From 927d61282163a76b26058666df28e90c363d982e Mon Sep 17 00:00:00 2001
From: Peter Munch <peterrmuench@gmail.com>
Date: Fri, 15 Jan 2021 19:30:49 +0100
Subject: [PATCH] Work on higher-order MappingFE

---
 include/deal.II/fe/mapping_fe.h               |    3 +
 include/deal.II/grid/reference_cell.h         |   69 +-
 source/fe/mapping_fe.cc                       |   93 +-
 source/grid/reference_cell.cc                 |    4 +
 tests/simplex/mapping_fe_01.cc                |   81 ++
 ...pping_fe_01.with_simplex_support=on.output | 1151 +++++++++++++++++
 6 files changed, 1389 insertions(+), 12 deletions(-)
 create mode 100644 tests/simplex/mapping_fe_01.cc
 create mode 100644 tests/simplex/mapping_fe_01.with_simplex_support=on.output

diff --git a/include/deal.II/fe/mapping_fe.h b/include/deal.II/fe/mapping_fe.h
index edcc1d2be5..95c8591884 100644
--- a/include/deal.II/fe/mapping_fe.h
+++ b/include/deal.II/fe/mapping_fe.h
@@ -467,6 +467,9 @@ protected:
   virtual std::vector<Point<spacedim>>
   compute_mapping_support_points(
     const typename Triangulation<dim, spacedim>::cell_iterator &cell) const;
+
+private:
+  Table<2, double> mapping_support_point_weights;
 };
 
 
diff --git a/include/deal.II/grid/reference_cell.h b/include/deal.II/grid/reference_cell.h
index ca56d20f89..86441b244a 100644
--- a/include/deal.II/grid/reference_cell.h
+++ b/include/deal.II/grid/reference_cell.h
@@ -31,6 +31,8 @@ template <int dim, int spacedim>
 class Mapping;
 template <int dim>
 class Quadrature;
+template <int dim>
+class ScalarPolynomialsBase;
 #endif
 
 /**
@@ -335,14 +337,75 @@ namespace ReferenceCell
         switch (i)
           {
             case 0:
-              return 1.0 - xi[0] - xi[1];
+              return 1.0 - xi[std::min(0, dim - 1)] - xi[std::min(1, dim - 1)];
+            case 1:
+              return xi[std::min(0, dim - 1)];
+            case 2:
+              return xi[std::min(1, dim - 1)];
+          }
+      }
+
+    if (reference_cell ==
+        Type::Tet) // see also Simplex::ScalarPolynomial::compute_value
+      {
+        switch (i)
+          {
+            case 0:
+              return 1.0 - xi[std::min(0, dim - 1)] - xi[std::min(1, dim - 1)] -
+                     xi[std::min(2, dim - 1)];
             case 1:
-              return xi[0];
+              return xi[std::min(0, dim - 1)];
             case 2:
-              return xi[1];
+              return xi[std::min(1, dim - 1)];
+            case 3:
+              return xi[std::min(2, dim - 1)];
           }
       }
 
+    if (reference_cell ==
+        Type::Wedge) // see also Simplex::ScalarWedgePolynomial::compute_value
+      {
+        return d_linear_shape_function<2>(Type::Tri,
+                                          Point<2>(xi[std::min(0, dim - 1)],
+                                                   xi[std::min(1, dim - 1)]),
+                                          i % 3) *
+               d_linear_shape_function<1>(Type::Line,
+                                          Point<1>(xi[std::min(2, dim - 1)]),
+                                          i / 3);
+      }
+
+    if (reference_cell ==
+        Type::Pyramid) // see also
+                       // Simplex::ScalarPyramidPolynomial::compute_value
+      {
+        const double Q14 = 0.25;
+        double       ration;
+
+        const double r = xi[std::min(0, dim - 1)];
+        const double s = xi[std::min(1, dim - 1)];
+        const double t = xi[std::min(2, dim - 1)];
+
+        if (fabs(t - 1.0) > 1.0e-14)
+          {
+            ration = (r * s * t) / (1.0 - t);
+          }
+        else
+          {
+            ration = 0.0;
+          }
+
+        if (i == 0)
+          return Q14 * ((1.0 - r) * (1.0 - s) - t + ration);
+        if (i == 1)
+          return Q14 * ((1.0 + r) * (1.0 - s) - t - ration);
+        if (i == 2)
+          return Q14 * ((1.0 - r) * (1.0 + s) - t - ration);
+        if (i == 3)
+          return Q14 * ((1.0 + r) * (1.0 + s) - t + ration);
+        else
+          return t;
+      }
+
     Assert(false, ExcNotImplemented());
 
     return 0.0;
diff --git a/source/fe/mapping_fe.cc b/source/fe/mapping_fe.cc
index 05e18198bc..be1982c505 100644
--- a/source/fe/mapping_fe.cc
+++ b/source/fe/mapping_fe.cc
@@ -853,8 +853,27 @@ MappingFE<dim, spacedim>::MappingFE(const FiniteElement<dim, spacedim> &fe)
   Assert(polynomial_degree >= 1,
          ExcMessage("It only makes sense to create polynomial mappings "
                     "with a polynomial degree greater or equal to one."));
-  Assert(fe.tensor_degree() == 1, ExcNotImplemented());
   Assert(fe.n_components() == 1, ExcNotImplemented());
+
+  Assert(fe.has_support_points(), ExcNotImplemented());
+
+  const auto &mapping_support_points = fe.get_unit_support_points();
+
+  const auto reference_cell_type = fe.reference_cell_type();
+
+  const unsigned int n_points = mapping_support_points.size();
+  const unsigned int n_shape_functions =
+    ReferenceCell::internal::Info::get_cell(reference_cell_type).n_vertices();
+
+  this->mapping_support_point_weights =
+    Table<2, double>(n_points, n_shape_functions);
+
+  for (unsigned int point = 0; point < n_points; ++point)
+    for (unsigned int i = 0; i < n_shape_functions; ++i)
+      mapping_support_point_weights(point, i) =
+        ReferenceCell::d_linear_shape_function(reference_cell_type,
+                                               mapping_support_points[point],
+                                               i);
 }
 
 
@@ -863,6 +882,7 @@ template <int dim, int spacedim>
 MappingFE<dim, spacedim>::MappingFE(const MappingFE<dim, spacedim> &mapping)
   : fe(mapping.fe->clone())
   , polynomial_degree(mapping.polynomial_degree)
+  , mapping_support_point_weights(mapping.mapping_support_point_weights)
 {}
 
 
@@ -2204,23 +2224,78 @@ MappingFE<dim, spacedim>::transform(
 
 
 
+namespace
+{
+  template <int spacedim>
+  bool
+  check_all_manifold_ids_identical(
+    const TriaIterator<CellAccessor<1, spacedim>> &)
+  {
+    return true;
+  }
+
+
+
+  template <int spacedim>
+  bool
+  check_all_manifold_ids_identical(
+    const TriaIterator<CellAccessor<2, spacedim>> &cell)
+  {
+    const auto b_id = cell->manifold_id();
+
+    for (const auto f : cell->face_indices())
+      if (b_id != cell->face(f)->manifold_id())
+        return false;
+
+    return true;
+  }
+
+
+
+  template <int spacedim>
+  bool
+  check_all_manifold_ids_identical(
+    const TriaIterator<CellAccessor<3, spacedim>> &cell)
+  {
+    const auto b_id = cell->manifold_id();
+
+    for (const auto f : cell->face_indices())
+      if (b_id != cell->face(f)->manifold_id())
+        return false;
+
+    for (const auto l : cell->line_indices())
+      if (b_id != cell->line(l)->manifold_id())
+        return false;
+
+    return true;
+  }
+} // namespace
+
+
+
 template <int dim, int spacedim>
 std::vector<Point<spacedim>>
 MappingFE<dim, spacedim>::compute_mapping_support_points(
   const typename Triangulation<dim, spacedim>::cell_iterator &cell) const
 {
-  // get the vertices first
-  std::vector<Point<spacedim>> a(cell->n_vertices());
+  Assert(
+    check_all_manifold_ids_identical(cell),
+    ExcMessage(
+      "All entities of a cell need to have the same boundary id as the cell has."));
+
+  std::vector<Point<spacedim>> vertices(cell->n_vertices());
 
   for (const unsigned int i : cell->vertex_indices())
-    a[i] = cell->vertex(i);
+    vertices[i] = cell->vertex(i);
 
-  if (this->polynomial_degree > 1)
-    {
-      Assert(false, ExcNotImplemented());
-    }
+  std::vector<Point<spacedim>> mapping_support_points(
+    fe->get_unit_support_points().size());
+
+  cell->get_manifold().get_new_points(vertices,
+                                      mapping_support_point_weights,
+                                      mapping_support_points);
 
-  return a;
+  return mapping_support_points;
 }
 
 
diff --git a/source/grid/reference_cell.cc b/source/grid/reference_cell.cc
index f670dde1f8..54ee83ba0a 100644
--- a/source/grid/reference_cell.cc
+++ b/source/grid/reference_cell.cc
@@ -13,7 +13,9 @@
 //
 // ---------------------------------------------------------------------
 
+#include <deal.II/base/polynomial.h>
 #include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/tensor_product_polynomials.h>
 
 #include <deal.II/fe/mapping_fe.h>
 #include <deal.II/fe/mapping_q1.h>
@@ -23,6 +25,7 @@
 #include <deal.II/grid/tria.h>
 
 #include <deal.II/simplex/fe_lib.h>
+#include <deal.II/simplex/polynomials.h>
 #include <deal.II/simplex/quadrature_lib.h>
 
 DEAL_II_NAMESPACE_OPEN
@@ -102,6 +105,7 @@ namespace ReferenceCell
   }
 
 
+
   template <int dim, int spacedim>
   const Mapping<dim, spacedim> &
   get_default_linear_mapping(const Type &reference_cell)
diff --git a/tests/simplex/mapping_fe_01.cc b/tests/simplex/mapping_fe_01.cc
new file mode 100644
index 0000000000..6bcb8ce79f
--- /dev/null
+++ b/tests/simplex/mapping_fe_01.cc
@@ -0,0 +1,81 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 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.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+// Distribute Simplex::FE_Wedge on a DoFHandler.
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_fe.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/numerics/data_out.h>
+
+#include <deal.II/simplex/fe_lib.h>
+#include <deal.II/simplex/quadrature_lib.h>
+
+#include "../tests.h"
+
+using namespace dealii;
+
+void
+test(const unsigned int mapping_degree)
+{
+  const int dim = 2;
+
+  Triangulation<dim> tria, tria_temp;
+  GridGenerator::hyper_shell(tria_temp, Point<dim>(), 1.0, 2.0);
+  GridGenerator::convert_hypercube_to_simplex_mesh(tria_temp, tria);
+  for (const auto i : tria_temp.get_manifold_ids())
+    if (i != numbers::flat_manifold_id)
+      tria.set_manifold(i, tria_temp.get_manifold(i));
+
+  Simplex::FE_P<dim> fe(2);
+
+  DoFHandler<dim> dof_handler(tria);
+  dof_handler.distribute_dofs(fe);
+
+  MappingFE<dim> mapping(Simplex::FE_P<dim>{mapping_degree});
+
+  {
+    DataOut<dim> data_out;
+
+    data_out.attach_dof_handler(dof_handler);
+
+    Vector<double> solution(dof_handler.n_dofs());
+    data_out.add_data_vector(solution, "solution");
+
+    data_out.build_patches(mapping, 2);
+
+#if false
+    std::ofstream output("test." + std::to_string(mapping_degree) +  ".vtk");
+    data_out.write_vtk(output);
+#else
+    data_out.write_vtk(deallog.get_file_stream());
+#endif
+  }
+}
+
+int
+main()
+{
+  initlog();
+
+  test(1);
+  test(2);
+}
diff --git a/tests/simplex/mapping_fe_01.with_simplex_support=on.output b/tests/simplex/mapping_fe_01.with_simplex_support=on.output
new file mode 100644
index 0000000000..d019ed1ae3
--- /dev/null
+++ b/tests/simplex/mapping_fe_01.with_simplex_support=on.output
@@ -0,0 +1,1151 @@
+
+# vtk DataFile Version 3.0
+#This file was generated 
+ASCII
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+
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