 +502,52 @@ void MappingQ<3>::set_laplace_on_hex_vector(Table<2,double> &lohvs) const;
 
 template <>
 void MappingQ<1>::compute_laplace_vector(Table<2,double> &) const;
-template <>
-void MappingQ<1>::add_line_support_points (const Triangulation<1>::cell_iterator &,
-                                           std::vector<Point<1> > &) const;
-template <>
-void MappingQ<1,2>::add_line_support_points (const Triangulation<1,2>::cell_iterator &,
-                                             std::vector<Point<2> > &) const;
-template <>
-void MappingQ<1,3>::add_line_support_points (const Triangulation<1,3>::cell_iterator &,
-                                             std::vector<Point<3> > &) const;
+
 
 template<>
 void MappingQ<3>::add_quad_support_points(const Triangulation<3>::cell_iterator &cell,
                                           std::vector<Point<3> >                &a) const;
 
+// ---- Templated functions ---- //
+template <int dim, int spacedim>
+template <class TriaIterator>
+void
+MappingQ<dim,spacedim>::get_intermediate_points_on_object(const Manifold<dim, spacedim> &manifold,
+                                                          const TriaIterator &iter,
+                                                          std::vector<Point<spacedim> > &points) const
+{
+  const unsigned int structdim = TriaIterator::AccessorType::structure_dimension;
+  // Try backward compatibility option.
+  const Boundary<dim,spacedim> *boundary = dynamic_cast<const Boundary<dim,spacedim> *>(&manifold);
+  if (boundary) // This is actually a boundary. Call old methods.
+    switch (structdim)
+      {
+      case 1:
+      {
+        const typename Triangulation<dim,spacedim>::line_iterator line = iter;
+        boundary->get_intermediate_points_on_line(line, points);
+        return;
+      }
+      case 2:
+      {
+        const typename Triangulation<dim,spacedim>::quad_iterator quad = iter;
+        boundary->get_intermediate_points_on_quad(quad, points);
+        return;
+      }
+      default:
+        Assert(false, ExcInternalError());
+        return;
+      }
+  else
+    {
+      std::vector<Point<spacedim> > sp(GeometryInfo<structdim>::vertices_per_cell);
+      for (unsigned int i=0; i<sp.size(); ++i)
+        sp[i] = iter->vertex(i);
+      get_intermediate_points(manifold, sp, points);
+    }
+}
+
+
 #endif // DOXYGEN
 
 DEAL_II_NAMESPACE_CLOSE

diff --git a/source/fe/mapping_q.cc b/source/fe/mapping_q.cc
index afc17259d3d71b36d4a83584c900bf2e6b91b101..835d8405f002fae87cada6bd9f66d079714ced1d 100644 (file)
--- a/source/fe/mapping_q.cc
+++ b/source/fe/mapping_q.cc
@@ -71,7 +71,8 @@ MappingQ<1>::MappingQ (const unsigned int,
   n_shape_functions(2),
   renumber(0),
   use_mapping_q_on_all_cells (false),
-  feq(degree)
+  feq(degree),
+  line_support_points(degree+1)
 {}
 
 
@@ -85,7 +86,8 @@ MappingQ<1>::MappingQ (const MappingQ<1> &m):
   n_shape_functions(2),
   renumber(0),
   use_mapping_q_on_all_cells (m.use_mapping_q_on_all_cells),
-  feq(degree)
+  feq(degree),
+  line_support_points(degree+1)
 {}
 
 template<>
@@ -128,13 +130,13 @@ MappingQ<dim,spacedim>::MappingQ (const unsigned int p,
                                      degree))),
   use_mapping_q_on_all_cells (use_mapping_q_on_all_cells
                               || (dim != spacedim)),
-  feq(degree)
+  feq(degree),
+  line_support_points(degree+1)
 {
   // Construct the tensor product polynomials used as shape functions for the
   // Qp mapping of cells at the boundary.
-  const QGaussLobatto<1> points(degree+1);
   tensor_pols = new TensorProductPolynomials<dim>
-  (Polynomials::generate_complete_Lagrange_basis(points.get_points()));
+  (Polynomials::generate_complete_Lagrange_basis(line_support_points.get_points()));
   Assert (n_shape_functions==tensor_pols->n(),
           ExcInternalError());
   Assert(n_inner+n_outer==n_shape_functions, ExcInternalError());
@@ -161,7 +163,8 @@ MappingQ<dim,spacedim>::MappingQ (const MappingQ<dim,spacedim> &mapping)
   n_shape_functions(mapping.n_shape_functions),
   renumber(mapping.renumber),
   use_mapping_q_on_all_cells (mapping.use_mapping_q_on_all_cells),
-  feq(degree)
+  feq(degree),
+  line_support_points(degree+1)
 {
   tensor_pols=new TensorProductPolynomials<dim> (*mapping.tensor_pols);
   laplace_on_quad_vector=mapping.laplace_on_quad_vector;
@@ -744,101 +747,26 @@ MappingQ<dim,spacedim>::compute_support_points_laplace(const typename Triangulat
 }
 
 
-
-template <>
-void
-MappingQ<1>::add_line_support_points (const Triangulation<1>::cell_iterator &,
-                                      std::vector<Point<1> > &) const
-{
-  // there are no points on bounding lines which are to be added
-  const unsigned int dim=1;
-  Assert (dim > 1, ExcImpossibleInDim(dim));
-}
-
-
-
-template <>
-void
-MappingQ<1,2>::add_line_support_points (const Triangulation<1,2>::cell_iterator &cell,
-                                        std::vector<Point<2> > &a) const
-{
-  const unsigned int dim      = 1;
-  const unsigned int spacedim = 2;
-  // Ask for the mid point, if that's the only thing we need.
-  if (degree==2)
-    {
-      const Boundary<dim,spacedim> *const boundary
-        = &(cell->get_triangulation().get_boundary(cell->material_id()));
-      a.push_back(boundary->get_new_point_on_line(cell));
-    }
-  else
-    // otherwise call the more complicated functions and ask for inner points
-    // from the boundary description
-    {
-      std::vector<Point<spacedim> > line_points (degree-1);
-
-      const Boundary<dim,spacedim> *const boundary
-        = &(cell->get_triangulation().get_boundary(cell->material_id()));
-
-      boundary->get_intermediate_points_on_line (cell, line_points);
-      // Append all points
-      a.insert (a.end(), line_points.begin(), line_points.end());
-    }
-}
-
-
-
-template <>
-void
-MappingQ<1,3>::add_line_support_points (const Triangulation<1,3>::cell_iterator &cell,
-                                        std::vector<Point<3> > &a) const
-{
-  const unsigned int dim      = 1;
-  const unsigned int spacedim = 3;
-  // Ask for the mid point, if that's the only thing we need.
-  if (degree==2)
-    {
-      const Boundary<dim,spacedim> *const boundary
-        = &(cell->get_triangulation().get_boundary(cell->material_id()));
-      a.push_back(boundary->get_new_point_on_line(cell));
-    }
-  else
-    // otherwise call the more complicated functions and ask for inner points
-    // from the boundary description
-    {
-      std::vector<Point<spacedim> > line_points (degree-1);
-
-      const Boundary<dim,spacedim> *const boundary
-        = &(cell->get_triangulation().get_boundary(cell->material_id()));
-
-      boundary->get_intermediate_points_on_line (cell, line_points);
-      // Append all points
-      a.insert (a.end(), line_points.begin(), line_points.end());
-    }
-}
-
-
-
 template<int dim, int spacedim>
 void
 MappingQ<dim,spacedim>::add_line_support_points (const typename Triangulation<dim,spacedim>::cell_iterator &cell,
                                                  std::vector<Point<spacedim> > &a) const
 {
-  static const StraightBoundary<dim,spacedim> straight_boundary;
   // if we only need the midpoint, then ask for it.
   if (degree==2)
     {
       for (unsigned int line_no=0; line_no<GeometryInfo<dim>::lines_per_cell; ++line_no)
         {
-          const typename Triangulation<dim,spacedim>::line_iterator line = cell->line(line_no);
-          const Boundary<dim,spacedim> *const boundary
-            = (line->at_boundary()?
-               &line->get_triangulation().get_boundary(line->boundary_indicator()):
-               (dim != spacedim) ?
-               &line->get_triangulation().get_boundary(cell->material_id()):
-               &straight_boundary);
-
-          a.push_back(boundary->get_new_point_on_line(line));
+          const typename Triangulation<dim,spacedim>::line_iterator line =
+            (dim == 1  ?
+             static_cast<typename Triangulation<dim,spacedim>::line_iterator>(cell) :
+             cell->line(line_no));
+
+          const Manifold<dim,spacedim> &manifold =
+            ( ( line->manifold_id() == numbers::invalid_manifold_id ) &&
+              ( dim < spacedim ) ? cell->get_manifold() :
+              line->get_manifold() );
+          a.push_back(manifold.get_new_point_on_line(line));
         };
     }
   else
@@ -846,21 +774,24 @@ MappingQ<dim,spacedim>::add_line_support_points (const typename Triangulation<di
     // from the boundary description
     {
       std::vector<Point<spacedim> > line_points (degree-1);
-
       // loop over each of the lines, and if it is at the boundary, then first
       // get the boundary description and second compute the points on it
       for (unsigned int line_no=0; line_no<GeometryInfo<dim>::lines_per_cell; ++line_no)
         {
-          const typename Triangulation<dim,spacedim>::line_iterator line = cell->line(line_no);
+          const typename Triangulation<dim,spacedim>::line_iterator
+          line = (dim == 1
+                  ?
+                  static_cast<typename Triangulation<dim,spacedim>::line_iterator>(cell)
+                  :
+                  cell->line(line_no));
 
-          const Boundary<dim,spacedim> *const boundary
-            = (line->at_boundary()?
-               &line->get_triangulation().get_boundary(line->boundary_indicator()) :
-               (dim != spacedim) ?
-               &line->get_triangulation().get_boundary(cell->material_id()) :
-               &straight_boundary);
+          const Manifold<dim,spacedim> &manifold =
+            ( ( line->manifold_id() == numbers::invalid_manifold_id ) &&
+              ( dim < spacedim ) ? cell->get_manifold() :
+              line->get_manifold() );
+
+          get_intermediate_points_on_object (manifold, line, line_points);
 
-          boundary->get_intermediate_points_on_line (line, line_points);
           if (dim==3)
             {
               // in 3D, lines might be in wrong orientation. if so, reverse
@@ -898,6 +829,9 @@ add_quad_support_points(const Triangulation<3>::cell_iterator &cell,
   // used if only one line of face quad is at boundary
   std::vector<Point<3> > b(4*degree);
 
+  // Used by the new Manifold interface. This vector collects the
+  // vertices used to compute the intermediate points.
+  std::vector<Point<3> > vertices(4);
 
   // loop over all faces and collect points on them
   for (unsigned int face_no=0; face_no<faces_per_cell; ++face_no)
@@ -931,8 +865,8 @@ add_quad_support_points(const Triangulation<3>::cell_iterator &cell,
       // points on it
       if (face->at_boundary())
         {
-          face->get_triangulation().get_boundary(face->boundary_indicator())
-          .get_intermediate_points_on_quad (face, quad_points);
+          get_intermediate_points_on_object(face->get_manifold(), face, quad_points);
+
           // in 3D, the orientation, flip and rotation of the face might not
           // match what we expect here, namely the standard orientation. thus
           // reorder points accordingly. since a Mapping uses the same shape
@@ -992,9 +926,12 @@ add_quad_support_points(const Triangulation<3>::cell_iterator &cell,
             }
           else
             {
-              // face is entirely in the interior. get intermediate points
-              // from a straight boundary object
-              straight_boundary.get_intermediate_points_on_quad (face, quad_points);
+              // face is entirely in the interior. get intermediate
+              // points from the relevant manifold object.
+              vertices.resize(4);
+              for (unsigned int i=0; i<4; ++i)
+                vertices[i] = face->vertex(i);
+              get_intermediate_points (face->get_manifold(), vertices, quad_points);
               // in 3D, the orientation, flip and rotation of the face might
               // not match what we expect here, namely the standard
               // orientation. thus reorder points accordingly. since a Mapping
@@ -1019,9 +956,7 @@ add_quad_support_points(const Triangulation<2,3>::cell_iterator &cell,
                         std::vector<Point<3> >                &a) const
 {
   std::vector<Point<3> > quad_points ((degree-1)*(degree-1));
-
-  cell->get_triangulation().get_boundary(cell->material_id())
-  .get_intermediate_points_on_quad (cell, quad_points);
+  get_intermediate_points_on_object (cell->get_manifold(), cell, quad_points);
   for (unsigned int i=0; i<quad_points.size(); ++i)
     a.push_back(quad_points[i]);
 }
@@ -1266,6 +1201,75 @@ MappingQ<dim,spacedim>::clone () const
 }
 
 
+template<int dim, int spacedim>
+void
+MappingQ<dim,spacedim>::get_intermediate_points (const Manifold<dim, spacedim> &manifold,
+                                                 const std::vector<Point<spacedim> > &surrounding_points,
+                                                 std::vector<Point<spacedim> > &points) const
+{
+  Assert(surrounding_points.size() >= 2, ExcMessage("At least 2 surrounding points are required"));
+  const unsigned int n=points.size();
+  Assert(n>0, ExcMessage("You can't ask for 0 intermediate points."));
+  std::vector<double> w(surrounding_points.size());
+
+  switch (surrounding_points.size())
+    {
+    case 2:
+    {
+      // If two points are passed, these are the two vertices, and
+      // we can only compute degree-1 intermediate points.
+      AssertDimension(n, degree-1);
+      for (unsigned int i=0; i<n; ++i)
+        {
+          const double x = line_support_points.point(i+1)[0];
+          w[1] = x;
+          w[0] = (1-x);
+          Quadrature<spacedim> quadrature(surrounding_points, w);
+          points[i] = manifold.get_new_point(quadrature);
+        }
+      break;
+    }
+
+    case 4:
+    {
+      Assert(spacedim >= 2, ExcImpossibleInDim(spacedim));
+      const unsigned m=
+        static_cast<unsigned int>(std::sqrt(static_cast<double>(n)));
+      // is n a square number
+      Assert(m*m==n, ExcInternalError());
+
+      // If four points are passed, these are the two vertices, and
+      // we can only compute (degree-1)*(degree-1) intermediate
+      // points.
+      AssertDimension(m, degree-1);
+
+      for (unsigned int i=0; i<m; ++i)
+        {
+          const double y=line_support_points.point(1+i)[0];
+          for (unsigned int j=0; j<m; ++j)
+            {
+              const double x=line_support_points.point(1+j)[0];
+
+              w[0] = (1-x)*(1-y);
+              w[1] =     x*(1-y);
+              w[2] = (1-x)*y    ;
+              w[3] =     x*y    ;
+              Quadrature<spacedim> quadrature(surrounding_points, w);
+              points[i*m+j]=manifold.get_new_point(quadrature);
+            }
+        }
+      break;
+    }
+
+    case 8:
+      Assert(false, ExcNotImplemented());
+      break;
+    default:
+      Assert(false, ExcInternalError());
+      break;
+    }
+}
+
 
 
 // explicit instantiations

diff --git a/tests/manifold/spherical_manifold_05.cc b/tests/manifold/spherical_manifold_05.cc
new file mode 100644 (file)
index 0000000..ee8708c
--- /dev/null
+++ b/tests/manifold/spherical_manifold_05.cc
@@ -0,0 +1,91 @@
+//----------------------------  spherical_manifold_01.cc  ---------------------------
+//    Copyright (C) 2011, 2013 by the mathLab team.
+//
+//    This file is subject to LGPL and may not be  distributed
+//    without copyright and license information. Please refer
+//    to the file deal.II/doc/license.html for the  text  and
+//    further information on this license.
+//
+//----------------------------  spherical_manifold_04.cc  ---------------------------
+
+
+// Test that the flat manifold does what it should on a sphere surface. 
+
+#include "../tests.h"
+
+#include <fstream>
+#include <base/logstream.h>
+
+
+// all include files you need here
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/grid/manifold_lib.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/grid_tools.h>
+
+#include <deal.II/dofs/dof_handler.h>
+#include <deal.II/fe/mapping_q.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_values.h>
+
+// Helper function
+template <int dim>
+void test(unsigned int degree)
+{
+  deallog << "Testing dim=" << dim <<", degree=" 
+         << degree << std::endl;
+  
+  SphericalManifold<dim> manifold;
+  Triangulation<dim> tria;
+  GridGenerator::hyper_shell(tria, Point<dim>(), .4, .6, 6);
+  typename Triangulation<dim>::active_cell_iterator cell;
+  
+  for(cell = tria.begin_active(); cell != tria.end(); ++cell) 
+    cell->set_all_manifold_ids(1);
+
+  tria.set_manifold(1, manifold);
+
+  MappingQ<dim> mapping(degree, true);
+  FE_Q<dim> fe(degree);
+  DoFHandler<dim> dh(tria);
+  dh.distribute_dofs(fe);
+  QGaussLobatto<dim> quad(degree+1);
+  
+  FEValues<dim> fe_v(mapping, fe, quad, update_quadrature_points);
+
+  // char fname[50];
+  // sprintf(fname, "out_%d_%d.gpl", dim, degree);
+  // std::ofstream ofile(fname);
+  std::ostream &ofile = deallog.get_file_stream(); 
+
+  for(typename DoFHandler<dim>::active_cell_iterator cell = dh.begin_active();
+      cell != dh.end(); ++cell) {
+    fe_v.reinit(cell);
+    for(unsigned int q=0; q<quad.size(); ++q) {
+      ofile << fe_v.get_quadrature_points()[q] << std::endl;
+    }
+    ofile << std::endl;
+  }
+  ofile << std::endl;
+}
+
+int main ()
+{
+  std::ofstream logfile("output");
+  deallog.attach(logfile);
+  deallog.depth_console(0);
+  deallog.threshold_double(1.e-10);
+
+  for(unsigned int d=1; d<5; ++d) {
+    test<2>(d);
+    test<3>(d);
+  }
+  return 0;
+}
+

diff --git a/tests/manifold/spherical_manifold_05.output b/tests/manifold/spherical_manifold_05.output
new file mode 100644 (file)
index 0000000..cb262e4
--- /dev/null
+++ b/tests/manifold/spherical_manifold_05.output
@@ -0,0 +1,1733 @@
+
+DEAL::Testing dim=2, degree=1
+0.600000 0.00000
+0.300000 0.519615
+0.400000 0.00000
+0.200000 0.346410
+
+0.300000 0.519615
+-0.300000 0.519615
+0.200000 0.346410
+-0.200000 0.346410
+
+-0.300000 0.519615
+-0.600000 7.34788e-17
+-0.200000 0.346410
+-0.400000 4.89859e-17
+
+-0.600000 7.34788e-17
+-0.300000 -0.519615
+-0.400000 4.89859e-17
+-0.200000 -0.346410
+
+-0.300000 -0.519615
+0.300000 -0.519615
+-0.200000 -0.346410
+0.200000 -0.346410
+
+0.300000 -0.519615
+0.600000 0.00000
+0.200000 -0.346410
+0.400000 0.00000
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