Fix MG transfer for Tetrahedrons

The prolongation and embedding matrices for Tetrahedral elements are incorrect, due to the new refinement strategy. Fix the interpolation operations by saving the refinement direction and using it to compute the matrices.

diff --git a/include/deal.II/fe/fe_simplex_p.h b/include/deal.II/fe/fe_simplex_p.h
index fce4b92a4b6d794117198bd90b29bbea6a896297..de1df4cf8e530d954df7393f8b7c724f295d088e 100644 (file)
--- a/include/deal.II/fe/fe_simplex_p.h
+++ b/include/deal.II/fe/fe_simplex_p.h
@@ -42,6 +42,7 @@ public:
   FE_SimplexPoly(
     const BarycentricPolynomials<dim>              polynomials,
     const FiniteElementData<dim>                  &fe_data,
+    const bool                                     prolongation_is_additive,
     const std::vector<Point<dim>>                 &unit_support_points,
     const std::vector<std::vector<Point<dim - 1>>> unit_face_support_points,
     const FullMatrix<double>                      &interface_constraints);
@@ -107,7 +108,7 @@ public:
     const std::vector<Vector<double>> &support_point_values,
     std::vector<double>               &nodal_values) const override;
 
-private:
+protected:
   /**
    * Mutex variables used for protecting the initialization of restriction
    * and embedding matrices.
@@ -225,6 +226,17 @@ public:
   std::vector<std::pair<unsigned int, unsigned int>>
   hp_line_dof_identities(
     const FiniteElement<dim, spacedim> &fe_other) const override;
+
+  /**
+   * @copydoc dealii::FiniteElement::get_restriction_matrix()
+   *
+   * @note Only implemented for RefinementCase::isotropic_refinement.
+   */
+  virtual const FullMatrix<double> &
+  get_restriction_matrix(
+    const unsigned int         child,
+    const RefinementCase<dim> &refinement_case =
+      RefinementCase<dim>::isotropic_refinement) const override;
 };
 
 DEAL_II_NAMESPACE_CLOSE

diff --git a/include/deal.II/fe/fe_tools.templates.h b/include/deal.II/fe/fe_tools.templates.h
index 5eac211eaeff4a2a3928f9f841c347bab68abfdb..898aea2e2b2916ebfb9eb0166a24c09177eade5e 100644 (file)
--- a/include/deal.II/fe/fe_tools.templates.h
+++ b/include/deal.II/fe/fe_tools.templates.h
@@ -1715,9 +1715,10 @@ namespace FETools
         const unsigned int                  ref_case,
         const double                        threshold)
       {
-        const unsigned int n = fe.n_dofs_per_cell();
-        const unsigned int nc =
-          GeometryInfo<dim>::n_children(RefinementCase<dim>(ref_case));
+        const unsigned int  n              = fe.n_dofs_per_cell();
+        const ReferenceCell reference_cell = fe.reference_cell();
+        const unsigned int  nc =
+          reference_cell.n_children(RefinementCase<dim>(ref_case));
 
         AssertDimension(matrices.size(), nc);
 
@@ -1729,13 +1730,19 @@ namespace FETools
                    ExcDimensionMismatch(matrices[i].m(), n));
           }
 
-        const ReferenceCell reference_cell = fe.reference_cell();
 
         // Set up meshes, one with a single
         // reference cell and refine it once
         Triangulation<dim, spacedim> tria;
         GridGenerator::reference_cell(tria, reference_cell);
-        tria.begin_active()->set_refine_flag(RefinementCase<dim>(ref_case));
+        if (reference_cell == ReferenceCells::Tetrahedron)
+          {
+            tria.begin_active()->set_refine_flag(
+              RefinementCase<dim>::isotropic_refinement);
+            tria.begin_active()->set_refine_choice(ref_case);
+          }
+        else
+          tria.begin_active()->set_refine_flag(RefinementCase<dim>(ref_case));
         tria.execute_coarsening_and_refinement();
 
         const unsigned int degree = fe.degree;
@@ -1862,10 +1869,23 @@ namespace FETools
     Threads::TaskGroup<void> task_group;
 
     // loop over all possible refinement cases
-    for (unsigned int ref_case =
-           (isotropic_only ? RefinementCase<dim>::isotropic_refinement :
-                             RefinementCase<dim>::cut_x);
-         ref_case <= RefinementCase<dim>::isotropic_refinement;
+    unsigned int ref_case_start, ref_case_end;
+
+    if (fe.reference_cell() == ReferenceCells::Tetrahedron)
+      {
+        ref_case_start =
+          static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_68);
+        ref_case_end =
+          static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49);
+      }
+    else
+      {
+        ref_case_start = isotropic_only ?
+                           RefinementCase<dim>::isotropic_refinement :
+                           RefinementCase<dim>::cut_x;
+        ref_case_end   = RefinementCase<dim>::isotropic_refinement;
+      }
+    for (unsigned int ref_case = ref_case_start; ref_case <= ref_case_end;
          ++ref_case)
       task_group += Threads::new_task(
         &internal::FEToolsComputeEmbeddingMatricesHelper::
@@ -2169,7 +2189,7 @@ namespace FETools
         const FullMatrix<double>        &inverse_mass_matrix,
         std::vector<FullMatrix<double>> &matrices) {
         const unsigned int nc =
-          GeometryInfo<dim>::n_children(RefinementCase<dim>(ref_case));
+          reference_cell.n_children(RefinementCase<dim>(ref_case));
 
         for (unsigned int i = 0; i < nc; ++i)
           {
@@ -2182,7 +2202,15 @@ namespace FETools
         // create a respective refinement on the triangulation
         Triangulation<dim, spacedim> tr;
         GridGenerator::reference_cell(tr, reference_cell);
-        tr.begin_active()->set_refine_flag(RefinementCase<dim>(ref_case));
+
+        if (reference_cell == ReferenceCells::Tetrahedron)
+          {
+            tr.begin_active()->set_refine_flag(
+              RefinementCase<dim>::isotropic_refinement);
+            tr.begin_active()->set_refine_choice(ref_case);
+          }
+        else
+          tr.begin_active()->set_refine_flag(RefinementCase<dim>(ref_case));
         tr.execute_coarsening_and_refinement();
 
         FEValues<dim, spacedim> fine(mapping,
@@ -2267,10 +2295,22 @@ namespace FETools
 
     // finally loop over all possible refinement cases
     Threads::TaskGroup<> tasks;
-    for (unsigned int ref_case =
-           (isotropic_only ? RefinementCase<dim>::isotropic_refinement :
-                             RefinementCase<dim>::cut_x);
-         ref_case <= RefinementCase<dim>::isotropic_refinement;
+    unsigned int         ref_case_start, ref_case_end;
+    if (reference_cell == ReferenceCells::Tetrahedron)
+      {
+        ref_case_start =
+          static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_68);
+        ref_case_end =
+          static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49);
+      }
+    else
+      {
+        ref_case_start =
+          (isotropic_only ? RefinementCase<dim>::isotropic_refinement :
+                            RefinementCase<dim>::cut_x);
+        ref_case_end = RefinementCase<dim>::isotropic_refinement;
+      }
+    for (unsigned int ref_case = ref_case_start; ref_case <= ref_case_end;
          ++ref_case)
       tasks += Threads::new_task([&, ref_case]() {
         compute_one_case(ref_case, mass, matrices[ref_case - 1]);

diff --git a/include/deal.II/grid/reference_cell.h b/include/deal.II/grid/reference_cell.h
index 803a5a00fb9172c6219b4d5f5f84e68e7d2cc5a0..35c5a2f048a0d7c92db9fa2f9a7438426485893b 100644 (file)
--- a/include/deal.II/grid/reference_cell.h
+++ b/include/deal.II/grid/reference_cell.h
@@ -65,6 +65,34 @@ namespace internal
 
 
 
+/**
+ * Enum of different choices for istropic refinement.
+ * There are 3 different ways to refine a tetrahedral, here we save the
+ * different possibilites. It is different to RefinementPossibilites are these
+ * are options in the case that an isotropic refinement is conducted.
+ */
+enum class IsotropicRefinementChoice : std::uint8_t
+{
+  /**
+   * Decide where to perform a cut based on the shortest edge length.
+   */
+  isotropic_refinement = 0,
+  /**
+   * Perform a cut in the along the edge (6,8).
+   */
+  cut_tet_68 = 1,
+  /**
+   * Perform a cut in the along the edge (5,7).
+   */
+  cut_tet_57 = 2,
+  /**
+   * Perform a cut in the along the edge (4,9).
+   */
+  cut_tet_49 = 3,
+};
+
+
+
 /**
  * A type that describes the kinds of reference cells that can be
  * used.  This includes quadrilaterals and hexahedra (i.e.,
@@ -305,6 +333,18 @@ public:
   std_cxx20::ranges::iota_view<unsigned int, unsigned int>
   face_indices() const;
 
+  /**
+   * Return the number of refinement directions of the cell.
+   */
+  unsigned int
+  n_isotropic_refinement_choices() const;
+
+  /**
+   * Return the refinement possibility @p ref_choice.
+   */
+  IsotropicRefinementChoice
+  get_isotropic_refinement_choice(const unsigned int ref_choice) const;
+
   /**
    * Return the number of cells one would get by isotropically
    * refining the current cell. Here, "isotropic refinement"
@@ -319,6 +359,15 @@ public:
   unsigned int
   n_isotropic_children() const;
 
+  /**
+   * Return the number of cells one would get by refining the
+   * current cell with the given refinement case.
+   */
+  template <int dim>
+  unsigned int
+  n_children(const RefinementCase<dim> ref_case =
+               RefinementCase<dim>::isotropic_refinement) const;
+
   /**
    * Return an object that can be thought of as an array containing all
    * indices from zero to n_isotropic_children().
@@ -725,6 +774,35 @@ public:
   ArrayView<const unsigned int>
   faces_for_given_vertex(const unsigned int vertex_index) const;
 
+  /**
+   * Return a vector of line indices for all new faces required for isotropic
+   * refinement.
+   */
+  constexpr dealii::ndarray<unsigned int, 12, 4>
+  new_isotropic_child_face_lines(const unsigned int refinement_choice) const;
+
+  /**
+   * Return a vector of vertex indices for all new face lines required for
+   * isotropic refinement.
+   */
+  constexpr dealii::ndarray<unsigned int, 12, 4, 2>
+  new_isotropic_child_face_line_vertices(
+    const unsigned int refinement_choice) const;
+
+  /**
+   * Return a vector of face indices for all new cells required for isotropic
+   * refinement.
+   */
+  constexpr dealii::ndarray<unsigned int, 8, 6>
+  new_isotropic_child_cell_faces(const unsigned int refinement_choice) const;
+
+  /**
+   * Return a vector of vertex indices for all new cells required for isotropic
+   * refinement.
+   */
+  constexpr dealii::ndarray<unsigned int, 8, 4>
+  new_isotropic_child_cell_vertices(const unsigned int refinement_choice) const;
+
   /**
    * @}
    */
@@ -1115,6 +1193,280 @@ ReferenceCell::faces_for_given_vertex(const unsigned int vertex) const
 }
 
 
+constexpr dealii::ndarray<unsigned int, 12, 4>
+ReferenceCell::new_isotropic_child_face_lines(
+  const unsigned int refienement_choice) const
+{
+  // AssertIndexRange(refienement_choice, n_isotropic_refinement_choices());
+  const unsigned int X = numbers::invalid_unsigned_int;
+  switch (this->kind)
+    {
+      case ReferenceCells::Tetrahedron:
+        {
+          constexpr dealii::ndarray<unsigned int, 3, 12, 4> new_quad_lines_tet =
+            {{// new line is (6,8)
+              {{{{2, 3, 8, X}},
+                {{0, 9, 5, X}},
+                {{1, 6, 11, X}},
+                {{4, 10, 7, X}},
+                {{2, 12, 5, X}},
+                {{1, 9, 12, X}},
+                {{4, 8, 12, X}},
+                {{6, 12, 10, X}},
+                {{X, X, X, X}},
+                {{X, X, X, X}},
+                {{X, X, X, X}},
+                {{X, X, X, X}}}},
+              // new line is (5,7)
+              {{{{2, 3, 8, X}},
+                {{0, 9, 5, X}},
+                {{1, 6, 11, X}},
+                {{4, 10, 7, X}},
+                {{0, 3, 12, X}},
+                {{1, 12, 8, X}},
+                {{4, 12, 9, X}},
+                {{7, 11, 12, X}},
+                {{X, X, X, X}},
+                {{X, X, X, X}},
+                {{X, X, X, X}},
+                {{X, X, X, X}}}},
+              // new line is (4,9)
+              {{{{2, 3, 8, X}},
+                {{0, 9, 5, X}},
+                {{1, 6, 11, X}},
+                {{4, 10, 7, X}},
+                {{0, 12, 11, X}},
+                {{2, 6, 12, X}},
+                {{3, 12, 7, X}},
+                {{5, 10, 12, X}},
+                {{X, X, X, X}},
+                {{X, X, X, X}},
+                {{X, X, X, X}},
+                {{X, X, X, X}}}}}};
+          return new_quad_lines_tet[refienement_choice];
+        }
+
+      case ReferenceCells::Hexahedron:
+        {
+          constexpr dealii::ndarray<unsigned int, 12, 4> new_quad_lines_hex = {
+            {{{10, 28, 16, 24}},
+             {{28, 14, 17, 25}},
+             {{11, 29, 24, 20}},
+             {{29, 15, 25, 21}},
+             {{18, 26, 0, 28}},
+             {{26, 22, 1, 29}},
+             {{19, 27, 28, 4}},
+             {{27, 23, 29, 5}},
+             {{2, 24, 8, 26}},
+             {{24, 6, 9, 27}},
+             {{3, 25, 26, 12}},
+             {{25, 7, 27, 13}}}};
+          return new_quad_lines_hex;
+        }
+      default:
+        DEAL_II_NOT_IMPLEMENTED();
+    }
+
+  return {};
+}
+
+
+
+constexpr dealii::ndarray<unsigned int, 12, 4, 2>
+ReferenceCell::new_isotropic_child_face_line_vertices(
+  const unsigned int refienement_choice) const
+{
+  // AssertIndexRange(refienement_choice, n_isotropic_refinement_choices());
+  const unsigned int X = numbers::invalid_unsigned_int;
+  switch (this->kind)
+    {
+      case ReferenceCells::Tetrahedron:
+        {
+          constexpr dealii::ndarray<unsigned int, 3, 12, 4, 2> table_tet = {
+            {// new line is (6, 8)
+             {{{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
+               {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
+               {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
+               {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
+               {{{{4, 6}}, {{6, 8}}, {{8, 4}}, {{X, X}}}},
+               {{{{6, 5}}, {{5, 8}}, {{8, 6}}, {{X, X}}}},
+               {{{{8, 7}}, {{7, 6}}, {{6, 8}}, {{X, X}}}},
+               {{{{9, 6}}, {{6, 8}}, {{8, 9}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}},
+             // new line is (5, 7)
+             {{{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
+               {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
+               {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
+               {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
+               {{{{5, 4}}, {{4, 7}}, {{7, 5}}, {{X, X}}}},
+               {{{{6, 5}}, {{5, 7}}, {{7, 6}}, {{X, X}}}},
+               {{{{8, 7}}, {{7, 5}}, {{5, 8}}, {{X, X}}}},
+               {{{{7, 9}}, {{9, 5}}, {{5, 7}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}},
+             // new line is (4, 9)
+             {{{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
+               {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
+               {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
+               {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
+               {{{{5, 4}}, {{4, 9}}, {{9, 5}}, {{X, X}}}},
+               {{{{4, 6}}, {{6, 9}}, {{9, 4}}, {{X, X}}}},
+               {{{{7, 4}}, {{4, 9}}, {{9, 7}}, {{X, X}}}},
+               {{{{4, 8}}, {{8, 9}}, {{9, 4}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
+               {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}}}};
+          return table_tet[refienement_choice];
+        }
+
+      case ReferenceCells::Hexahedron:
+        {
+          constexpr dealii::ndarray<unsigned int, 12, 4, 2> table_hex = {
+            {{{{{10, 22}}, {{24, 26}}, {{10, 24}}, {{22, 26}}}},
+             {{{{24, 26}}, {{11, 23}}, {{24, 11}}, {{26, 23}}}},
+             {{{{22, 14}}, {{26, 25}}, {{22, 26}}, {{14, 25}}}},
+             {{{{26, 25}}, {{23, 15}}, {{26, 23}}, {{25, 15}}}},
+             {{{{8, 24}}, {{20, 26}}, {{8, 20}}, {{24, 26}}}},
+             {{{{20, 26}}, {{12, 25}}, {{20, 12}}, {{26, 25}}}},
+             {{{{24, 9}}, {{26, 21}}, {{24, 26}}, {{9, 21}}}},
+             {{{{26, 21}}, {{25, 13}}, {{26, 25}}, {{21, 13}}}},
+             {{{{16, 20}}, {{22, 26}}, {{16, 22}}, {{20, 26}}}},
+             {{{{22, 26}}, {{17, 21}}, {{22, 17}}, {{26, 21}}}},
+             {{{{20, 18}}, {{26, 23}}, {{20, 26}}, {{18, 23}}}},
+             {{{{26, 23}}, {{21, 19}}, {{26, 21}}, {{23, 19}}}}}};
+          return table_hex;
+        }
+      default:
+        DEAL_II_NOT_IMPLEMENTED();
+    }
+
+  return {};
+}
+
+
+
+constexpr dealii::ndarray<unsigned int, 8, 6>
+ReferenceCell::new_isotropic_child_cell_faces(
+  const unsigned int refienement_choice) const
+{
+  // AssertIndexRange(refienement_choice, n_isotropic_refinement_choices());
+  const unsigned int X = numbers::invalid_unsigned_int;
+  switch (this->kind)
+    {
+      case ReferenceCells::Tetrahedron:
+        {
+          constexpr dealii::ndarray<unsigned int, 3, 8, 6> cell_quads_tet = {
+            {// new line is (6, 8)
+             {{{{8, 13, 16, 0, X, X}},
+               {{9, 12, 1, 21, X, X}},
+               {{10, 2, 17, 20, X, X}},
+               {{3, 14, 18, 22, X, X}},
+               {{11, 1, 4, 5, X, X}},
+               {{15, 0, 4, 6, X, X}},
+               {{19, 7, 6, 3, X, X}},
+               {{23, 5, 2, 7, X, X}}}},
+             // new line is (5, 7)
+             {{
+               {{8, 13, 16, 0, X, X}},
+               {{9, 12, 1, 21, X, X}},
+               {{10, 2, 17, 20, X, X}},
+               {{3, 14, 18, 22, X, X}},
+               {{11, 4, 0, 5, X, X}},
+               {{15, 4, 1, 6, X, X}},
+               {{19, 2, 5, 7, X, X}},
+               {{23, 6, 7, 3, X, X}},
+             }},
+             // new line is (4, 9)
+             {{
+               {{8, 13, 16, 0, X, X}},
+               {{9, 12, 1, 21, X, X}},
+               {{10, 2, 17, 20, X, X}},
+               {{3, 14, 18, 22, X, X}},
+               {{11, 4, 5, 2, X, X}},
+               {{15, 6, 7, 3, X, X}},
+               {{19, 5, 0, 6, X, X}},
+               {{23, 1, 4, 7, X, X}},
+             }}}};
+          return cell_quads_tet[refienement_choice];
+        }
+
+      case ReferenceCells::Hexahedron:
+        {
+          constexpr dealii::ndarray<unsigned int, 8, 6> cell_quads_hex = {{
+            {{12, 0, 20, 4, 28, 8}},  // bottom children
+            {{0, 16, 22, 6, 29, 9}},  //
+            {{13, 1, 4, 24, 30, 10}}, //
+            {{1, 17, 6, 26, 31, 11}}, //
+            {{14, 2, 21, 5, 8, 32}},  // top children
+            {{2, 18, 23, 7, 9, 33}},  //
+            {{15, 3, 5, 25, 10, 34}}, //
+            {{3, 19, 7, 27, 11, 35}}  //
+          }};
+          return cell_quads_hex;
+        }
+      default:
+        DEAL_II_NOT_IMPLEMENTED();
+    }
+
+  return {};
+}
+
+
+
+constexpr dealii::ndarray<unsigned int, 8, 4>
+ReferenceCell::new_isotropic_child_cell_vertices(
+  const unsigned int refienement_choice) const
+{
+  // AssertIndexRange(refienement_choice, n_isotropic_refinement_choices());
+
+  switch (this->kind)
+    {
+      case ReferenceCells::Tetrahedron:
+        {
+          constexpr dealii::ndarray<unsigned int, 3, 8, 4> cell_vertices_tet = {
+            {// new line is (6,8)
+             {{{{0, 4, 6, 7}},
+               {{4, 1, 5, 8}},
+               {{6, 5, 2, 9}},
+               {{7, 8, 9, 3}},
+               {{4, 5, 6, 8}},
+               {{4, 7, 8, 6}},
+               {{6, 9, 7, 8}},
+               {{5, 8, 9, 6}}}},
+             // new line is (5,7)
+             {{{{0, 4, 6, 7}},
+               {{4, 1, 5, 8}},
+               {{6, 5, 2, 9}},
+               {{7, 8, 9, 3}},
+               {{4, 5, 6, 7}},
+               {{4, 7, 8, 5}},
+               {{6, 9, 7, 5}},
+               {{5, 8, 9, 7}}}},
+             // new line is (4,9)
+             {{{{0, 4, 6, 7}},
+               {{4, 1, 5, 8}},
+               {{6, 5, 2, 9}},
+               {{7, 8, 9, 3}},
+               {{4, 5, 6, 9}},
+               {{4, 7, 8, 9}},
+               {{6, 9, 7, 4}},
+               {{5, 8, 9, 4}}}}}};
+          return cell_vertices_tet[refienement_choice];
+        }
+      default:
+        DEAL_II_NOT_IMPLEMENTED();
+    }
+
+  return {};
+}
+
+
 
 inline bool
 ReferenceCell::is_hyper_cube() const
@@ -1390,6 +1742,62 @@ ReferenceCell::face_indices() const
 
 
 
+inline unsigned int
+ReferenceCell::n_isotropic_refinement_choices() const
+{
+  switch (this->kind)
+    {
+      case ReferenceCells::Vertex:
+        return 1;
+      case ReferenceCells::Line:
+        return 1;
+      case ReferenceCells::Triangle:
+        return 1;
+      case ReferenceCells::Quadrilateral:
+        return 1;
+      case ReferenceCells::Tetrahedron:
+        return 3;
+      case ReferenceCells::Pyramid:
+        return 1;
+      case ReferenceCells::Wedge:
+        return 1;
+      case ReferenceCells::Hexahedron:
+        return 1;
+      default:
+        DEAL_II_ASSERT_UNREACHABLE();
+    }
+
+  return numbers::invalid_unsigned_int;
+}
+
+
+
+inline IsotropicRefinementChoice
+ReferenceCell::get_isotropic_refinement_choice(
+  const unsigned int ref_choice) const
+{
+  AssertIndexRange(ref_choice, n_isotropic_refinement_choices());
+  switch (this->kind)
+    {
+      case ReferenceCells::Tetrahedron:
+        {
+          static constexpr ndarray<IsotropicRefinementChoice, 3>
+            isotropic_ref_choices = {{IsotropicRefinementChoice::cut_tet_68,
+                                      IsotropicRefinementChoice::cut_tet_57,
+                                      IsotropicRefinementChoice::cut_tet_49}};
+          return isotropic_ref_choices[ref_choice];
+        }
+      default:
+        {
+          DEAL_II_NOT_IMPLEMENTED();
+        }
+    }
+
+  return IsotropicRefinementChoice::isotropic_refinement;
+}
+
+
+
 inline unsigned int
 ReferenceCell::n_isotropic_children() const
 {
@@ -1408,14 +1816,13 @@ ReferenceCell::n_isotropic_children() const
       case ReferenceCells::Pyramid:
         // We haven't yet decided how to refine pyramids. Update this when we
         // have
-        DEAL_II_NOT_IMPLEMENTED();
-        return numbers::invalid_unsigned_int;
+        return 0;
       case ReferenceCells::Wedge:
         return 8;
       case ReferenceCells::Hexahedron:
         return 8;
       default:
-        DEAL_II_NOT_IMPLEMENTED();
+        DEAL_II_ASSERT_UNREACHABLE();
     }
 
   return numbers::invalid_unsigned_int;
@@ -1423,6 +1830,19 @@ ReferenceCell::n_isotropic_children() const
 
 
 
+template <int dim>
+unsigned int
+ReferenceCell::n_children(const RefinementCase<dim> ref_case) const
+{
+  // Use GeometryInfo here to keep it the single source of truth
+  if (this->is_hyper_cube())
+    return GeometryInfo<dim>::n_children(ref_case);
+  else
+    return this->n_isotropic_children();
+}
+
+
+
 inline std_cxx20::ranges::iota_view<unsigned int, unsigned int>
 ReferenceCell::isotropic_child_indices() const
 {

diff --git a/include/deal.II/grid/tria_accessor.h b/include/deal.II/grid/tria_accessor.h
index 1b783c7d26053bd9e3a4cc437f4f4a469d26f1ab..b8f7dc8e46dcd7cf2d0af5a9c1709e8f77454eaa 100644 (file)
--- a/include/deal.II/grid/tria_accessor.h
+++ b/include/deal.II/grid/tria_accessor.h
@@ -3630,6 +3630,27 @@ public:
   void
   clear_refine_flag() const;
 
+  /**
+   * Return the @p IsotropicRefinementChoices this cell was flagged to be refined
+   * with.
+   */
+  std::uint8_t
+  refine_choice() const;
+
+  /**
+   * Set the @p IsotropicRefinementChoices this cell is flagged to be refined
+   * with.
+   */
+  void
+  set_refine_choice(const std::uint8_t refinement_choice = static_cast<char>(
+                      IsotropicRefinementChoice::isotropic_refinement)) const;
+
+  /**
+   * Clear the @p IsotropicRefinementChoices flag.
+   */
+  void
+  clear_refine_choice() const;
+
   /**
    * Modify the refinement flag of the cell to ensure (at least) the given
    * refinement case @p face_refinement_case at face <tt>face_no</tt>, taking

diff --git a/include/deal.II/grid/tria_accessor.templates.h b/include/deal.II/grid/tria_accessor.templates.h
index 6fd99cee448fedbad57a40634ffe0837adc93d37..b355a63752a54c1ccabae9224beb5df1a949b0c2 100644 (file)
--- a/include/deal.II/grid/tria_accessor.templates.h
+++ b/include/deal.II/grid/tria_accessor.templates.h
@@ -1735,7 +1735,14 @@ template <int structdim, int dim, int spacedim>
 inline unsigned int
 TriaAccessor<structdim, dim, spacedim>::n_children() const
 {
-  return GeometryInfo<structdim>::n_children(refinement_case());
+  Assert(this->state() == IteratorState::valid,
+         TriaAccessorExceptions::ExcDereferenceInvalidObject<TriaAccessor>(
+           *this));
+  if (reference_cell() == ReferenceCells::Tetrahedron)
+    return GeometryInfo<structdim>::n_children(
+      RefinementCase<structdim>::isotropic_refinement);
+  else
+    return GeometryInfo<structdim>::n_children(refinement_case());
 }
 
 
@@ -3643,6 +3650,41 @@ CellAccessor<dim, spacedim>::clear_refine_flag() const
 }
 
 
+template <int dim, int spacedim>
+inline std::uint8_t
+CellAccessor<dim, spacedim>::refine_choice() const
+{
+  Assert(this->used(), TriaAccessorExceptions::ExcCellNotUsed());
+  if (this->tria->levels[this->present_level]->refine_choice.size() == 0)
+    return 0U;
+  return this->tria->levels[this->present_level]
+    ->refine_choice[this->present_index];
+}
+
+
+template <int dim, int spacedim>
+inline void
+CellAccessor<dim, spacedim>::set_refine_choice(
+  const std::uint8_t refinement_choice) const
+{
+  Assert(this->used() && this->is_active(), ExcRefineCellNotActive());
+  if (this->tria->levels[this->present_level]->refine_choice.size() != 0)
+    this->tria->levels[this->present_level]
+      ->refine_choice[this->present_index] = refinement_choice;
+}
+
+
+template <int dim, int spacedim>
+inline void
+CellAccessor<dim, spacedim>::clear_refine_choice() const
+{
+  Assert(this->used() && this->is_active(), ExcRefineCellNotActive());
+  if (this->tria->levels[this->present_level]->refine_choice.size() != 0)
+    this->tria->levels[this->present_level]
+      ->refine_choice[this->present_index] =
+      static_cast<char>(IsotropicRefinementChoice::isotropic_refinement);
+}
+
 
 template <int dim, int spacedim>
 inline bool

diff --git a/include/deal.II/grid/tria_levels.h b/include/deal.II/grid/tria_levels.h
index 96384a48e98071f16982c76797aead6e70866bc2..468820f8c087637f676f9644e05a5d11b9505a7b 100644 (file)
--- a/include/deal.II/grid/tria_levels.h
+++ b/include/deal.II/grid/tria_levels.h
@@ -88,6 +88,13 @@ namespace internal
        */
       std::vector<std::uint8_t> refine_flags;
 
+      /**
+       * @p IsotropicRefinementChoices direction for the tetrahedral cells to be
+       * refined with
+       * or choose the optimal way @p ReferenceCell::isotropic_refinement.
+       */
+      std::vector<std::uint8_t> refine_choice;
+
       /**
        * Same meaning as the one above, but specifies whether a cell must be
        * coarsened.

diff --git a/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h b/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h
index a0e12f38a1d7b6b23efc92984a442dea0633fd40..35f8bb1714510385f6a068ecb38f54028c524aaa 100644 (file)
--- a/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h
+++ b/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h
@@ -376,14 +376,16 @@ namespace internal
 
     template <int dim, int spacedim>
     FullMatrix<double>
-    get_restriction_matrix(const FiniteElement<dim, spacedim> &fe,
-                           const unsigned int                  child)
+    get_restriction_matrix(
+      const FiniteElement<dim, spacedim> &fe,
+      const unsigned int                  child,
+      RefinementCase<dim> ref_case = RefinementCase<dim>::isotropic_refinement)
     {
-      auto matrix = fe.get_restriction_matrix(child);
+      auto matrix = fe.get_restriction_matrix(child, ref_case);
 
       for (unsigned int c_other = 0; c_other < child; ++c_other)
         {
-          auto matrix_other = fe.get_restriction_matrix(c_other);
+          auto matrix_other = fe.get_restriction_matrix(c_other, ref_case);
           for (unsigned int i = 0; i < fe.n_dofs_per_cell(); ++i)
             {
               if (fe.restriction_is_additive(i) == true)
@@ -1973,13 +1975,20 @@ namespace internal
               for (unsigned int c = 0;
                    c < GeometryInfo<dim>::max_children_per_cell;
                    ++c)
-                for (unsigned int i = 0; i < n_dofs_per_cell; ++i)
-                  for (unsigned int j = 0; j < n_dofs_per_cell; ++j)
-                    transfer.schemes[1].prolongation_matrix
-                      [i * n_dofs_per_cell *
-                         GeometryInfo<dim>::max_children_per_cell +
-                       j + c * n_dofs_per_cell] =
-                      fe.get_prolongation_matrix(c)(j, i);
+                {
+                  const auto matrix =
+                    reference_cell == ReferenceCells::Tetrahedron ?
+                      fe.get_prolongation_matrix(c, RefinementCase<dim>(1)) :
+                      fe.get_prolongation_matrix(c);
+
+
+                  for (unsigned int i = 0; i < n_dofs_per_cell; ++i)
+                    for (unsigned int j = 0; j < n_dofs_per_cell; ++j)
+                      transfer.schemes[1].prolongation_matrix
+                        [i * n_dofs_per_cell *
+                           GeometryInfo<dim>::max_children_per_cell +
+                         j + c * n_dofs_per_cell] = matrix(j, i);
+                }
             }
             {
               transfer.schemes[1].restriction_matrix.resize(
@@ -1990,7 +1999,10 @@ namespace internal
                    c < GeometryInfo<dim>::max_children_per_cell;
                    ++c)
                 {
-                  const auto matrix = get_restriction_matrix(fe, c);
+                  const auto matrix =
+                    reference_cell == ReferenceCells::Tetrahedron ?
+                      get_restriction_matrix(fe, c, RefinementCase<dim>(1)) :
+                      get_restriction_matrix(fe, c);
                   for (unsigned int i = 0; i < n_dofs_per_cell; ++i)
                     for (unsigned int j = 0; j < n_dofs_per_cell; ++j)
                       transfer.schemes[1].restriction_matrix

diff --git a/source/fe/fe.cc b/source/fe/fe.cc
index a114eff2f76ade4e35b5eea2494e2eef80293512..b8785c5ce591819c737f923039368d68dab81530 100644 (file)
--- a/source/fe/fe.cc
+++ b/source/fe/fe.cc
@@ -139,10 +139,10 @@ FiniteElement<dim, spacedim>::FiniteElement(
        RefinementCase<dim>::all_refinement_cases())
     if (ref_case != RefinementCase<dim>::no_refinement)
       {
-        prolongation[ref_case - 1].resize(GeometryInfo<dim>::n_children(
+        prolongation[ref_case - 1].resize(this->reference_cell().n_children(
                                             RefinementCase<dim>(ref_case)),
                                           FullMatrix<double>());
-        restriction[ref_case - 1].resize(GeometryInfo<dim>::n_children(
+        restriction[ref_case - 1].resize(this->reference_cell().n_children(
                                            RefinementCase<dim>(ref_case)),
                                          FullMatrix<double>());
       }
@@ -305,7 +305,7 @@ FiniteElement<dim, spacedim>::reinit_restriction_and_prolongation_matrices(
     if (ref_case != RefinementCase<dim>::no_refinement)
       {
         const unsigned int nc =
-          GeometryInfo<dim>::n_children(RefinementCase<dim>(ref_case));
+          this->reference_cell().n_children(RefinementCase<dim>(ref_case));
 
         for (unsigned int i = 0; i < nc; ++i)
           {
@@ -337,8 +337,9 @@ FiniteElement<dim, spacedim>::get_restriction_matrix(
   Assert(refinement_case != RefinementCase<dim>::no_refinement,
          ExcMessage(
            "Restriction matrices are only available for refined cells!"));
-  AssertIndexRange(
-    child, GeometryInfo<dim>::n_children(RefinementCase<dim>(refinement_case)));
+  AssertIndexRange(child,
+                   this->reference_cell().n_children(
+                     RefinementCase<dim>(refinement_case)));
   // we use refinement_case-1 here. the -1 takes care of the origin of the
   // vector, as for RefinementCase<dim>::no_refinement (=0) there is no data
   // available and so the vector indices are shifted
@@ -360,8 +361,9 @@ FiniteElement<dim, spacedim>::get_prolongation_matrix(
   Assert(refinement_case != RefinementCase<dim>::no_refinement,
          ExcMessage(
            "Prolongation matrices are only available for refined cells!"));
-  AssertIndexRange(
-    child, GeometryInfo<dim>::n_children(RefinementCase<dim>(refinement_case)));
+  AssertIndexRange(child,
+                   this->reference_cell().n_children(
+                     RefinementCase<dim>(refinement_case)));
   // we use refinement_case-1 here. the -1 takes care
   // of the origin of the vector, as for
   // RefinementCase::no_refinement (=0) there is no
@@ -703,7 +705,7 @@ FiniteElement<dim, spacedim>::prolongation_is_implemented() const
        RefinementCase<dim>::all_refinement_cases())
     if (ref_case != RefinementCase<dim>::no_refinement)
       for (unsigned int c = 0;
-           c < GeometryInfo<dim>::n_children(RefinementCase<dim>(ref_case));
+           c < this->reference_cell().n_children(RefinementCase<dim>(ref_case));
            ++c)
         {
           // make sure also the lazily initialized matrices are created
@@ -733,7 +735,7 @@ FiniteElement<dim, spacedim>::restriction_is_implemented() const
        RefinementCase<dim>::all_refinement_cases())
     if (ref_case != RefinementCase<dim>::no_refinement)
       for (unsigned int c = 0;
-           c < GeometryInfo<dim>::n_children(RefinementCase<dim>(ref_case));
+           c < this->reference_cell().n_children(RefinementCase<dim>(ref_case));
            ++c)
         {
           // make sure also the lazily initialized matrices are created
@@ -763,7 +765,7 @@ FiniteElement<dim, spacedim>::isotropic_prolongation_is_implemented() const
     RefinementCase<dim>::isotropic_refinement;
 
   for (unsigned int c = 0;
-       c < GeometryInfo<dim>::n_children(RefinementCase<dim>(ref_case));
+       c < this->reference_cell().n_children(RefinementCase<dim>(ref_case));
        ++c)
     {
       // make sure also the lazily initialized matrices are created
@@ -791,7 +793,7 @@ FiniteElement<dim, spacedim>::isotropic_restriction_is_implemented() const
     RefinementCase<dim>::isotropic_refinement;
 
   for (unsigned int c = 0;
-       c < GeometryInfo<dim>::n_children(RefinementCase<dim>(ref_case));
+       c < this->reference_cell().n_children(RefinementCase<dim>(ref_case));
        ++c)
     {
       // make sure also the lazily initialized matrices are created

diff --git a/source/fe/fe_simplex_p.cc b/source/fe/fe_simplex_p.cc
index 4e342f3453250accc5544a7a687941d28d43db28..3586bb8ee412edf3b001c8c4e527e62df9bd14b5 100644 (file)
--- a/source/fe/fe_simplex_p.cc
+++ b/source/fe/fe_simplex_p.cc
@@ -22,6 +22,9 @@
 #include <deal.II/fe/fe_q.h>
 #include <deal.II/fe/fe_simplex_p.h>
 #include <deal.II/fe/fe_tools.h>
+#include <deal.II/fe/mapping.h>
+
+#include <deal.II/grid/grid_generator.h>
 
 DEAL_II_NAMESPACE_OPEN
 
@@ -323,13 +326,14 @@ template <int dim, int spacedim>
 FE_SimplexPoly<dim, spacedim>::FE_SimplexPoly(
   const BarycentricPolynomials<dim>              polynomials,
   const FiniteElementData<dim>                  &fe_data,
+  const bool                                     prolongation_is_additive,
   const std::vector<Point<dim>>                 &unit_support_points,
   const std::vector<std::vector<Point<dim - 1>>> unit_face_support_points,
   const FullMatrix<double>                      &interface_constraints)
   : dealii::FE_Poly<dim, spacedim>(
       polynomials,
       fe_data,
-      std::vector<bool>(fe_data.dofs_per_cell),
+      std::vector<bool>(fe_data.dofs_per_cell, prolongation_is_additive),
       std::vector<ComponentMask>(fe_data.dofs_per_cell,
                                  ComponentMask(std::vector<bool>(1, true))))
 {
@@ -358,8 +362,21 @@ FE_SimplexPoly<dim, spacedim>::get_prolongation_matrix(
   const unsigned int         child,
   const RefinementCase<dim> &refinement_case) const
 {
-  Assert(refinement_case == RefinementCase<dim>::isotropic_refinement,
-         ExcNotImplemented());
+  if (dim == 3)
+    Assert(RefinementCase<dim>(refinement_case) ==
+               RefinementCase<dim>(
+                 static_cast<char>(IsotropicRefinementChoice::cut_tet_68)) ||
+             RefinementCase<dim>(refinement_case) ==
+               RefinementCase<dim>(
+                 static_cast<char>(IsotropicRefinementChoice::cut_tet_57)) ||
+             RefinementCase<dim>(refinement_case) ==
+               RefinementCase<dim>(
+                 static_cast<char>(IsotropicRefinementChoice::cut_tet_49)),
+           ExcNotImplemented());
+  else
+    Assert(refinement_case ==
+             RefinementCase<dim>(RefinementCase<dim>::isotropic_refinement),
+           ExcNotImplemented());
   AssertDimension(dim, spacedim);
 
   // initialization upon first request
@@ -376,16 +393,41 @@ FE_SimplexPoly<dim, spacedim>::get_prolongation_matrix(
       // be able to modify them inside a const function
       auto &this_nonconst = const_cast<FE_SimplexPoly<dim, spacedim> &>(*this);
 
-      std::vector<std::vector<FullMatrix<double>>> isotropic_matrices(
-        RefinementCase<dim>::isotropic_refinement);
-      isotropic_matrices.back().resize(
-        GeometryInfo<dim>::n_children(RefinementCase<dim>(refinement_case)),
-        FullMatrix<double>(this->n_dofs_per_cell(), this->n_dofs_per_cell()));
-
-      FETools::compute_embedding_matrices(*this, isotropic_matrices, true);
-
-      this_nonconst.prolongation[refinement_case - 1] =
-        std::move(isotropic_matrices.back());
+      if (dim == 2)
+        {
+          std::vector<std::vector<FullMatrix<double>>> isotropic_matrices(
+            RefinementCase<dim>::isotropic_refinement);
+          isotropic_matrices.back().resize(
+            this->reference_cell().n_children(
+              RefinementCase<dim>(refinement_case)),
+            FullMatrix<double>(this->n_dofs_per_cell(),
+                               this->n_dofs_per_cell()));
+
+          FETools::compute_embedding_matrices(*this, isotropic_matrices, true);
+
+          this_nonconst.prolongation[refinement_case - 1] =
+            std::move(isotropic_matrices.back());
+        }
+      else if (dim == 3)
+        {
+          std::vector<std::vector<FullMatrix<double>>> matrices(
+            static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49),
+            std::vector<FullMatrix<double>>(
+              this->reference_cell().n_children(
+                RefinementCase<dim>(refinement_case)),
+              FullMatrix<double>(this->n_dofs_per_cell(),
+                                 this->n_dofs_per_cell())));
+          FETools::compute_embedding_matrices(*this, matrices, true);
+          for (unsigned int refinement_direction = static_cast<unsigned int>(
+                 IsotropicRefinementChoice::cut_tet_68);
+               refinement_direction <=
+               static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49);
+               refinement_direction++)
+            this_nonconst.prolongation[refinement_direction - 1] =
+              std::move(matrices[refinement_direction - 1]);
+        }
+      else
+        DEAL_II_ASSERT_UNREACHABLE();
     }
 
   // finally return the matrix
@@ -400,8 +442,20 @@ FE_SimplexPoly<dim, spacedim>::get_restriction_matrix(
   const unsigned int         child,
   const RefinementCase<dim> &refinement_case) const
 {
-  Assert(refinement_case == RefinementCase<dim>::isotropic_refinement,
-         ExcNotImplemented());
+  if (dim == 3)
+    Assert(RefinementCase<dim>(refinement_case) ==
+               RefinementCase<dim>(
+                 static_cast<char>(IsotropicRefinementChoice::cut_tet_68)) ||
+             RefinementCase<dim>(refinement_case) ==
+               RefinementCase<dim>(
+                 static_cast<char>(IsotropicRefinementChoice::cut_tet_57)) ||
+             RefinementCase<dim>(refinement_case) ==
+               RefinementCase<dim>(
+                 static_cast<char>(IsotropicRefinementChoice::cut_tet_49)),
+           ExcNotImplemented());
+  else
+    Assert(refinement_case == RefinementCase<dim>::isotropic_refinement,
+           ExcNotImplemented());
   AssertDimension(dim, spacedim);
 
   // initialization upon first request
@@ -414,20 +468,91 @@ FE_SimplexPoly<dim, spacedim>::get_restriction_matrix(
           this->n_dofs_per_cell())
         return this->restriction[refinement_case - 1][child];
 
-      // now do the work. need to get a non-const version of data in order to
-      // be able to modify them inside a const function
-      auto &this_nonconst = const_cast<FE_SimplexPoly<dim, spacedim> &>(*this);
-
-      std::vector<std::vector<FullMatrix<double>>> isotropic_matrices(
+      // get the restriction matrix
+      // Refine a unit cell. As the parent cell is a unit
+      // cell, the reference cell of the children equals the parent, i.e. they
+      // have the support points at the same locations. So we just have to check
+      // if a support point of the parent is one of the interpolation points of
+      // the child. If this is not the case we find the interpolation of the
+      // point.
+
+      const double       eps = 1e-12;
+      FullMatrix<double> restriction_mat(this->n_dofs_per_cell(),
+                                         this->n_dofs_per_cell());
+
+      // first get all support points on the reference cell
+      const std::vector<Point<dim>> unit_support_points =
+        this->get_unit_support_points();
+
+      // now create children on the reference cell
+      Triangulation<dim> tria;
+      GridGenerator::reference_cell(tria, this->reference_cell());
+      tria.begin_active()->set_refine_flag(
         RefinementCase<dim>::isotropic_refinement);
-      isotropic_matrices.back().resize(
-        GeometryInfo<dim>::n_children(RefinementCase<dim>(refinement_case)),
-        FullMatrix<double>(this->n_dofs_per_cell(), this->n_dofs_per_cell()));
+      if (dim == 3)
+        tria.begin_active()->set_refine_choice(refinement_case);
+      tria.execute_coarsening_and_refinement();
+
+      const auto &child_cell = tria.begin(0)->child(child);
 
-      FETools::compute_projection_matrices(*this, isotropic_matrices, true);
+      const auto &mapping =
+        this->reference_cell()
+          .template get_default_linear_mapping<dim, spacedim>();
 
-      this_nonconst.restriction[refinement_case - 1] =
-        std::move(isotropic_matrices.back());
+      // iterate over all support points and transfom them to the unit cell of
+      // the child
+      for (unsigned int i = 0; i < unit_support_points.size(); i++)
+        {
+          std::vector<Point<dim>>            transformed_point(1);
+          const std::vector<Point<spacedim>> unit_support_point = {
+            dim == 2 ? Point<spacedim>(unit_support_points[i][0],
+                                       unit_support_points[i][1]) :
+                       Point<spacedim>(unit_support_points[i][0],
+                                       unit_support_points[i][1],
+                                       unit_support_points[i][2])};
+          mapping.transform_points_real_to_unit_cell(
+            child_cell,
+            make_array_view(unit_support_point),
+            make_array_view(transformed_point));
+
+          // if point is inside the unit cell iterate over all shape functions
+          if (this->reference_cell().contains_point(transformed_point[0], eps))
+            for (unsigned int j = 0; j < this->n_dofs_per_cell(); j++)
+              restriction_mat[i][j] =
+                this->shape_value(j, transformed_point[0]);
+        }
+#ifdef DEBUG
+      for (unsigned int i = 0; i < this->n_dofs_per_cell(); i++)
+        {
+          double sum = 0.;
+
+          for (unsigned int j = 0; j < this->n_dofs_per_cell(); j++)
+            sum += restriction_mat[i][j];
+
+          Assert(std::fabs(sum - 1) < eps || std::fabs(sum) < eps,
+                 ExcInternalError(
+                   "The entries in a row of the local "
+                   "restriction matrix do not add to zero or one. "
+                   "This typically indicates that the "
+                   "polynomial interpolation is "
+                   "ill-conditioned such that round-off "
+                   "prevents the sum to be one."));
+        }
+#endif
+
+      // Remove small entries from the matrix
+      for (unsigned int i = 0; i < restriction_mat.m(); ++i)
+        for (unsigned int j = 0; j < restriction_mat.n(); ++j)
+          {
+            if (std::fabs(restriction_mat(i, j)) < eps)
+              restriction_mat(i, j) = 0.;
+            if (std::fabs(restriction_mat(i, j) - 1) < eps)
+              restriction_mat(i, j) = 1.;
+          }
+
+      const_cast<FullMatrix<double> &>(
+        this->restriction[refinement_case - 1][child]) =
+        std::move(restriction_mat);
     }
 
   // finally return the matrix
@@ -619,6 +744,7 @@ FE_SimplexP<dim, spacedim>::FE_SimplexP(const unsigned int degree)
                              1,
                              degree,
                              FiniteElementData<dim>::H1),
+      false,
       unit_support_points_fe_p<dim>(degree),
       unit_face_support_points_fe_p<dim>(degree, FiniteElementData<dim>::H1),
       constraints_fe_p<dim>(degree))
@@ -873,6 +999,7 @@ FE_SimplexDGP<dim, spacedim>::FE_SimplexDGP(const unsigned int degree)
                              1,
                              degree,
                              FiniteElementData<dim>::L2),
+      true,
       unit_support_points_fe_p<dim>(degree),
       unit_face_support_points_fe_p<dim>(degree, FiniteElementData<dim>::L2),
       constraints_fe_p<dim>(degree))
@@ -979,6 +1106,85 @@ FE_SimplexDGP<dim, spacedim>::hp_line_dof_identities(
   return {};
 }
 
+
+
+template <int dim, int spacedim>
+const FullMatrix<double> &
+FE_SimplexDGP<dim, spacedim>::get_restriction_matrix(
+  const unsigned int         child,
+  const RefinementCase<dim> &refinement_case) const
+{
+  if (dim == 3)
+    Assert(RefinementCase<dim>(refinement_case) ==
+               RefinementCase<dim>(
+                 static_cast<char>(IsotropicRefinementChoice::cut_tet_68)) ||
+             RefinementCase<dim>(refinement_case) ==
+               RefinementCase<dim>(
+                 static_cast<char>(IsotropicRefinementChoice::cut_tet_57)) ||
+             RefinementCase<dim>(refinement_case) ==
+               RefinementCase<dim>(
+                 static_cast<char>(IsotropicRefinementChoice::cut_tet_49)),
+           ExcNotImplemented());
+  else
+    Assert(refinement_case == RefinementCase<dim>::isotropic_refinement,
+           ExcNotImplemented());
+  AssertDimension(dim, spacedim);
+
+  // initialization upon first request
+  if (this->restriction[refinement_case - 1][child].n() == 0)
+    {
+      std::lock_guard<std::mutex> lock(this->restriction_matrix_mutex);
+
+      // if matrix got updated while waiting for the lock
+      if (this->restriction[refinement_case - 1][child].n() ==
+          this->n_dofs_per_cell())
+        return this->restriction[refinement_case - 1][child];
+
+      // now do the work. need to get a non-const version of data in order to
+      // be able to modify them inside a const function
+      auto &this_nonconst = const_cast<FE_SimplexDGP<dim, spacedim> &>(*this);
+
+      if (dim == 2)
+        {
+          std::vector<std::vector<FullMatrix<double>>> isotropic_matrices(
+            RefinementCase<dim>::isotropic_refinement);
+          isotropic_matrices.back().resize(
+            this->reference_cell().n_children(
+              RefinementCase<dim>(refinement_case)),
+            FullMatrix<double>(this->n_dofs_per_cell(),
+                               this->n_dofs_per_cell()));
+
+          FETools::compute_projection_matrices(*this, isotropic_matrices, true);
+
+          this_nonconst.restriction[refinement_case - 1] =
+            std::move(isotropic_matrices.back());
+        }
+      else if (dim == 3)
+        {
+          std::vector<std::vector<FullMatrix<double>>> matrices(
+            static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49),
+            std::vector<FullMatrix<double>>(
+              this->reference_cell().n_children(
+                RefinementCase<dim>(refinement_case)),
+              FullMatrix<double>(this->n_dofs_per_cell(),
+                                 this->n_dofs_per_cell())));
+          FETools::compute_projection_matrices(*this, matrices, true);
+          for (unsigned int refinement_direction = static_cast<unsigned int>(
+                 IsotropicRefinementChoice::cut_tet_68);
+               refinement_direction <=
+               static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49);
+               refinement_direction++)
+            this_nonconst.restriction[refinement_direction - 1] =
+              std::move(matrices[refinement_direction - 1]);
+        }
+      else
+        DEAL_II_ASSERT_UNREACHABLE();
+    }
+
+  // finally return the matrix
+  return this->restriction[refinement_case - 1][child];
+}
+
 // explicit instantiations
 #include "fe_simplex_p.inst"
 

diff --git a/source/fe/fe_simplex_p_bubbles.cc b/source/fe/fe_simplex_p_bubbles.cc
index d06208ae33d577d1b331e3a54fa165e36de3468d..98463d7eccb563ad19c86b2a262219c0fc93079d 100644 (file)
--- a/source/fe/fe_simplex_p_bubbles.cc
+++ b/source/fe/fe_simplex_p_bubbles.cc
@@ -267,6 +267,7 @@ FE_SimplexP_Bubbles<dim, spacedim>::FE_SimplexP_Bubbles(
   : FE_SimplexPoly<dim, spacedim>(
       FE_P_BubblesImplementation::get_basis<dim>(degree),
       FE_P_BubblesImplementation::get_fe_data<dim>(degree),
+      false,
       FE_P_BubblesImplementation::unit_support_points<dim>(degree),
       {FE_P_BubblesImplementation::unit_support_points<dim - 1>(degree)},
       // Interface constraints are not yet implemented

diff --git a/source/fe/fe_system.cc b/source/fe/fe_system.cc
index 76cd9def6d96f0d78b39bb849582beb6e0c06e99..d54003b6080d02d51116d7f5224f7de7e196ba2f 100644 (file)
--- a/source/fe/fe_system.cc
+++ b/source/fe/fe_system.cc
@@ -892,7 +892,9 @@ FESystem<dim, spacedim>::get_restriction_matrix(
   Assert(refinement_case != RefinementCase<dim>::no_refinement,
          ExcMessage(
            "Restriction matrices are only available for refined cells!"));
-  AssertIndexRange(child, GeometryInfo<dim>::n_children(refinement_case));
+  AssertIndexRange(child, this->reference_cell().n_children(refinement_case));
+
+
 
   // initialization upon first request
   if (this->restriction[refinement_case - 1][child].n() == 0)
@@ -974,7 +976,7 @@ FESystem<dim, spacedim>::get_prolongation_matrix(
   Assert(refinement_case != RefinementCase<dim>::no_refinement,
          ExcMessage(
            "Restriction matrices are only available for refined cells!"));
-  AssertIndexRange(child, GeometryInfo<dim>::n_children(refinement_case));
+  AssertIndexRange(child, this->reference_cell().n_children(refinement_case));
 
   // initialization upon first request, construction completely analogous to
   // restriction matrix

diff --git a/source/grid/tria.cc b/source/grid/tria.cc
index b56a89137f0766437f3752a4a8bf3acd1102afee..e09bca6dc37661eaf5587340e184912ebd308721 100644 (file)
--- a/source/grid/tria.cc
+++ b/source/grid/tria.cc
@@ -2076,7 +2076,8 @@ namespace internal
     reserve_space(TriaLevel         &tria_level,
                   const unsigned int total_cells,
                   const unsigned int dimension,
-                  const unsigned int space_dimension)
+                  const unsigned int space_dimension,
+                  const bool         tetraheder_in_mesh = false)
     {
       // we need space for total_cells cells. Maybe we have more already
       // with those cells which are unused, so only allocate new space if
@@ -2092,6 +2093,16 @@ namespace internal
                                            tria_level.refine_flags.size(),
                                          /*RefinementCase::no_refinement=*/0);
 
+          if (tetraheder_in_mesh)
+            {
+              tria_level.refine_choice.reserve(total_cells);
+              tria_level.refine_choice.insert(
+                tria_level.refine_choice.end(),
+                total_cells - tria_level.refine_choice.size(),
+                static_cast<char>(
+                  IsotropicRefinementChoice::isotropic_refinement));
+            }
+
           tria_level.coarsen_flags.reserve(total_cells);
           tria_level.coarsen_flags.insert(tria_level.coarsen_flags.end(),
                                           total_cells -
@@ -3588,6 +3599,7 @@ namespace internal
         level.level_subdomain_ids.assign(size, 0);
 
         level.refine_flags.assign(size, 0u);
+        level.refine_choice.assign(size, 0u);
         level.coarsen_flags.assign(size, false);
 
         level.parents.assign((size + 1) / 2, -1);
@@ -6016,10 +6028,18 @@ namespace internal
                          triangulation.levels[level + 1]->cells.used.end(),
                          true);
 
-            reserve_space(*triangulation.levels[level + 1],
-                          used_cells + new_cells,
-                          3,
-                          spacedim);
+            if (triangulation.all_reference_cells_are_hyper_cube())
+              reserve_space(*triangulation.levels[level + 1],
+                            used_cells + new_cells,
+                            3,
+                            spacedim,
+                            false);
+            else
+              reserve_space(*triangulation.levels[level + 1],
+                            used_cells + new_cells,
+                            3,
+                            spacedim,
+                            true);
 
             reserve_space(triangulation.levels[level + 1]->cells, new_cells);
           }
@@ -6666,23 +6686,65 @@ namespace internal
                       static constexpr dealii::ndarray<unsigned int, 3, 2>
                         new_line_vertices = {{{{6, 8}}, {{5, 7}}, {{4, 9}}}};
 
-                      const auto &vertices = triangulation.get_vertices();
-                      double      min_distance =
-                        std::numeric_limits<double>::infinity();
-                      for (unsigned int i = 0; i < new_line_vertices.size();
-                           ++i)
+                      // choose line to cut either by refinement case or by
+                      // shortest distance between edge midpoints
+                      std::uint8_t refinement_choice = hex->refine_choice();
+                      if (refinement_choice ==
+                          static_cast<char>(
+                            IsotropicRefinementChoice::isotropic_refinement))
                         {
-                          const double current_distance =
-                            vertices[vertex_indices[new_line_vertices[i][0]]]
-                              .distance(
-                                vertices
-                                  [vertex_indices[new_line_vertices[i][1]]]);
-                          if (current_distance < min_distance)
+                          const auto &vertices = triangulation.get_vertices();
+                          double      min_distance =
+                            std::numeric_limits<double>::infinity();
+                          for (unsigned int i = 0; i < new_line_vertices.size();
+                               ++i)
                             {
-                              chosen_line_tetrahedron = i;
-                              min_distance            = current_distance;
+                              const double current_distance =
+                                vertices
+                                  [vertex_indices[new_line_vertices[i][0]]]
+                                    .distance(
+                                      vertices[vertex_indices
+                                                 [new_line_vertices[i][1]]]);
+                              if (current_distance < min_distance)
+                                {
+                                  chosen_line_tetrahedron = i;
+                                  min_distance            = current_distance;
+                                }
                             }
                         }
+                      else if (refinement_choice ==
+                               static_cast<char>(
+                                 IsotropicRefinementChoice::cut_tet_68))
+                        chosen_line_tetrahedron = 0;
+                      else if (refinement_choice ==
+                               static_cast<char>(
+                                 IsotropicRefinementChoice::cut_tet_57))
+                        chosen_line_tetrahedron = 1;
+                      else if (refinement_choice ==
+                               static_cast<char>(
+                                 IsotropicRefinementChoice::cut_tet_49))
+                        chosen_line_tetrahedron = 2;
+                      else
+                        DEAL_II_NOT_IMPLEMENTED();
+
+                      switch (chosen_line_tetrahedron)
+                        {
+                          case 0:
+                            hex->set_refinement_case(
+                              RefinementCase<dim>(static_cast<char>(
+                                IsotropicRefinementChoice::cut_tet_68)));
+                            break;
+                          case 1:
+                            hex->set_refinement_case(
+                              RefinementCase<dim>(static_cast<char>(
+                                IsotropicRefinementChoice::cut_tet_57)));
+                            break;
+                          case 2:
+                            hex->set_refinement_case(
+                              RefinementCase<dim>(static_cast<char>(
+                                IsotropicRefinementChoice::cut_tet_49)));
+                            break;
+                        }
 
                       new_lines[0]->set_bounding_object_indices(
                         {vertex_indices
@@ -6780,27 +6842,16 @@ namespace internal
                          ++i)
                       relevant_line_indices[i] = relevant_lines[i]->index();
 
-                    static constexpr dealii::ndarray<unsigned int, 12, 4>
-                      new_quad_lines_hex = {{{{10, 28, 16, 24}},
-                                             {{28, 14, 17, 25}},
-                                             {{11, 29, 24, 20}},
-                                             {{29, 15, 25, 21}},
-                                             {{18, 26, 0, 28}},
-                                             {{26, 22, 1, 29}},
-                                             {{19, 27, 28, 4}},
-                                             {{27, 23, 29, 5}},
-                                             {{2, 24, 8, 26}},
-                                             {{24, 6, 9, 27}},
-                                             {{3, 25, 26, 12}},
-                                             {{25, 7, 27, 13}}}};
-
-                    // It is easierst to start at table cell_vertices_tet,
+                    // It is easierst to start at table cell_vertices,
                     // there the vertices are listed which build up the
                     // 8 child tets. To build the child tets, 8 new faces are
                     // needed. The the vertices, which define the lines of these
                     // new faces are listed in table_tet. Now only the
                     // corresponding index of the lines and quads have to be
                     // listed in new_quad_lines_tet and cell_quads_tet.
+                    const auto &new_quad_lines =
+                      hex->reference_cell().new_isotropic_child_face_lines(
+                        chosen_line_tetrahedron);
 
                     // The first 4 define the faces which cut off the
                     // parent tetrahedron at the edges. the numbers are the
@@ -6809,116 +6860,13 @@ namespace internal
                     // of these contain line number 12. the ordering of the
                     // faces is arbitrary, the ordering within the faces has to
                     // follow the righthand convention for triangles
-                    static constexpr dealii::ndarray<unsigned int, 3, 12, 4>
-                      new_quad_lines_tet = {{// new line is (6,8)
-                                             {{{{2, 3, 8, X}},
-                                               {{0, 9, 5, X}},
-                                               {{1, 6, 11, X}},
-                                               {{4, 10, 7, X}},
-                                               {{2, 12, 5, X}},
-                                               {{1, 9, 12, X}},
-                                               {{4, 8, 12, X}},
-                                               {{6, 12, 10, X}},
-                                               {{X, X, X, X}},
-                                               {{X, X, X, X}},
-                                               {{X, X, X, X}},
-                                               {{X, X, X, X}}}},
-                                             // new line is (5,7)
-                                             {{{{2, 3, 8, X}},
-                                               {{0, 9, 5, X}},
-                                               {{1, 6, 11, X}},
-                                               {{4, 10, 7, X}},
-                                               {{0, 3, 12, X}},
-                                               {{1, 12, 8, X}},
-                                               {{4, 12, 9, X}},
-                                               {{7, 11, 12, X}},
-                                               {{X, X, X, X}},
-                                               {{X, X, X, X}},
-                                               {{X, X, X, X}},
-                                               {{X, X, X, X}}}},
-                                             // new line is (4,9)
-                                             {{{{2, 3, 8, X}},
-                                               {{0, 9, 5, X}},
-                                               {{1, 6, 11, X}},
-                                               {{4, 10, 7, X}},
-                                               {{0, 12, 11, X}},
-                                               {{2, 6, 12, X}},
-                                               {{3, 12, 7, X}},
-                                               {{5, 10, 12, X}},
-                                               {{X, X, X, X}},
-                                               {{X, X, X, X}},
-                                               {{X, X, X, X}},
-                                               {{X, X, X, X}}}}}};
-
-                    static constexpr dealii::ndarray<unsigned int, 12, 4, 2>
-                      table_hex = {
-                        {{{{{10, 22}}, {{24, 26}}, {{10, 24}}, {{22, 26}}}},
-                         {{{{24, 26}}, {{11, 23}}, {{24, 11}}, {{26, 23}}}},
-                         {{{{22, 14}}, {{26, 25}}, {{22, 26}}, {{14, 25}}}},
-                         {{{{26, 25}}, {{23, 15}}, {{26, 23}}, {{25, 15}}}},
-                         {{{{8, 24}}, {{20, 26}}, {{8, 20}}, {{24, 26}}}},
-                         {{{{20, 26}}, {{12, 25}}, {{20, 12}}, {{26, 25}}}},
-                         {{{{24, 9}}, {{26, 21}}, {{24, 26}}, {{9, 21}}}},
-                         {{{{26, 21}}, {{25, 13}}, {{26, 25}}, {{21, 13}}}},
-                         {{{{16, 20}}, {{22, 26}}, {{16, 22}}, {{20, 26}}}},
-                         {{{{22, 26}}, {{17, 21}}, {{22, 17}}, {{26, 21}}}},
-                         {{{{20, 18}}, {{26, 23}}, {{20, 26}}, {{18, 23}}}},
-                         {{{{26, 23}}, {{21, 19}}, {{26, 21}}, {{23, 19}}}}}};
-
                     // The table defines the vertices of the lines above
                     // see relevant_lines for mapping between line indices and
                     // vertex numbering
-                    static constexpr dealii::ndarray<unsigned int, 3, 12, 4, 2>
-                      table_tet = {
-                        {// new line is (6, 8)
-                         {{{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
-                           {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
-                           {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
-                           {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
-                           {{{{4, 6}}, {{6, 8}}, {{8, 4}}, {{X, X}}}},
-                           {{{{6, 5}}, {{5, 8}}, {{8, 6}}, {{X, X}}}},
-                           {{{{8, 7}}, {{7, 6}}, {{6, 8}}, {{X, X}}}},
-                           {{{{9, 6}}, {{6, 8}}, {{8, 9}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}},
-                         // new line is (5, 7)
-                         {{{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
-                           {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
-                           {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
-                           {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
-                           {{{{5, 4}}, {{4, 7}}, {{7, 5}}, {{X, X}}}},
-                           {{{{6, 5}}, {{5, 7}}, {{7, 6}}, {{X, X}}}},
-                           {{{{8, 7}}, {{7, 5}}, {{5, 8}}, {{X, X}}}},
-                           {{{{7, 9}}, {{9, 5}}, {{5, 7}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}},
-                         // new line is (4, 9)
-                         {{{{{{6, 4}}, {{4, 7}}, {{7, 6}}, {{X, X}}}},
-                           {{{{4, 5}}, {{5, 8}}, {{8, 4}}, {{X, X}}}},
-                           {{{{5, 6}}, {{6, 9}}, {{9, 5}}, {{X, X}}}},
-                           {{{{7, 8}}, {{8, 9}}, {{9, 7}}, {{X, X}}}},
-                           {{{{5, 4}}, {{4, 9}}, {{9, 5}}, {{X, X}}}},
-                           {{{{4, 6}}, {{6, 9}}, {{9, 4}}, {{X, X}}}},
-                           {{{{7, 4}}, {{4, 9}}, {{9, 7}}, {{X, X}}}},
-                           {{{{4, 8}}, {{8, 9}}, {{9, 4}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}},
-                           {{{{X, X}}, {{X, X}}, {{X, X}}, {{X, X}}}}}}}};
-
-                    const auto &new_quad_lines =
-                      (reference_cell_type == ReferenceCells::Hexahedron) ?
-                        new_quad_lines_hex :
-                        new_quad_lines_tet[chosen_line_tetrahedron];
-
                     const auto &table =
-                      (reference_cell_type == ReferenceCells::Hexahedron) ?
-                        table_hex :
-                        table_tet[chosen_line_tetrahedron];
+                      hex->reference_cell()
+                        .new_isotropic_child_face_line_vertices(
+                          chosen_line_tetrahedron);
 
                     static constexpr dealii::ndarray<unsigned int, 4, 2>
                       representative_lines{
@@ -7041,18 +6989,6 @@ namespace internal
                         DEAL_II_NOT_IMPLEMENTED();
                       }
 
-                    static constexpr dealii::ndarray<unsigned int, 8, 6>
-                      cell_quads_hex = {{
-                        {{12, 0, 20, 4, 28, 8}},  // bottom children
-                        {{0, 16, 22, 6, 29, 9}},  //
-                        {{13, 1, 4, 24, 30, 10}}, //
-                        {{1, 17, 6, 26, 31, 11}}, //
-                        {{14, 2, 21, 5, 8, 32}},  // top children
-                        {{2, 18, 23, 7, 9, 33}},  //
-                        {{15, 3, 5, 25, 10, 34}}, //
-                        {{3, 19, 7, 27, 11, 35}}  //
-                      }};
-
                     // indices of the faces which define the new tets
                     // the ordering of the tets is arbitrary
                     // the first 4 determine the tets cutting of the corners
@@ -7061,85 +6997,9 @@ namespace internal
                     // the ordering within the faces is determined by
                     // convention for the tetrahedron unit cell, see
                     // cell_vertices_tet below
-                    static constexpr dealii::ndarray<unsigned int, 3, 8, 6>
-                      cell_quads_tet = {{// new line is (6, 8)
-                                         {{{{8, 13, 16, 0, X, X}},
-                                           {{9, 12, 1, 21, X, X}},
-                                           {{10, 2, 17, 20, X, X}},
-                                           {{3, 14, 18, 22, X, X}},
-                                           {{11, 1, 4, 5, X, X}},
-                                           {{15, 0, 4, 6, X, X}},
-                                           {{19, 7, 6, 3, X, X}},
-                                           {{23, 5, 2, 7, X, X}}}},
-                                         // new line is (5, 7)
-                                         {{
-                                           {{8, 13, 16, 0, X, X}},
-                                           {{9, 12, 1, 21, X, X}},
-                                           {{10, 2, 17, 20, X, X}},
-                                           {{3, 14, 18, 22, X, X}},
-                                           {{11, 4, 0, 5, X, X}},
-                                           {{15, 4, 1, 6, X, X}},
-                                           {{19, 2, 5, 7, X, X}},
-                                           {{23, 6, 7, 3, X, X}},
-                                         }},
-                                         // new line is (4, 9)
-                                         {{
-                                           {{8, 13, 16, 0, X, X}},
-                                           {{9, 12, 1, 21, X, X}},
-                                           {{10, 2, 17, 20, X, X}},
-                                           {{3, 14, 18, 22, X, X}},
-                                           {{11, 4, 5, 2, X, X}},
-                                           {{15, 6, 7, 3, X, X}},
-                                           {{19, 5, 0, 6, X, X}},
-                                           {{23, 1, 4, 7, X, X}},
-                                         }}}};
-
-                    // the 4 faces of the reference tet are defined by 3
-                    // vertices each and follow the order of the unit cell
-                    static constexpr dealii::ndarray<unsigned int, 4, 3>
-                      reference_cell_face_vertices = {
-                        {{{0, 1, 2}}, {{1, 0, 3}}, {{0, 2, 3}}, {{2, 1, 3}}}};
-
-                    // the 8 child tets are each defined by 4 vertices
-                    // the ordering of the tets has to be consistent with above
-                    // the ordering within the tets is given by the reference
-                    // tet i.e. looking at the fifth line the first 3 vertices
-                    // are given by face 11, the last vertex is the remaining of
-                    // the tet
-                    static constexpr dealii::ndarray<unsigned int, 3, 8, 4>
-                      cell_vertices_tet = {{// new line is (6,8)
-                                            {{{{0, 4, 6, 7}},
-                                              {{4, 1, 5, 8}},
-                                              {{6, 5, 2, 9}},
-                                              {{7, 8, 9, 3}},
-                                              {{4, 5, 6, 8}},
-                                              {{4, 7, 8, 6}},
-                                              {{6, 9, 7, 8}},
-                                              {{5, 8, 9, 6}}}},
-                                            // new line is (5,7)
-                                            {{{{0, 4, 6, 7}},
-                                              {{4, 1, 5, 8}},
-                                              {{6, 5, 2, 9}},
-                                              {{7, 8, 9, 3}},
-                                              {{4, 5, 6, 7}},
-                                              {{4, 7, 8, 5}},
-                                              {{6, 9, 7, 5}},
-                                              {{5, 8, 9, 7}}}},
-                                            // new line is (4,9)
-                                            {{{{0, 4, 6, 7}},
-                                              {{4, 1, 5, 8}},
-                                              {{6, 5, 2, 9}},
-                                              {{7, 8, 9, 3}},
-                                              {{4, 5, 6, 9}},
-                                              {{4, 7, 8, 9}},
-                                              {{6, 9, 7, 4}},
-                                              {{5, 8, 9, 4}}}}}};
-
-
                     const auto &cell_quads =
-                      (reference_cell_type == ReferenceCells::Hexahedron) ?
-                        cell_quads_hex :
-                        cell_quads_tet[chosen_line_tetrahedron];
+                      hex->reference_cell().new_isotropic_child_cell_faces(
+                        chosen_line_tetrahedron);
 
                     for (unsigned int c = 0;
                          c < GeometryInfo<dim>::max_children_per_cell;
@@ -7170,19 +7030,34 @@ namespace internal
                                    face->vertex_index(1),
                                    face->vertex_index(2)}};
 
-                                const auto &new_hex_vertices =
-                                  cell_vertices_tet[chosen_line_tetrahedron][c];
-                                const auto face_f_vertices =
-                                  reference_cell_face_vertices[f];
-
+                                // the 8 child tets are each defined by 4
+                                // vertices the ordering of the tets has to be
+                                // consistent with above the ordering within the
+                                // tets is given by the reference tet i.e.
+                                // looking at the fifth line the first 3
+                                // vertices are given by face 11, the last
+                                // vertex is the remaining of the tet
+                                const auto new_hex_vertices =
+                                  hex->reference_cell()
+                                    .new_isotropic_child_cell_vertices(
+                                      chosen_line_tetrahedron)[c];
+
+                                // arrange after vertices of the faces of the
+                                // unit cell
                                 const std::array<unsigned int, 3> vertices_1 = {
                                   {
                                     vertex_indices
-                                      [new_hex_vertices[face_f_vertices[0]]],
+                                      [new_hex_vertices
+                                         [hex->reference_cell()
+                                            .face_to_cell_vertices(f, 0, 1)]],
                                     vertex_indices
-                                      [new_hex_vertices[face_f_vertices[1]]],
+                                      [new_hex_vertices
+                                         [hex->reference_cell()
+                                            .face_to_cell_vertices(f, 1, 1)]],
                                     vertex_indices
-                                      [new_hex_vertices[face_f_vertices[2]]],
+                                      [new_hex_vertices
+                                         [hex->reference_cell()
+                                            .face_to_cell_vertices(f, 2, 1)]],
                                   }};
 
                                 new_hex->set_combined_face_orientation(
@@ -12998,6 +12873,7 @@ void Triangulation<dim, spacedim>::set_all_refine_flags()
     {
       cell->clear_coarsen_flag();
       cell->set_refine_flag();
+      cell->set_refine_choice();
     }
 }
 

diff --git a/source/grid/tria_levels.cc b/source/grid/tria_levels.cc
index 365ee39a21ccd5fd7563b3552d9755e8e25f9068..652aeb012e079e9ca7eed0b23239410c78c5cbe5 100644 (file)
--- a/source/grid/tria_levels.cc
+++ b/source/grid/tria_levels.cc
@@ -28,6 +28,7 @@ namespace internal
     {
       return (
         MemoryConsumption::memory_consumption(refine_flags) +
+        MemoryConsumption::memory_consumption(refine_choice) +
         MemoryConsumption::memory_consumption(coarsen_flags) +
         MemoryConsumption::memory_consumption(active_cell_indices) +
         MemoryConsumption::memory_consumption(global_active_cell_indices) +

diff --git a/tests/fe/prolongation_restriction.cc b/tests/fe/prolongation_restriction.cc
new file mode 100644 (file)
index 0000000..339c5c3
--- /dev/null
+++ b/tests/fe/prolongation_restriction.cc
@@ -0,0 +1,172 @@
+// ------------------------------------------------------------------------
+//
+// SPDX-License-Identifier: LGPL-2.1-or-later
+// Copyright (C) 2002 - 2024 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// Part of the source code is dual licensed under Apache-2.0 WITH
+// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
+// governing the source code and code contributions can be found in
+// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
+//
+// ------------------------------------------------------------------------
+
+// Compute all refinement and restriction matrices for Tetrahedral elements.
+// Each element has 8 children and there are a total of 3 different
+// isotropic refinement choices for Tets. Also check for the DG case.
+
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_accessor.h>
+
+#include <deal.II/fe/fe_simplex_p.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_iterator.h>
+
+#include <deal.II/lac/vector.h>
+
+#include <string>
+#include <vector>
+
+#include "../tests.h"
+
+#define PRECISION 6
+
+
+
+template <int dim>
+void
+test_prolongation(int degree)
+{
+  FE_SimplexP<dim, dim> fe(degree);
+
+  const unsigned int                           nc = 8;
+  std::vector<std::vector<FullMatrix<double>>> matrices(
+    static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49),
+    std::vector<FullMatrix<double>>(
+      GeometryInfo<dim>::n_children(RefinementCase<dim>::isotropic_refinement),
+      FullMatrix<double>(fe.n_dofs_per_cell(), fe.n_dofs_per_cell())));
+
+  for (unsigned int refinement_direction =
+         static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_68);
+       refinement_direction <=
+       static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49);
+       refinement_direction++)
+    {
+      deallog << "Refinement Direction: " << refinement_direction << std::endl;
+      for (unsigned int i = 0; i < nc; ++i)
+        {
+          matrices[refinement_direction - 1][i] = fe.get_prolongation_matrix(
+            i, RefinementCase<dim>(refinement_direction));
+
+          deallog << "Child: " << i << std::endl;
+          for (unsigned int j = 0; j < fe.n_dofs_per_cell(); ++j)
+            {
+              for (unsigned int k = 0; k < fe.n_dofs_per_cell(); ++k)
+                deallog << matrices[refinement_direction - 1][i][j][k] << " ";
+              deallog << std::endl;
+            }
+          deallog << std::endl;
+        }
+    }
+}
+
+template <int dim>
+void
+test_restriction(int degree)
+{
+  FE_SimplexP<dim, dim> fe(degree);
+
+  const unsigned int                           nc = 8;
+  std::vector<std::vector<FullMatrix<double>>> matrices(
+    static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49),
+    std::vector<FullMatrix<double>>(
+      GeometryInfo<dim>::n_children(RefinementCase<dim>::isotropic_refinement),
+      FullMatrix<double>(fe.n_dofs_per_cell(), fe.n_dofs_per_cell())));
+
+  for (unsigned int refinement_direction =
+         static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_68);
+       refinement_direction <=
+       static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49);
+       refinement_direction++)
+    {
+      deallog << "Refinement Direction: " << refinement_direction << std::endl;
+      for (unsigned int i = 0; i < nc; ++i)
+        {
+          matrices[refinement_direction - 1][i] = fe.get_restriction_matrix(
+            i, RefinementCase<dim>(refinement_direction));
+
+          deallog << "Child: " << i << std::endl;
+          for (unsigned int j = 0; j < fe.n_dofs_per_cell(); ++j)
+            {
+              for (unsigned int k = 0; k < fe.n_dofs_per_cell(); ++k)
+                deallog << matrices[refinement_direction - 1][i][j][k] << " ";
+              deallog << std::endl;
+            }
+          deallog << std::endl;
+        }
+    }
+}
+
+template <int dim>
+void
+test_restriction_additive(int degree)
+{
+  FE_SimplexDGP<dim, dim> fe(degree);
+
+  const unsigned int                           nc = 8;
+  std::vector<std::vector<FullMatrix<double>>> matrices(
+    static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49),
+    std::vector<FullMatrix<double>>(
+      GeometryInfo<dim>::n_children(RefinementCase<dim>::isotropic_refinement),
+      FullMatrix<double>(fe.n_dofs_per_cell(), fe.n_dofs_per_cell())));
+
+  for (unsigned int refinement_direction =
+         static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_68);
+       refinement_direction <=
+       static_cast<unsigned int>(IsotropicRefinementChoice::cut_tet_49);
+       refinement_direction++)
+    {
+      deallog << "Refinement Direction: " << refinement_direction << std::endl;
+      for (unsigned int i = 0; i < nc; ++i)
+        {
+          matrices[refinement_direction - 1][i] = fe.get_restriction_matrix(
+            i, RefinementCase<dim>(refinement_direction));
+
+          deallog << "Child: " << i << std::endl;
+          for (unsigned int j = 0; j < fe.n_dofs_per_cell(); ++j)
+            {
+              for (unsigned int k = 0; k < fe.n_dofs_per_cell(); ++k)
+                deallog << matrices[refinement_direction - 1][i][j][k] << " ";
+              deallog << std::endl;
+            }
+          deallog << std::endl;
+        }
+    }
+}
+
+
+
+int
+main()
+{
+  std::ofstream logfile("output");
+  deallog << std::setprecision(PRECISION);
+  deallog << std::fixed;
+  deallog.attach(logfile);
+
+  for (int degree = 1; degree < 4; degree++)
+    {
+      test_prolongation<3>(degree);
+      test_restriction<3>(degree);
+      test_restriction_additive<3>(degree);
+    }
+
+  return 0;
+}

diff --git a/tests/fe/prolongation_restriction.output b/tests/fe/prolongation_restriction.output
new file mode 100644 (file)
index 0000000..8d6979b
--- /dev/null
+++ b/tests/fe/prolongation_restriction.output
@@ -0,0 +1,2908 @@
+
+DEAL::Refinement Direction: 1
+DEAL::Child: 0
+DEAL::1.000000 0.000000 0.000000 0.000000 
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::
+DEAL::Child: 1
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.000000 1.000000 0.000000 0.000000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::
+DEAL::Child: 2
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.000000 0.000000 1.000000 0.000000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::
+DEAL::Child: 3
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::0.000000 0.000000 0.000000 1.000000 
+DEAL::
+DEAL::Child: 4
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::
+DEAL::Child: 5
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::
+DEAL::Child: 6
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::
+DEAL::Child: 7
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::
+DEAL::Refinement Direction: 2
+DEAL::Child: 0
+DEAL::1.000000 0.000000 0.000000 0.000000 
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::
+DEAL::Child: 1
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.000000 1.000000 0.000000 0.000000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::
+DEAL::Child: 2
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.000000 0.000000 1.000000 0.000000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::
+DEAL::Child: 3
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::0.000000 0.000000 0.000000 1.000000 
+DEAL::
+DEAL::Child: 4
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::
+DEAL::Child: 5
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::
+DEAL::Child: 6
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::
+DEAL::Child: 7
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::
+DEAL::Refinement Direction: 3
+DEAL::Child: 0
+DEAL::1.000000 0.000000 0.000000 0.000000 
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::
+DEAL::Child: 1
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.000000 1.000000 0.000000 0.000000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::
+DEAL::Child: 2
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.000000 0.000000 1.000000 0.000000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::
+DEAL::Child: 3
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::0.000000 0.000000 0.000000 1.000000 
+DEAL::
+DEAL::Child: 4
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::
+DEAL::Child: 5
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::
+DEAL::Child: 6
+DEAL::0.500000 0.000000 0.500000 0.000000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::0.500000 0.000000 0.000000 0.500000 
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 7
+DEAL::0.000000 0.500000 0.500000 0.000000 
+DEAL::0.000000 0.500000 0.000000 0.500000 
+DEAL::0.000000 0.000000 0.500000 0.500000 
+DEAL::0.500000 0.500000 0.000000 0.000000 
+DEAL::
+DEAL::Refinement Direction: 1
+DEAL::Child: 0
+DEAL::1.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 1
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 1.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 2
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 1.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 3
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 1.000000 
+DEAL::
+DEAL::Child: 4
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 5
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 6
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 7
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Refinement Direction: 2
+DEAL::Child: 0
+DEAL::1.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 1
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 1.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 2
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 1.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 3
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 1.000000 
+DEAL::
+DEAL::Child: 4
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 5
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 6
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 7
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Refinement Direction: 3
+DEAL::Child: 0
+DEAL::1.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 1
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 1.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 2
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 1.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 3
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 1.000000 
+DEAL::
+DEAL::Child: 4
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 5
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 6
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Child: 7
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::0.000000 0.000000 0.000000 0.000000 
+DEAL::
+DEAL::Refinement Direction: 1
+DEAL::Child: 0
+DEAL::0.312500 0.250000 0.250000 0.250000 
+DEAL::-0.062500 0.000000 -0.062500 -0.062500 
+DEAL::-0.062500 -0.062500 0.000000 -0.062500 
+DEAL::-0.062500 -0.062500 -0.062500 0.000000 
+DEAL::
+DEAL::Child: 1
+DEAL::0.000000 -0.062500 -0.062500 -0.062500 
+DEAL::0.250000 0.312500 0.250000 0.250000 
+DEAL::-0.062500 -0.062500 0.000000 -0.062500 
+DEAL::-0.062500 -0.062500 -0.062500 0.000000 
+DEAL::
+DEAL::Child: 2
+DEAL::0.000000 -0.062500 -0.062500 -0.062500 
+DEAL::-0.062500 0.000000 -0.062500 -0.062500 
+DEAL::0.250000 0.250000 0.312500 0.250000 
+DEAL::-0.062500 -0.062500 -0.062500 0.000000 
+DEAL::
+DEAL::Child: 3
+DEAL::0.000000 -0.062500 -0.062500 -0.062500 
+DEAL::-0.062500 0.000000 -0.062500 -0.062500 
+DEAL::-0.062500 -0.062500 0.000000 -0.062500 
+DEAL::0.250000 0.250000 0.250000 0.312500 
+DEAL::
+DEAL::Child: 4
+DEAL::0.062500 0.000000 0.062500 0.000000 
+DEAL::0.125000 0.125000 0.062500 0.125000 
+DEAL::0.000000 0.062500 0.062500 0.000000 
+DEAL::-0.062500 -0.062500 -0.062500 0.000000 
+DEAL::
+DEAL::Child: 5
+DEAL::0.125000 0.125000 0.062500 0.125000 
+DEAL::0.062500 0.000000 0.062500 0.000000 
+DEAL::-0.062500 -0.062500 -0.062500 0.000000 
+DEAL::0.000000 0.062500 0.062500 0.000000 
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+DEAL::0.003906 0.003906 0.031250 0.007813 -0.078125 -0.046875 -0.046875 -0.046875 -0.046875 -0.031250 
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+DEAL::-0.031250 0.031250 -0.035156 -0.035156 0.125000 0.109375 0.031250 0.031250 0.109375 0.000000 
+DEAL::
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+DEAL::0.003906 0.003906 0.031250 0.007813 -0.078125 -0.046875 -0.046875 -0.046875 -0.046875 -0.031250 
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+DEAL::-0.019531 0.039062 -0.019531 0.000000 0.062500 0.062500 0.000000 -0.015625 0.031250 -0.015625 
+DEAL::-0.035156 -0.031250 0.031250 -0.035156 0.031250 0.125000 0.109375 0.000000 0.031250 0.109375 
+DEAL::
+DEAL::Refinement Direction: 2
+DEAL::Child: 0
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+DEAL::-0.019531 0.035156 -0.042969 -0.042969 0.203125 0.125000 0.015625 0.015625 0.125000 -0.031250 
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+DEAL::-0.019531 -0.042969 0.035156 -0.042969 0.015625 0.125000 0.203125 0.015625 -0.031250 0.125000 
+DEAL::-0.019531 -0.042969 -0.042969 0.035156 0.015625 -0.031250 0.015625 0.203125 0.125000 0.125000 
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+DEAL::0.015625 0.015625 -0.015625 -0.015625 0.062500 0.000000 0.000000 0.000000 0.000000 -0.031250 
+DEAL::
+DEAL::Child: 1
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+DEAL::0.015625 0.015625 -0.015625 0.015625 0.062500 -0.062500 -0.062500 0.062500 0.062500 -0.062500 
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+DEAL::0.035156 -0.019531 -0.042969 -0.042969 0.203125 0.015625 0.125000 0.125000 0.015625 -0.031250 
+DEAL::-0.042969 -0.019531 0.035156 -0.042969 0.015625 0.203125 0.125000 -0.031250 0.015625 0.125000 
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+DEAL::-0.042969 -0.019531 -0.042969 0.035156 0.015625 0.015625 -0.031250 0.125000 0.203125 0.125000 
+DEAL::0.015625 0.015625 -0.015625 -0.015625 0.062500 0.000000 0.000000 0.000000 0.000000 -0.031250 
+DEAL::
+DEAL::Child: 2
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+DEAL::0.015625 -0.015625 0.015625 0.015625 -0.062500 -0.062500 0.062500 0.062500 -0.062500 0.062500 
+DEAL::-0.156250 -0.156250 0.031250 -0.156250 0.312500 0.625000 0.625000 0.312500 0.312500 0.625000 
+DEAL::0.015625 0.015625 0.015625 -0.015625 0.062500 0.062500 0.062500 -0.062500 -0.062500 -0.062500 
+DEAL::-0.015625 -0.015625 0.015625 0.015625 -0.031250 0.000000 0.000000 0.000000 0.000000 0.062500 
+DEAL::-0.042969 0.035156 -0.019531 -0.042969 0.125000 0.203125 0.015625 -0.031250 0.125000 0.015625 
+DEAL::0.035156 -0.042969 -0.019531 -0.042969 0.125000 0.015625 0.203125 0.125000 -0.031250 0.015625 
+DEAL::-0.015625 0.015625 0.015625 -0.015625 0.000000 0.062500 0.000000 -0.031250 0.000000 0.000000 
+DEAL::0.015625 -0.015625 0.015625 -0.015625 0.000000 0.000000 0.062500 0.000000 -0.031250 0.000000 
+DEAL::-0.042969 -0.042969 -0.019531 0.035156 -0.031250 0.015625 0.015625 0.125000 0.125000 0.203125 
+DEAL::
+DEAL::Child: 3
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+DEAL::0.015625 -0.015625 0.015625 0.015625 -0.062500 -0.062500 0.062500 0.062500 -0.062500 0.062500 
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+DEAL::-0.042969 0.035156 -0.042969 -0.019531 0.125000 0.125000 -0.031250 0.015625 0.203125 0.015625 
+DEAL::-0.042969 -0.042969 0.035156 -0.019531 -0.031250 0.125000 0.125000 0.015625 0.015625 0.203125 
+DEAL::
+DEAL::Child: 4
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+DEAL::0.031250 0.003906 0.003906 0.007813 -0.046875 -0.078125 -0.046875 -0.031250 -0.046875 -0.046875 
+DEAL::
+DEAL::Child: 5
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+DEAL::
+DEAL::Child: 6
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+DEAL::0.046875 0.031250 0.031250 0.046875 -0.125000 -0.125000 -0.125000 -0.062500 -0.125000 -0.125000 
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+DEAL::-0.035156 0.031250 -0.031250 -0.035156 0.109375 0.125000 0.031250 0.000000 0.109375 0.031250 
+DEAL::
+DEAL::Child: 7
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+DEAL::0.031250 0.031250 0.031250 0.031250 -0.125000 -0.062500 -0.125000 -0.125000 -0.062500 -0.062500 
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+DEAL::-0.031250 -0.035156 0.031250 -0.035156 0.031250 0.109375 0.125000 0.031250 0.000000 0.109375 
+DEAL::
+DEAL::Refinement Direction: 3
+DEAL::Child: 0
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+DEAL::0.015625 -0.015625 0.015625 0.015625 -0.062500 -0.062500 0.062500 0.062500 -0.062500 0.062500 
+DEAL::0.015625 0.015625 -0.015625 0.015625 0.062500 -0.062500 -0.062500 0.062500 0.062500 -0.062500 
+DEAL::0.015625 0.015625 0.015625 -0.015625 0.062500 0.062500 0.062500 -0.062500 -0.062500 -0.062500 
+DEAL::-0.019531 0.035156 -0.042969 -0.042969 0.203125 0.125000 0.015625 0.015625 0.125000 -0.031250 
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+DEAL::-0.019531 -0.042969 0.035156 -0.042969 0.015625 0.125000 0.203125 0.015625 -0.031250 0.125000 
+DEAL::-0.019531 -0.042969 -0.042969 0.035156 0.015625 -0.031250 0.015625 0.203125 0.125000 0.125000 
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+DEAL::0.015625 0.015625 -0.015625 -0.015625 0.062500 0.000000 0.000000 0.000000 0.000000 -0.031250 
+DEAL::
+DEAL::Child: 1
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+DEAL::0.035156 -0.019531 -0.042969 -0.042969 0.203125 0.015625 0.125000 0.125000 0.015625 -0.031250 
+DEAL::-0.042969 -0.019531 0.035156 -0.042969 0.015625 0.203125 0.125000 -0.031250 0.015625 0.125000 
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+DEAL::-0.042969 -0.019531 -0.042969 0.035156 0.015625 0.015625 -0.031250 0.125000 0.203125 0.125000 
+DEAL::0.015625 0.015625 -0.015625 -0.015625 0.062500 0.000000 0.000000 0.000000 0.000000 -0.031250 
+DEAL::
+DEAL::Child: 2
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+DEAL::0.015625 -0.015625 0.015625 0.015625 -0.062500 -0.062500 0.062500 0.062500 -0.062500 0.062500 
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+DEAL::0.035156 -0.042969 -0.019531 -0.042969 0.125000 0.015625 0.203125 0.125000 -0.031250 0.015625 
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+DEAL::-0.042969 -0.042969 -0.019531 0.035156 -0.031250 0.015625 0.015625 0.125000 0.125000 0.203125 
+DEAL::
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+DEAL::0.015625 0.015625 -0.015625 0.015625 0.062500 -0.062500 -0.062500 0.062500 0.062500 -0.062500 
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+DEAL::0.035156 -0.042969 -0.042969 -0.019531 0.125000 -0.031250 0.125000 0.203125 0.015625 0.015625 
+DEAL::-0.042969 0.035156 -0.042969 -0.019531 0.125000 0.125000 -0.031250 0.015625 0.203125 0.015625 
+DEAL::-0.042969 -0.042969 0.035156 -0.019531 -0.031250 0.125000 0.125000 0.015625 0.015625 0.203125 
+DEAL::
+DEAL::Child: 4
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+DEAL::0.031250 0.031250 0.031250 0.031250 -0.125000 -0.062500 -0.125000 -0.125000 -0.062500 -0.062500 
+DEAL::0.015625 0.015625 0.015625 -0.015625 0.062500 0.062500 0.062500 -0.062500 -0.062500 -0.062500 
+DEAL::0.039062 -0.019531 -0.019531 0.000000 0.062500 0.000000 0.062500 0.031250 -0.015625 -0.015625 
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+DEAL::
+DEAL::Child: 1
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+DEAL::0.007812 0.003472 0.018229 0.007812 0.015625 -0.007813 -0.031250 0.101562 0.058594 -0.035156 0.019531 0.019531 -0.007813 0.015625 0.058594 -0.035156 -0.039063 0.007813 -0.062500 -0.039063 
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+DEAL::0.000000 0.000000 0.005208 -0.005208 -0.035156 -0.035156 -0.023437 0.023437 0.023437 -0.023437 -0.011719 0.035156 -0.011719 0.035156 -0.015625 0.000000 0.000000 0.070313 0.046875 0.046875 
+DEAL::-0.002604 0.003472 -0.002604 0.007813 0.003906 -0.019531 -0.019531 0.003906 0.027344 0.027344 -0.007812 -0.007813 -0.007812 0.015625 -0.007812 -0.007813 0.070313 -0.015625 0.031250 -0.015625 
+DEAL::-0.002604 0.003472 0.007813 -0.002604 0.003906 -0.019531 -0.007813 0.015625 -0.007813 -0.007812 0.027344 0.027344 -0.019531 0.003906 -0.007813 -0.007812 -0.015625 0.070313 0.031250 -0.015625 
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+DEAL::0.007813 0.003472 -0.002604 -0.002604 0.015625 -0.007812 -0.019531 0.003906 -0.007813 -0.007813 -0.007813 -0.007812 -0.019531 0.003906 0.027344 0.027344 -0.015625 -0.015625 0.031250 0.070312 
+DEAL::
+DEAL::Child: 2
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+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070312 0.140625 0.140625 0.140625 
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+DEAL::0.005208 -0.005208 0.000000 0.000000 -0.015625 0.000000 0.035156 -0.011719 -0.023438 0.023437 0.023437 -0.023437 0.035156 -0.011719 -0.035156 -0.035156 0.046875 0.046875 0.000000 0.070313 
+DEAL::0.007812 0.018229 0.003472 0.007812 -0.035156 0.058594 0.101562 -0.031250 -0.007813 0.015625 0.019531 0.019531 0.058594 -0.035156 -0.007813 0.015625 -0.039063 -0.062500 0.007813 -0.039063 
+DEAL::0.046875 -0.005208 0.017361 0.046875 -0.164062 0.210937 0.265625 0.046875 0.019531 -0.121094 -0.050781 -0.050781 0.210938 -0.164062 0.019531 -0.121094 0.343750 0.109375 -0.101562 0.343750 
+DEAL::-0.005208 0.046875 0.017361 0.046875 0.210938 -0.164063 -0.121094 0.019531 0.046875 0.265625 0.210938 -0.164062 -0.050781 -0.050781 0.019531 -0.121094 0.343750 0.109375 0.343750 -0.101562 
+DEAL::0.018229 0.007813 0.003472 0.007813 0.058594 -0.035156 0.015625 -0.007813 -0.031250 0.101563 0.058594 -0.035156 0.019531 0.019531 -0.007813 0.015625 -0.039062 -0.062500 -0.039062 0.007813 
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+DEAL::0.000000 0.005208 0.000000 -0.005208 -0.023437 0.023438 0.023438 -0.023438 -0.035156 -0.035156 -0.011719 0.035156 -0.015625 0.000000 -0.011719 0.035156 0.000000 0.046875 0.070313 0.046875 
+DEAL::0.046875 0.046875 0.017361 -0.005208 -0.050781 -0.050781 -0.121094 0.019531 0.019531 -0.121094 -0.164063 0.210937 -0.164063 0.210937 0.046875 0.265625 -0.101562 0.109375 0.343750 0.343750 
+DEAL::0.007812 0.007812 0.003472 0.018229 0.019531 0.019531 0.015625 -0.007813 -0.007813 0.015625 -0.035156 0.058594 -0.035156 0.058594 -0.031250 0.101563 0.007813 -0.062500 -0.039062 -0.039062 
+DEAL::-0.002604 -0.002604 0.003472 0.007813 0.027344 0.027344 0.003906 -0.019531 -0.019531 0.003906 -0.007812 -0.007813 -0.007812 -0.007813 -0.007813 0.015625 0.070313 0.031250 -0.015625 -0.015625 
+DEAL::0.005208 0.005208 0.000000 0.005208 0.003906 0.003906 0.023437 -0.023437 -0.023437 0.023437 0.003906 0.003906 0.003906 0.003906 -0.023437 0.023437 0.023438 0.015625 0.023438 0.023438 
+DEAL::-0.002604 0.007813 0.003472 -0.002604 -0.007812 -0.007813 0.015625 -0.007813 -0.019531 0.003906 0.027344 0.027344 -0.007813 -0.007813 -0.019531 0.003906 -0.015625 0.031250 0.070313 -0.015625 
+DEAL::0.007813 -0.002604 0.003472 -0.002604 -0.007813 -0.007813 0.003906 -0.019531 -0.007813 0.015625 -0.007813 -0.007812 0.027344 0.027344 -0.019531 0.003906 -0.015625 0.031250 -0.015625 0.070313 
+DEAL::
+DEAL::Child: 3
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+DEAL::0.000000 0.000000 -0.015625 0.000000 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.140625 -0.070312 0.140625 0.140625 
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+DEAL::-0.005208 0.005208 0.000000 0.000000 0.000000 -0.015625 0.023438 -0.023437 -0.011719 0.035156 0.035156 -0.011719 0.023437 -0.023437 -0.035156 -0.035156 0.046875 0.046875 0.070312 0.000000 
+DEAL::0.005208 -0.005208 0.000000 0.000000 -0.015625 0.000000 0.035156 -0.011719 -0.023437 0.023437 0.023437 -0.023437 0.035156 -0.011719 -0.035156 -0.035156 0.046875 0.046875 0.000000 0.070313 
+DEAL::0.000000 -0.005208 0.005208 0.000000 -0.011719 0.035156 0.000000 -0.015625 0.023437 -0.023437 -0.035156 -0.035156 0.035156 -0.011719 0.023437 -0.023437 0.046875 0.070313 0.000000 0.046875 
+DEAL::0.000000 0.005208 -0.005208 0.000000 -0.023437 0.023437 -0.015625 0.000000 0.035156 -0.011719 -0.035156 -0.035156 0.023437 -0.023437 0.035156 -0.011719 0.046875 0.000000 0.070313 0.046875 
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+DEAL::0.018229 0.007812 0.007812 0.003472 0.058594 -0.035156 0.019531 0.019531 -0.035156 0.058594 0.101562 -0.031250 0.015625 -0.007813 0.015625 -0.007813 -0.062500 -0.039063 -0.039063 0.007813 
+DEAL::-0.005208 0.046875 0.046875 0.017361 0.210938 -0.164063 -0.050781 -0.050781 -0.164062 0.210937 0.265625 0.046875 -0.121094 0.019531 -0.121094 0.019531 0.109375 0.343750 0.343750 -0.101562 
+DEAL::0.007812 0.018229 0.007812 0.003472 -0.035156 0.058594 0.058594 -0.035156 0.019531 0.019531 0.015625 -0.007813 0.101562 -0.031250 0.015625 -0.007813 -0.062500 -0.039063 0.007813 -0.039062 
+DEAL::0.046875 -0.005208 0.046875 0.017361 -0.164062 0.210938 0.210938 -0.164063 -0.050781 -0.050781 -0.121094 0.019531 0.265625 0.046875 -0.121094 0.019531 0.109375 0.343750 -0.101562 0.343750 
+DEAL::0.007812 0.007813 0.018229 0.003472 0.019531 0.019531 -0.035156 0.058594 0.058594 -0.035156 0.015625 -0.007813 0.015625 -0.007813 0.101563 -0.031250 -0.062500 0.007813 -0.039062 -0.039062 
+DEAL::0.046875 0.046875 -0.005208 0.017361 -0.050781 -0.050781 -0.164063 0.210938 0.210938 -0.164063 -0.121094 0.019531 -0.121094 0.019531 0.265625 0.046875 0.109375 -0.101562 0.343750 0.343750 
+DEAL::0.005208 0.005208 0.005208 0.000000 0.003906 0.003906 0.003906 0.003906 0.003906 0.003906 0.023438 -0.023438 0.023437 -0.023437 0.023438 -0.023437 0.015625 0.023437 0.023437 0.023437 
+DEAL::-0.002604 -0.002604 0.007813 0.003472 0.027344 0.027344 -0.007813 -0.007813 -0.007813 -0.007813 0.003906 -0.019531 0.003906 -0.019531 0.015625 -0.007812 0.031250 0.070313 -0.015625 -0.015625 
+DEAL::-0.002604 0.007813 -0.002604 0.003472 -0.007812 -0.007813 -0.007813 -0.007813 0.027344 0.027344 0.003906 -0.019531 0.015625 -0.007812 0.003906 -0.019531 0.031250 -0.015625 0.070313 -0.015625 
+DEAL::0.007813 -0.002604 -0.002604 0.003472 -0.007813 -0.007812 0.027344 0.027344 -0.007812 -0.007813 0.015625 -0.007813 0.003906 -0.019531 0.003906 -0.019531 0.031250 -0.015625 -0.015625 0.070313 
+DEAL::
+DEAL::Child: 4
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+DEAL::-0.023437 -0.023437 -0.062500 -0.023438 -0.035156 -0.035156 -0.070312 0.140625 0.140625 -0.070313 -0.035156 -0.035156 -0.035156 -0.035156 0.140625 -0.070312 -0.210937 -0.421875 -0.210937 -0.210937 
+DEAL::-0.015625 0.007812 0.007812 -0.015625 0.070313 -0.070313 -0.070313 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.140625 0.140625 0.000000 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::0.004340 0.000868 -0.003472 0.000868 0.074219 -0.040365 -0.005208 -0.007812 -0.031250 0.101563 0.074219 -0.040365 0.014323 0.014323 -0.007813 -0.005208 -0.101563 -0.114583 -0.101563 -0.138021 
+DEAL::0.000868 0.000000 0.009549 0.000000 0.117187 -0.049479 -0.002604 -0.023437 -0.070312 0.101562 0.117187 -0.049479 -0.010417 -0.010417 -0.023437 -0.002604 -0.062500 -0.026042 -0.062500 -0.119792 
+DEAL::0.000000 0.000868 0.009549 0.000000 -0.049479 0.117187 0.101562 -0.070312 -0.023438 -0.002604 -0.010417 -0.010417 0.117187 -0.049479 -0.023438 -0.002604 -0.062500 -0.026042 -0.119792 -0.062500 
+DEAL::0.000868 0.004340 -0.003472 0.000868 -0.040365 0.074219 0.101562 -0.031250 -0.007813 -0.005208 0.014323 0.014323 0.074219 -0.040365 -0.007813 -0.005208 -0.101562 -0.114583 -0.138021 -0.101562 
+DEAL::0.004340 -0.003472 0.016493 -0.012153 -0.013021 -0.002604 -0.018229 0.054688 0.039063 -0.028646 0.002604 0.023438 0.005208 0.031250 0.007812 0.007813 -0.093750 -0.046875 -0.083333 -0.057292 
+DEAL::-0.003472 0.004340 0.016493 -0.012153 -0.002604 -0.013021 -0.028646 0.039063 0.054688 -0.018229 0.005208 0.031250 0.002604 0.023438 0.007812 0.007813 -0.093750 -0.046875 -0.057292 -0.083333 
+DEAL::0.001736 -0.010417 0.001736 0.012153 0.001302 0.027344 0.027344 0.001302 -0.006510 -0.006510 -0.002604 -0.023438 0.015625 -0.015625 -0.002604 -0.023438 0.091146 0.031250 -0.026042 0.031250 
+DEAL::0.004340 -0.005208 0.004340 0.006944 0.018229 -0.007812 -0.007812 0.018229 0.018229 0.018229 0.002604 -0.023438 0.015625 0.000000 0.002604 -0.023438 0.072917 0.015625 -0.020833 0.015625 
+DEAL::0.005208 0.005208 -0.006944 0.022569 -0.014323 -0.014323 -0.006510 0.040365 0.040365 -0.006510 -0.033854 0.059896 -0.033854 0.059896 0.005208 0.005208 0.044271 -0.026042 -0.010417 -0.010417 
+DEAL::0.000868 0.000868 -0.006944 0.028646 0.022135 0.022135 0.026042 0.002604 0.002604 0.026042 -0.001302 -0.001302 -0.001302 -0.001302 0.010417 -0.013021 0.049479 -0.067708 -0.059896 -0.059896 
+DEAL::-0.010417 0.001736 0.001736 0.012153 0.027344 0.001302 -0.006510 -0.006510 0.001302 0.027344 0.015625 -0.015625 -0.002604 -0.023438 -0.002604 -0.023437 0.091146 0.031250 0.031250 -0.026042 
+DEAL::-0.005208 0.004340 0.004340 0.006944 -0.007812 0.018229 0.018229 0.018229 0.018229 -0.007812 0.015625 0.000000 0.002604 -0.023438 0.002604 -0.023438 0.072917 0.015625 0.015625 -0.020833 
+DEAL::0.013889 0.013889 0.008681 0.039063 0.016927 0.016927 0.009115 0.035156 0.035156 0.009115 0.005208 -0.059896 0.005208 -0.059896 0.039063 -0.067708 0.335938 0.135417 0.161458 0.161458 
+DEAL::-0.001736 0.006076 0.006076 -0.007813 -0.010417 -0.005208 0.002604 -0.002604 -0.010417 -0.010417 0.013021 0.041667 -0.013021 0.010417 -0.018229 0.026042 -0.057292 0.010417 0.020833 -0.020833 
+DEAL::-0.000868 -0.000868 -0.001736 -0.001736 0.006510 0.006510 0.010417 -0.018229 -0.018229 0.010417 0.006510 0.003906 0.006510 0.003906 -0.002604 0.007813 -0.065104 -0.031250 -0.044271 -0.044271 
+DEAL::0.006076 -0.001736 0.006076 -0.007813 -0.005208 -0.010417 -0.010417 -0.010417 -0.002604 0.002604 -0.013021 0.010417 0.013021 0.041667 -0.018229 0.026042 -0.057292 0.010417 -0.020833 0.020833 
+DEAL::
+DEAL::Child: 5
+DEAL::-0.023438 -0.023438 -0.062500 -0.023438 -0.035156 -0.035156 -0.070312 0.140625 0.140625 -0.070313 -0.035156 -0.035156 -0.035156 -0.035156 0.140625 -0.070312 -0.210937 -0.421875 -0.210937 -0.210937 
+DEAL::0.007812 -0.015625 0.007812 -0.015625 -0.070312 0.070312 0.070312 -0.070312 -0.070312 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070312 0.000000 0.140625 0.000000 0.140625 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::-0.015625 0.007812 0.007812 -0.015625 0.070312 -0.070312 -0.070312 -0.070312 -0.070312 0.070313 0.000000 0.000000 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.140625 0.140625 0.000000 
+DEAL::0.000868 0.000000 0.009549 0.000000 0.117187 -0.049479 -0.002604 -0.023438 -0.070312 0.101562 0.117187 -0.049479 -0.010417 -0.010417 -0.023438 -0.002604 -0.062500 -0.026042 -0.062500 -0.119792 
+DEAL::0.004340 0.000868 -0.003472 0.000868 0.074219 -0.040365 -0.005208 -0.007813 -0.031250 0.101563 0.074219 -0.040365 0.014323 0.014323 -0.007813 -0.005208 -0.101563 -0.114583 -0.101563 -0.138021 
+DEAL::0.001736 -0.010417 0.001736 0.012153 0.001302 0.027344 0.027344 0.001302 -0.006510 -0.006510 -0.002604 -0.023438 0.015625 -0.015625 -0.002604 -0.023437 0.091146 0.031250 -0.026042 0.031250 
+DEAL::0.004340 -0.005208 0.004340 0.006944 0.018229 -0.007812 -0.007813 0.018229 0.018229 0.018229 0.002604 -0.023438 0.015625 0.000000 0.002604 -0.023438 0.072917 0.015625 -0.020833 0.015625 
+DEAL::0.000868 0.000868 -0.006944 0.028646 0.022135 0.022135 0.026042 0.002604 0.002604 0.026042 -0.001302 -0.001302 -0.001302 -0.001302 0.010417 -0.013021 0.049479 -0.067708 -0.059896 -0.059896 
+DEAL::0.005208 0.005208 -0.006944 0.022569 -0.014323 -0.014323 -0.006510 0.040365 0.040365 -0.006510 -0.033854 0.059896 -0.033854 0.059896 0.005208 0.005208 0.044271 -0.026042 -0.010417 -0.010417 
+DEAL::0.000000 0.000868 0.009549 0.000000 -0.049479 0.117188 0.101562 -0.070313 -0.023438 -0.002604 -0.010417 -0.010417 0.117187 -0.049479 -0.023438 -0.002604 -0.062500 -0.026042 -0.119792 -0.062500 
+DEAL::0.000868 0.004340 -0.003472 0.000868 -0.040365 0.074219 0.101563 -0.031250 -0.007813 -0.005208 0.014323 0.014323 0.074219 -0.040365 -0.007813 -0.005208 -0.101563 -0.114583 -0.138021 -0.101562 
+DEAL::-0.003472 0.004340 0.016493 -0.012153 -0.002604 -0.013021 -0.028646 0.039063 0.054688 -0.018229 0.005208 0.031250 0.002604 0.023437 0.007813 0.007812 -0.093750 -0.046875 -0.057292 -0.083333 
+DEAL::0.004340 -0.003472 0.016493 -0.012153 -0.013021 -0.002604 -0.018229 0.054688 0.039063 -0.028646 0.002604 0.023438 0.005208 0.031250 0.007813 0.007812 -0.093750 -0.046875 -0.083333 -0.057292 
+DEAL::-0.005208 0.004340 0.004340 0.006944 -0.007812 0.018229 0.018229 0.018229 0.018229 -0.007812 0.015625 0.000000 0.002604 -0.023438 0.002604 -0.023438 0.072917 0.015625 0.015625 -0.020833 
+DEAL::-0.010417 0.001736 0.001736 0.012153 0.027344 0.001302 -0.006510 -0.006510 0.001302 0.027344 0.015625 -0.015625 -0.002604 -0.023438 -0.002604 -0.023438 0.091146 0.031250 0.031250 -0.026042 
+DEAL::-0.001736 0.006076 0.006076 -0.007813 -0.010417 -0.005208 0.002604 -0.002604 -0.010417 -0.010417 0.013021 0.041667 -0.013021 0.010417 -0.018229 0.026042 -0.057292 0.010417 0.020833 -0.020833 
+DEAL::0.013889 0.013889 0.008681 0.039063 0.016927 0.016927 0.009115 0.035156 0.035156 0.009115 0.005208 -0.059896 0.005208 -0.059896 0.039063 -0.067708 0.335938 0.135417 0.161458 0.161458 
+DEAL::0.006076 -0.001736 0.006076 -0.007813 -0.005208 -0.010417 -0.010417 -0.010417 -0.002604 0.002604 -0.013021 0.010417 0.013021 0.041667 -0.018229 0.026042 -0.057292 0.010417 -0.020833 0.020833 
+DEAL::-0.000868 -0.000868 -0.001736 -0.001736 0.006510 0.006510 0.010417 -0.018229 -0.018229 0.010417 0.006510 0.003906 0.006510 0.003906 -0.002604 0.007813 -0.065104 -0.031250 -0.044271 -0.044271 
+DEAL::
+DEAL::Child: 6
+DEAL::0.007812 -0.015625 0.007812 -0.015625 -0.070312 0.070313 0.070313 -0.070312 -0.070312 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070312 0.000000 0.140625 0.000000 0.140625 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::0.007812 0.007812 -0.015625 -0.015625 -0.070312 -0.070313 -0.070312 0.070312 0.070312 -0.070312 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.000000 0.000000 0.000000 0.140625 0.140625 
+DEAL::-0.062500 -0.023437 -0.023437 -0.023437 0.140625 -0.070312 -0.035156 -0.035156 -0.070312 0.140625 0.140625 -0.070312 -0.035156 -0.035156 -0.035156 -0.035156 -0.210937 -0.210937 -0.210937 -0.421875 
+DEAL::0.001736 -0.010417 0.001736 0.012153 0.001302 0.027344 0.027344 0.001302 -0.006510 -0.006510 -0.002604 -0.023438 0.015625 -0.015625 -0.002604 -0.023438 0.091146 0.031250 -0.026042 0.031250 
+DEAL::0.004340 -0.005208 0.004340 0.006944 0.018229 -0.007812 -0.007812 0.018229 0.018229 0.018229 0.002604 -0.023438 0.015625 0.000000 0.002604 -0.023438 0.072917 0.015625 -0.020833 0.015625 
+DEAL::0.004340 0.004340 -0.005208 0.006944 0.018229 0.018229 0.018229 -0.007812 -0.007812 0.018229 0.002604 -0.023438 0.002604 -0.023438 0.015625 0.000000 0.072917 -0.020833 0.015625 0.015625 
+DEAL::0.001736 0.001736 -0.010417 0.012153 -0.006510 -0.006510 0.001302 0.027344 0.027344 0.001302 -0.002604 -0.023437 -0.002604 -0.023438 0.015625 -0.015625 0.091146 -0.026042 0.031250 0.031250 
+DEAL::0.016493 -0.003472 0.004340 -0.012153 0.054688 -0.018229 -0.002604 -0.013021 -0.028646 0.039063 0.007813 0.007813 0.005208 0.031250 0.002604 0.023438 -0.093750 -0.057292 -0.083333 -0.046875 
+DEAL::0.016493 0.004340 -0.003472 -0.012153 0.039063 -0.028646 -0.013021 -0.002604 -0.018229 0.054688 0.007812 0.007813 0.002604 0.023438 0.005208 0.031250 -0.093750 -0.083333 -0.057292 -0.046875 
+DEAL::-0.003472 0.000868 0.004340 0.000868 -0.007813 -0.005208 -0.040365 0.074219 0.101562 -0.031250 -0.007813 -0.005208 0.014323 0.014323 0.074219 -0.040365 -0.101563 -0.138021 -0.101562 -0.114583 
+DEAL::0.009549 0.000000 0.000868 0.000000 -0.023438 -0.002604 -0.049479 0.117187 0.101562 -0.070312 -0.023437 -0.002604 -0.010417 -0.010417 0.117187 -0.049479 -0.062500 -0.119792 -0.062500 -0.026042 
+DEAL::-0.006944 0.000868 0.000868 0.028646 0.002604 0.026042 0.022135 0.022135 0.026042 0.002604 0.010417 -0.013021 -0.001302 -0.001302 -0.001302 -0.001302 0.049479 -0.059896 -0.059896 -0.067708 
+DEAL::-0.006944 0.005208 0.005208 0.022569 0.040365 -0.006510 -0.014323 -0.014323 -0.006510 0.040365 0.005208 0.005208 -0.033854 0.059896 -0.033854 0.059896 0.044271 -0.010417 -0.010417 -0.026042 
+DEAL::-0.003472 0.004340 0.000868 0.000868 -0.031250 0.101563 0.074219 -0.040365 -0.005208 -0.007813 -0.007813 -0.005208 0.074219 -0.040365 0.014323 0.014323 -0.101562 -0.101562 -0.138021 -0.114583 
+DEAL::0.009549 0.000868 0.000000 0.000000 -0.070313 0.101563 0.117187 -0.049479 -0.002604 -0.023438 -0.023438 -0.002604 0.117187 -0.049479 -0.010417 -0.010417 -0.062500 -0.062500 -0.119792 -0.026042 
+DEAL::-0.001736 -0.000868 -0.000868 -0.001736 -0.018229 0.010417 0.006510 0.006510 0.010417 -0.018229 -0.002604 0.007813 0.006510 0.003906 0.006510 0.003906 -0.065104 -0.044271 -0.044271 -0.031250 
+DEAL::0.006076 0.006076 -0.001736 -0.007813 -0.002604 0.002604 -0.005208 -0.010417 -0.010417 -0.010417 -0.018229 0.026042 -0.013021 0.010417 0.013021 0.041667 -0.057292 -0.020833 0.020833 0.010417 
+DEAL::0.008681 0.013889 0.013889 0.039063 0.035156 0.009115 0.016927 0.016927 0.009115 0.035156 0.039063 -0.067708 0.005208 -0.059896 0.005208 -0.059896 0.335938 0.161458 0.161458 0.135417 
+DEAL::0.006076 -0.001736 0.006076 -0.007813 -0.010417 -0.010417 -0.010417 -0.005208 0.002604 -0.002604 -0.018229 0.026042 0.013021 0.041667 -0.013021 0.010417 -0.057292 0.020833 -0.020833 0.010417 
+DEAL::
+DEAL::Child: 7
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::0.007812 0.007812 -0.015625 -0.015625 -0.070313 -0.070312 -0.070312 0.070312 0.070312 -0.070312 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.000000 0.000000 0.000000 0.140625 0.140625 
+DEAL::-0.023438 -0.062500 -0.023438 -0.023437 -0.070313 0.140625 0.140625 -0.070312 -0.035156 -0.035156 -0.035156 -0.035156 0.140625 -0.070312 -0.035156 -0.035156 -0.210937 -0.210937 -0.421875 -0.210937 
+DEAL::-0.015625 0.007813 0.007812 -0.015625 0.070313 -0.070312 -0.070312 -0.070313 -0.070313 0.070313 0.000000 0.000000 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.140625 0.140625 0.000000 
+DEAL::0.004340 0.004340 -0.005208 0.006944 0.018229 0.018229 0.018229 -0.007812 -0.007812 0.018229 0.002604 -0.023438 0.002604 -0.023438 0.015625 0.000000 0.072917 -0.020833 0.015625 0.015625 
+DEAL::0.001736 0.001736 -0.010417 0.012153 -0.006510 -0.006510 0.001302 0.027344 0.027344 0.001302 -0.002604 -0.023438 -0.002604 -0.023437 0.015625 -0.015625 0.091146 -0.026042 0.031250 0.031250 
+DEAL::0.004340 -0.003472 0.000868 0.000868 0.101562 -0.031250 -0.007812 -0.005208 -0.040365 0.074219 0.074219 -0.040365 -0.007813 -0.005208 0.014323 0.014323 -0.101563 -0.101562 -0.114583 -0.138021 
+DEAL::0.000868 0.009549 0.000000 0.000000 0.101562 -0.070312 -0.023438 -0.002604 -0.049479 0.117187 0.117187 -0.049479 -0.023438 -0.002604 -0.010417 -0.010417 -0.062500 -0.062500 -0.026042 -0.119792 
+DEAL::0.005208 -0.006944 0.005208 0.022569 -0.006510 0.040365 0.040365 -0.006510 -0.014323 -0.014323 -0.033854 0.059896 0.005208 0.005208 -0.033854 0.059896 0.044271 -0.010417 -0.026042 -0.010417 
+DEAL::0.000868 -0.006944 0.000868 0.028646 0.026042 0.002604 0.002604 0.026042 0.022135 0.022135 -0.001302 -0.001302 0.010417 -0.013021 -0.001302 -0.001302 0.049479 -0.059896 -0.067708 -0.059896 
+DEAL::-0.005208 0.004340 0.004340 0.006944 -0.007812 0.018229 0.018229 0.018229 0.018229 -0.007812 0.015625 0.000000 0.002604 -0.023438 0.002604 -0.023438 0.072917 0.015625 0.015625 -0.020833 
+DEAL::-0.010417 0.001736 0.001736 0.012153 0.027344 0.001302 -0.006510 -0.006510 0.001302 0.027344 0.015625 -0.015625 -0.002604 -0.023437 -0.002604 -0.023438 0.091146 0.031250 0.031250 -0.026042 
+DEAL::-0.003472 0.016493 0.004340 -0.012153 -0.018229 0.054687 0.039062 -0.028646 -0.013021 -0.002604 0.005208 0.031250 0.007812 0.007813 0.002604 0.023438 -0.093750 -0.057292 -0.046875 -0.083333 
+DEAL::0.004340 0.016493 -0.003472 -0.012153 -0.028646 0.039062 0.054687 -0.018229 -0.002604 -0.013021 0.002604 0.023438 0.007812 0.007813 0.005208 0.031250 -0.093750 -0.083333 -0.046875 -0.057292 
+DEAL::0.000000 0.009549 0.000868 0.000000 -0.002604 -0.023438 -0.070312 0.101562 0.117187 -0.049479 -0.010417 -0.010417 -0.023438 -0.002604 0.117187 -0.049479 -0.062500 -0.119792 -0.026042 -0.062500 
+DEAL::0.000868 -0.003472 0.004340 0.000868 -0.005208 -0.007813 -0.031250 0.101563 0.074219 -0.040365 0.014323 0.014323 -0.007813 -0.005208 0.074219 -0.040365 -0.101562 -0.138021 -0.114583 -0.101562 
+DEAL::-0.001736 0.006076 0.006076 -0.007813 -0.010417 -0.010417 -0.002604 0.002604 -0.005208 -0.010417 0.013021 0.041667 -0.018229 0.026042 -0.013021 0.010417 -0.057292 0.020833 0.010417 -0.020833 
+DEAL::-0.000868 -0.001736 -0.000868 -0.001736 0.010417 -0.018229 -0.018229 0.010417 0.006510 0.006510 0.006510 0.003906 -0.002604 0.007812 0.006510 0.003906 -0.065104 -0.044271 -0.031250 -0.044271 
+DEAL::0.006076 0.006076 -0.001736 -0.007813 0.002604 -0.002604 -0.010417 -0.010417 -0.010417 -0.005208 -0.013021 0.010417 -0.018229 0.026042 0.013021 0.041667 -0.057292 -0.020833 0.010417 0.020833 
+DEAL::0.013889 0.008681 0.013889 0.039063 0.009115 0.035156 0.035156 0.009115 0.016927 0.016927 0.005208 -0.059896 0.039063 -0.067708 0.005208 -0.059896 0.335938 0.161458 0.135417 0.161458 
+DEAL::
+DEAL::Refinement Direction: 2
+DEAL::Child: 0
+DEAL::0.031250 0.070313 0.070313 0.070313 0.703125 -0.351563 -0.105469 -0.105469 -0.351563 0.703125 0.703125 -0.351563 -0.105469 -0.105469 -0.105469 -0.105469 0.351563 0.351563 0.351563 -0.281250 
+DEAL::0.000000 -0.015625 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 -0.035156 -0.035156 0.140625 0.140625 -0.070312 0.140625 
+DEAL::0.000000 0.000000 -0.015625 0.000000 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.140625 -0.070312 0.140625 0.140625 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070312 0.140625 0.140625 0.140625 
+DEAL::0.017361 -0.005208 0.046875 0.046875 0.046875 0.265625 0.210937 -0.164063 -0.121094 0.019531 0.019531 -0.121094 0.210937 -0.164062 -0.050781 -0.050781 0.343750 0.343750 -0.101562 0.109375 
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+DEAL::0.003472 -0.002604 -0.002604 0.007813 -0.019531 0.003906 0.027344 0.027344 0.003906 -0.019531 -0.007812 0.015625 -0.007813 -0.007813 -0.007812 -0.007813 0.070313 -0.015625 -0.015625 0.031250 
+DEAL::0.003472 -0.002604 0.007813 -0.002604 -0.019531 0.003906 -0.007812 -0.007813 0.015625 -0.007812 -0.019531 0.003906 0.027344 0.027344 -0.007813 -0.007813 -0.015625 0.070313 -0.015625 0.031250 
+DEAL::0.003472 0.007813 -0.002604 -0.002604 -0.007812 0.015625 -0.007813 -0.007813 0.003906 -0.019531 -0.019531 0.003906 -0.007813 -0.007813 0.027344 0.027344 -0.015625 -0.015625 0.070312 0.031250 
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+DEAL::
+DEAL::Child: 1
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+DEAL::0.000000 0.000000 -0.015625 0.000000 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.140625 -0.070312 0.140625 0.140625 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070312 0.140625 0.140625 0.140625 
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+DEAL::-0.005208 0.017361 0.046875 0.046875 0.265625 0.046875 0.019531 -0.121094 -0.164063 0.210938 0.210938 -0.164062 0.019531 -0.121094 -0.050781 -0.050781 0.343750 0.343750 0.109375 -0.101562 
+DEAL::0.046875 0.017361 -0.005208 0.046875 -0.121094 0.019531 0.046875 0.265625 0.210937 -0.164062 -0.050781 -0.050781 0.019531 -0.121094 0.210937 -0.164062 0.343750 -0.101562 0.109375 0.343750 
+DEAL::0.007812 0.003472 0.018229 0.007812 0.015625 -0.007813 -0.031250 0.101562 0.058594 -0.035156 0.019531 0.019531 -0.007813 0.015625 0.058594 -0.035156 -0.039063 0.007813 -0.062500 -0.039063 
+DEAL::0.005208 0.000000 -0.005208 0.000000 0.023437 -0.023437 -0.011719 0.035156 0.000000 -0.015625 0.023437 -0.023437 -0.035156 -0.035156 0.035156 -0.011719 0.046875 0.000000 0.046875 0.070313 
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+DEAL::0.046875 0.017361 0.046875 -0.005208 -0.121094 0.019531 0.019531 -0.121094 -0.050781 -0.050781 -0.164062 0.210938 0.046875 0.265625 -0.164062 0.210937 -0.101562 0.343750 0.109375 0.343750 
+DEAL::0.007812 0.003472 0.007813 0.018229 0.015625 -0.007813 -0.007813 0.015625 0.019531 0.019531 -0.035156 0.058594 -0.031250 0.101563 -0.035156 0.058594 0.007813 -0.039062 -0.062500 -0.039062 
+DEAL::0.000000 0.000000 -0.005208 0.005208 -0.035156 -0.035156 -0.011719 0.035156 0.035156 -0.011719 -0.023437 0.023437 -0.023437 0.023437 0.000000 -0.015625 0.070313 0.000000 0.046875 0.046875 
+DEAL::0.000000 0.000000 0.005208 -0.005208 -0.035156 -0.035156 -0.023437 0.023437 0.023437 -0.023437 -0.011719 0.035156 -0.011719 0.035156 -0.015625 0.000000 0.000000 0.070313 0.046875 0.046875 
+DEAL::-0.002604 0.003472 -0.002604 0.007813 0.003906 -0.019531 -0.019531 0.003906 0.027344 0.027344 -0.007812 -0.007813 -0.007812 0.015625 -0.007812 -0.007813 0.070313 -0.015625 0.031250 -0.015625 
+DEAL::-0.002604 0.003472 0.007813 -0.002604 0.003906 -0.019531 -0.007813 0.015625 -0.007813 -0.007812 0.027344 0.027344 -0.019531 0.003906 -0.007813 -0.007812 -0.015625 0.070313 0.031250 -0.015625 
+DEAL::0.005208 0.000000 0.005208 0.005208 0.023438 -0.023437 -0.023437 0.023437 0.003906 0.003906 0.003906 0.003906 -0.023437 0.023438 0.003906 0.003906 0.023438 0.023438 0.015625 0.023438 
+DEAL::0.007813 0.003472 -0.002604 -0.002604 0.015625 -0.007812 -0.019531 0.003906 -0.007813 -0.007813 -0.007813 -0.007812 -0.019531 0.003906 0.027344 0.027344 -0.015625 -0.015625 0.031250 0.070312 
+DEAL::
+DEAL::Child: 2
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+DEAL::0.000000 -0.015625 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 -0.035156 -0.035156 0.140625 0.140625 -0.070313 0.140625 
+DEAL::0.070312 0.070313 0.031250 0.070312 -0.105469 -0.105469 -0.351563 0.703125 0.703125 -0.351562 -0.105469 -0.105469 -0.105469 -0.105469 0.703125 -0.351562 0.351563 -0.281250 0.351563 0.351563 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070312 0.140625 0.140625 0.140625 
+DEAL::-0.005208 0.005208 0.000000 0.000000 0.000000 -0.015625 0.023437 -0.023438 -0.011719 0.035156 0.035156 -0.011719 0.023437 -0.023437 -0.035156 -0.035156 0.046875 0.046875 0.070312 0.000000 
+DEAL::0.005208 -0.005208 0.000000 0.000000 -0.015625 0.000000 0.035156 -0.011719 -0.023438 0.023437 0.023437 -0.023437 0.035156 -0.011719 -0.035156 -0.035156 0.046875 0.046875 0.000000 0.070313 
+DEAL::0.007812 0.018229 0.003472 0.007812 -0.035156 0.058594 0.101562 -0.031250 -0.007813 0.015625 0.019531 0.019531 0.058594 -0.035156 -0.007813 0.015625 -0.039063 -0.062500 0.007813 -0.039063 
+DEAL::0.046875 -0.005208 0.017361 0.046875 -0.164062 0.210937 0.265625 0.046875 0.019531 -0.121094 -0.050781 -0.050781 0.210938 -0.164062 0.019531 -0.121094 0.343750 0.109375 -0.101562 0.343750 
+DEAL::-0.005208 0.046875 0.017361 0.046875 0.210938 -0.164063 -0.121094 0.019531 0.046875 0.265625 0.210938 -0.164062 -0.050781 -0.050781 0.019531 -0.121094 0.343750 0.109375 0.343750 -0.101562 
+DEAL::0.018229 0.007813 0.003472 0.007813 0.058594 -0.035156 0.015625 -0.007813 -0.031250 0.101563 0.058594 -0.035156 0.019531 0.019531 -0.007813 0.015625 -0.039062 -0.062500 -0.039062 0.007813 
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+DEAL::0.000000 -0.005208 0.000000 0.005208 -0.011719 0.035156 0.035156 -0.011719 -0.035156 -0.035156 -0.023437 0.023438 0.000000 -0.015625 -0.023438 0.023437 0.070313 0.046875 0.000000 0.046875 
+DEAL::0.000000 0.005208 0.000000 -0.005208 -0.023437 0.023438 0.023438 -0.023438 -0.035156 -0.035156 -0.011719 0.035156 -0.015625 0.000000 -0.011719 0.035156 0.000000 0.046875 0.070313 0.046875 
+DEAL::0.046875 0.046875 0.017361 -0.005208 -0.050781 -0.050781 -0.121094 0.019531 0.019531 -0.121094 -0.164063 0.210937 -0.164063 0.210937 0.046875 0.265625 -0.101562 0.109375 0.343750 0.343750 
+DEAL::0.007812 0.007812 0.003472 0.018229 0.019531 0.019531 0.015625 -0.007813 -0.007813 0.015625 -0.035156 0.058594 -0.035156 0.058594 -0.031250 0.101563 0.007813 -0.062500 -0.039062 -0.039062 
+DEAL::-0.002604 -0.002604 0.003472 0.007813 0.027344 0.027344 0.003906 -0.019531 -0.019531 0.003906 -0.007812 -0.007813 -0.007812 -0.007813 -0.007813 0.015625 0.070313 0.031250 -0.015625 -0.015625 
+DEAL::0.005208 0.005208 0.000000 0.005208 0.003906 0.003906 0.023437 -0.023437 -0.023437 0.023437 0.003906 0.003906 0.003906 0.003906 -0.023437 0.023437 0.023438 0.015625 0.023438 0.023438 
+DEAL::-0.002604 0.007813 0.003472 -0.002604 -0.007812 -0.007813 0.015625 -0.007813 -0.019531 0.003906 0.027344 0.027344 -0.007813 -0.007813 -0.019531 0.003906 -0.015625 0.031250 0.070313 -0.015625 
+DEAL::0.007813 -0.002604 0.003472 -0.002604 -0.007813 -0.007813 0.003906 -0.019531 -0.007813 0.015625 -0.007813 -0.007812 0.027344 0.027344 -0.019531 0.003906 -0.015625 0.031250 -0.015625 0.070313 
+DEAL::
+DEAL::Child: 3
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+DEAL::0.000000 -0.015625 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 -0.035156 -0.035156 0.140625 0.140625 -0.070313 0.140625 
+DEAL::0.000000 0.000000 -0.015625 0.000000 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.140625 -0.070312 0.140625 0.140625 
+DEAL::0.070313 0.070313 0.070313 0.031250 -0.105469 -0.105469 -0.105469 -0.105469 -0.105469 -0.105469 -0.351562 0.703125 -0.351563 0.703125 -0.351563 0.703125 -0.281250 0.351563 0.351563 0.351563 
+DEAL::-0.005208 0.005208 0.000000 0.000000 0.000000 -0.015625 0.023438 -0.023437 -0.011719 0.035156 0.035156 -0.011719 0.023437 -0.023437 -0.035156 -0.035156 0.046875 0.046875 0.070312 0.000000 
+DEAL::0.005208 -0.005208 0.000000 0.000000 -0.015625 0.000000 0.035156 -0.011719 -0.023437 0.023437 0.023437 -0.023437 0.035156 -0.011719 -0.035156 -0.035156 0.046875 0.046875 0.000000 0.070313 
+DEAL::0.000000 -0.005208 0.005208 0.000000 -0.011719 0.035156 0.000000 -0.015625 0.023437 -0.023437 -0.035156 -0.035156 0.035156 -0.011719 0.023437 -0.023437 0.046875 0.070313 0.000000 0.046875 
+DEAL::0.000000 0.005208 -0.005208 0.000000 -0.023437 0.023437 -0.015625 0.000000 0.035156 -0.011719 -0.035156 -0.035156 0.023437 -0.023437 0.035156 -0.011719 0.046875 0.000000 0.070313 0.046875 
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+DEAL::-0.005208 0.000000 0.005208 0.000000 0.035156 -0.011719 -0.023437 0.023438 -0.015625 0.000000 0.035156 -0.011719 -0.035156 -0.035156 0.023438 -0.023438 0.046875 0.070313 0.046875 0.000000 
+DEAL::0.018229 0.007812 0.007812 0.003472 0.058594 -0.035156 0.019531 0.019531 -0.035156 0.058594 0.101562 -0.031250 0.015625 -0.007813 0.015625 -0.007813 -0.062500 -0.039063 -0.039063 0.007813 
+DEAL::-0.005208 0.046875 0.046875 0.017361 0.210938 -0.164063 -0.050781 -0.050781 -0.164062 0.210937 0.265625 0.046875 -0.121094 0.019531 -0.121094 0.019531 0.109375 0.343750 0.343750 -0.101562 
+DEAL::0.007812 0.018229 0.007812 0.003472 -0.035156 0.058594 0.058594 -0.035156 0.019531 0.019531 0.015625 -0.007813 0.101562 -0.031250 0.015625 -0.007813 -0.062500 -0.039063 0.007813 -0.039062 
+DEAL::0.046875 -0.005208 0.046875 0.017361 -0.164062 0.210938 0.210938 -0.164063 -0.050781 -0.050781 -0.121094 0.019531 0.265625 0.046875 -0.121094 0.019531 0.109375 0.343750 -0.101562 0.343750 
+DEAL::0.007812 0.007813 0.018229 0.003472 0.019531 0.019531 -0.035156 0.058594 0.058594 -0.035156 0.015625 -0.007813 0.015625 -0.007813 0.101563 -0.031250 -0.062500 0.007813 -0.039062 -0.039062 
+DEAL::0.046875 0.046875 -0.005208 0.017361 -0.050781 -0.050781 -0.164063 0.210938 0.210938 -0.164063 -0.121094 0.019531 -0.121094 0.019531 0.265625 0.046875 0.109375 -0.101562 0.343750 0.343750 
+DEAL::0.005208 0.005208 0.005208 0.000000 0.003906 0.003906 0.003906 0.003906 0.003906 0.003906 0.023438 -0.023438 0.023437 -0.023437 0.023438 -0.023437 0.015625 0.023437 0.023437 0.023437 
+DEAL::-0.002604 -0.002604 0.007813 0.003472 0.027344 0.027344 -0.007813 -0.007813 -0.007813 -0.007813 0.003906 -0.019531 0.003906 -0.019531 0.015625 -0.007812 0.031250 0.070313 -0.015625 -0.015625 
+DEAL::-0.002604 0.007813 -0.002604 0.003472 -0.007812 -0.007813 -0.007813 -0.007813 0.027344 0.027344 0.003906 -0.019531 0.015625 -0.007812 0.003906 -0.019531 0.031250 -0.015625 0.070313 -0.015625 
+DEAL::0.007813 -0.002604 -0.002604 0.003472 -0.007813 -0.007812 0.027344 0.027344 -0.007812 -0.007813 0.015625 -0.007813 0.003906 -0.019531 0.003906 -0.019531 0.031250 -0.015625 -0.015625 0.070313 
+DEAL::
+DEAL::Child: 4
+DEAL::-0.023438 -0.062500 -0.023438 -0.023438 -0.070313 0.140625 0.140625 -0.070313 -0.035156 -0.035156 -0.035156 -0.035156 0.140625 -0.070312 -0.035156 -0.035156 -0.210937 -0.210937 -0.421875 -0.210937 
+DEAL::0.007812 0.007812 -0.015625 -0.015625 -0.070313 -0.070312 -0.070312 0.070312 0.070312 -0.070312 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.000000 0.000000 0.000000 0.140625 0.140625 
+DEAL::-0.015625 0.007812 0.007812 -0.015625 0.070312 -0.070312 -0.070312 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.140625 0.140625 0.000000 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::0.000868 0.009549 0.000000 0.000000 0.101562 -0.070312 -0.023438 -0.002604 -0.049479 0.117187 0.117187 -0.049479 -0.023438 -0.002604 -0.010417 -0.010417 -0.062500 -0.062500 -0.026042 -0.119792 
+DEAL::0.004340 -0.003472 0.000868 0.000868 0.101563 -0.031250 -0.007813 -0.005208 -0.040365 0.074219 0.074219 -0.040365 -0.007813 -0.005208 0.014323 0.014323 -0.101562 -0.101562 -0.114583 -0.138021 
+DEAL::-0.003472 0.016493 0.004340 -0.012153 -0.018229 0.054687 0.039063 -0.028646 -0.013021 -0.002604 0.005208 0.031250 0.007812 0.007813 0.002604 0.023438 -0.093750 -0.057292 -0.046875 -0.083333 
+DEAL::0.004340 0.016493 -0.003472 -0.012153 -0.028646 0.039062 0.054688 -0.018229 -0.002604 -0.013021 0.002604 0.023438 0.007813 0.007813 0.005208 0.031250 -0.093750 -0.083333 -0.046875 -0.057292 
+DEAL::0.000868 -0.003472 0.004340 0.000868 -0.005208 -0.007813 -0.031250 0.101563 0.074219 -0.040365 0.014323 0.014323 -0.007813 -0.005208 0.074219 -0.040365 -0.101563 -0.138021 -0.114583 -0.101563 
+DEAL::0.000000 0.009549 0.000868 0.000000 -0.002604 -0.023438 -0.070312 0.101563 0.117188 -0.049479 -0.010417 -0.010417 -0.023438 -0.002604 0.117187 -0.049479 -0.062500 -0.119792 -0.026042 -0.062500 
+DEAL::0.005208 -0.006944 0.005208 0.022569 -0.006510 0.040365 0.040365 -0.006510 -0.014323 -0.014323 -0.033854 0.059896 0.005208 0.005208 -0.033854 0.059896 0.044271 -0.010417 -0.026042 -0.010417 
+DEAL::0.000868 -0.006944 0.000868 0.028646 0.026042 0.002604 0.002604 0.026042 0.022135 0.022135 -0.001302 -0.001302 0.010417 -0.013021 -0.001302 -0.001302 0.049479 -0.059896 -0.067708 -0.059896 
+DEAL::0.001736 0.001736 -0.010417 0.012153 -0.006510 -0.006510 0.001302 0.027344 0.027344 0.001302 -0.002604 -0.023438 -0.002604 -0.023438 0.015625 -0.015625 0.091146 -0.026042 0.031250 0.031250 
+DEAL::0.004340 0.004340 -0.005208 0.006944 0.018229 0.018229 0.018229 -0.007813 -0.007812 0.018229 0.002604 -0.023438 0.002604 -0.023438 0.015625 0.000000 0.072917 -0.020833 0.015625 0.015625 
+DEAL::-0.010417 0.001736 0.001736 0.012153 0.027344 0.001302 -0.006510 -0.006510 0.001302 0.027344 0.015625 -0.015625 -0.002604 -0.023438 -0.002604 -0.023438 0.091146 0.031250 0.031250 -0.026042 
+DEAL::-0.005208 0.004340 0.004340 0.006944 -0.007812 0.018229 0.018229 0.018229 0.018229 -0.007812 0.015625 0.000000 0.002604 -0.023438 0.002604 -0.023438 0.072917 0.015625 0.015625 -0.020833 
+DEAL::0.013889 0.008681 0.013889 0.039063 0.009115 0.035156 0.035156 0.009115 0.016927 0.016927 0.005208 -0.059896 0.039063 -0.067708 0.005208 -0.059896 0.335938 0.161458 0.135417 0.161458 
+DEAL::-0.001736 0.006076 0.006076 -0.007813 -0.010417 -0.010417 -0.002604 0.002604 -0.005208 -0.010417 0.013021 0.041667 -0.018229 0.026042 -0.013021 0.010417 -0.057292 0.020833 0.010417 -0.020833 
+DEAL::0.006076 0.006076 -0.001736 -0.007813 0.002604 -0.002604 -0.010417 -0.010417 -0.010417 -0.005208 -0.013021 0.010417 -0.018229 0.026042 0.013021 0.041667 -0.057292 -0.020833 0.010417 0.020833 
+DEAL::-0.000868 -0.001736 -0.000868 -0.001736 0.010417 -0.018229 -0.018229 0.010417 0.006510 0.006510 0.006510 0.003906 -0.002604 0.007813 0.006510 0.003906 -0.065104 -0.044271 -0.031250 -0.044271 
+DEAL::
+DEAL::Child: 5
+DEAL::0.007813 0.007813 -0.015625 -0.015625 -0.070313 -0.070312 -0.070313 0.070313 0.070313 -0.070313 -0.070312 0.070313 -0.070312 0.070312 0.000000 0.000000 0.000000 0.000000 0.140625 0.140625 
+DEAL::-0.023438 -0.062500 -0.023438 -0.023438 -0.070313 0.140625 0.140625 -0.070313 -0.035156 -0.035156 -0.035156 -0.035156 0.140625 -0.070312 -0.035156 -0.035156 -0.210937 -0.210937 -0.421875 -0.210937 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::-0.015625 0.007812 0.007812 -0.015625 0.070312 -0.070312 -0.070312 -0.070313 -0.070313 0.070313 0.000000 0.000000 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.140625 0.140625 0.000000 
+DEAL::0.004340 -0.003472 0.000868 0.000868 0.101563 -0.031250 -0.007813 -0.005208 -0.040365 0.074219 0.074219 -0.040365 -0.007812 -0.005208 0.014323 0.014323 -0.101563 -0.101563 -0.114583 -0.138021 
+DEAL::0.000868 0.009549 0.000000 0.000000 0.101562 -0.070312 -0.023438 -0.002604 -0.049479 0.117187 0.117187 -0.049479 -0.023437 -0.002604 -0.010417 -0.010417 -0.062500 -0.062500 -0.026042 -0.119792 
+DEAL::0.005208 -0.006944 0.005208 0.022569 -0.006510 0.040365 0.040365 -0.006510 -0.014323 -0.014323 -0.033854 0.059896 0.005208 0.005208 -0.033854 0.059896 0.044271 -0.010417 -0.026042 -0.010417 
+DEAL::0.000868 -0.006944 0.000868 0.028646 0.026042 0.002604 0.002604 0.026042 0.022135 0.022135 -0.001302 -0.001302 0.010417 -0.013021 -0.001302 -0.001302 0.049479 -0.059896 -0.067708 -0.059896 
+DEAL::0.004340 0.004340 -0.005208 0.006944 0.018229 0.018229 0.018229 -0.007812 -0.007812 0.018229 0.002604 -0.023438 0.002604 -0.023438 0.015625 0.000000 0.072917 -0.020833 0.015625 0.015625 
+DEAL::0.001736 0.001736 -0.010417 0.012153 -0.006510 -0.006510 0.001302 0.027344 0.027344 0.001302 -0.002604 -0.023438 -0.002604 -0.023438 0.015625 -0.015625 0.091146 -0.026042 0.031250 0.031250 
+DEAL::-0.003472 0.016493 0.004340 -0.012153 -0.018229 0.054688 0.039062 -0.028646 -0.013021 -0.002604 0.005208 0.031250 0.007812 0.007813 0.002604 0.023438 -0.093750 -0.057292 -0.046875 -0.083333 
+DEAL::0.004340 0.016493 -0.003472 -0.012153 -0.028646 0.039062 0.054687 -0.018229 -0.002604 -0.013021 0.002604 0.023438 0.007812 0.007813 0.005208 0.031250 -0.093750 -0.083333 -0.046875 -0.057292 
+DEAL::0.000000 0.009549 0.000868 0.000000 -0.002604 -0.023438 -0.070312 0.101562 0.117187 -0.049479 -0.010417 -0.010417 -0.023438 -0.002604 0.117187 -0.049479 -0.062500 -0.119792 -0.026042 -0.062500 
+DEAL::0.000868 -0.003472 0.004340 0.000868 -0.005208 -0.007813 -0.031250 0.101563 0.074219 -0.040365 0.014323 0.014323 -0.007813 -0.005208 0.074219 -0.040365 -0.101562 -0.138021 -0.114583 -0.101562 
+DEAL::-0.005208 0.004340 0.004340 0.006944 -0.007812 0.018229 0.018229 0.018229 0.018229 -0.007812 0.015625 0.000000 0.002604 -0.023438 0.002604 -0.023438 0.072917 0.015625 0.015625 -0.020833 
+DEAL::-0.010417 0.001736 0.001736 0.012153 0.027344 0.001302 -0.006510 -0.006510 0.001302 0.027344 0.015625 -0.015625 -0.002604 -0.023438 -0.002604 -0.023438 0.091146 0.031250 0.031250 -0.026042 
+DEAL::-0.001736 0.006076 0.006076 -0.007813 -0.010417 -0.010417 -0.002604 0.002604 -0.005208 -0.010417 0.013021 0.041667 -0.018229 0.026042 -0.013021 0.010417 -0.057292 0.020833 0.010417 -0.020833 
+DEAL::0.013889 0.008681 0.013889 0.039063 0.009115 0.035156 0.035156 0.009115 0.016927 0.016927 0.005208 -0.059896 0.039063 -0.067708 0.005208 -0.059896 0.335938 0.161458 0.135417 0.161458 
+DEAL::-0.000868 -0.001736 -0.000868 -0.001736 0.010417 -0.018229 -0.018229 0.010417 0.006510 0.006510 0.006510 0.003906 -0.002604 0.007813 0.006510 0.003906 -0.065104 -0.044271 -0.031250 -0.044271 
+DEAL::0.006076 0.006076 -0.001736 -0.007813 0.002604 -0.002604 -0.010417 -0.010417 -0.010417 -0.005208 -0.013021 0.010417 -0.018229 0.026042 0.013021 0.041667 -0.057292 -0.020833 0.010417 0.020833 
+DEAL::
+DEAL::Child: 6
+DEAL::0.007812 -0.015625 0.007812 -0.015625 -0.070312 0.070313 0.070312 -0.070312 -0.070312 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070312 0.000000 0.140625 0.000000 0.140625 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::-0.023437 -0.023438 -0.062500 -0.023438 -0.035156 -0.035156 -0.070312 0.140625 0.140625 -0.070312 -0.035156 -0.035156 -0.035156 -0.035156 0.140625 -0.070312 -0.210937 -0.421875 -0.210937 -0.210937 
+DEAL::-0.015625 0.007813 0.007813 -0.015625 0.070313 -0.070312 -0.070313 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.140625 0.140625 0.000000 
+DEAL::0.001736 -0.010417 0.001736 0.012153 0.001302 0.027344 0.027344 0.001302 -0.006510 -0.006510 -0.002604 -0.023438 0.015625 -0.015625 -0.002604 -0.023438 0.091146 0.031250 -0.026042 0.031250 
+DEAL::0.004340 -0.005208 0.004340 0.006944 0.018229 -0.007812 -0.007812 0.018229 0.018229 0.018229 0.002604 -0.023438 0.015625 0.000000 0.002604 -0.023438 0.072917 0.015625 -0.020833 0.015625 
+DEAL::0.000868 0.000868 -0.006944 0.028646 0.022135 0.022135 0.026042 0.002604 0.002604 0.026042 -0.001302 -0.001302 -0.001302 -0.001302 0.010417 -0.013021 0.049479 -0.067708 -0.059896 -0.059896 
+DEAL::0.005208 0.005208 -0.006944 0.022569 -0.014323 -0.014323 -0.006510 0.040365 0.040365 -0.006510 -0.033854 0.059896 -0.033854 0.059896 0.005208 0.005208 0.044271 -0.026042 -0.010417 -0.010417 
+DEAL::0.000868 0.000000 0.009549 0.000000 0.117187 -0.049479 -0.002604 -0.023438 -0.070313 0.101563 0.117188 -0.049479 -0.010417 -0.010417 -0.023438 -0.002604 -0.062500 -0.026042 -0.062500 -0.119792 
+DEAL::0.004340 0.000868 -0.003472 0.000868 0.074219 -0.040365 -0.005208 -0.007813 -0.031250 0.101563 0.074219 -0.040365 0.014323 0.014323 -0.007813 -0.005208 -0.101563 -0.114583 -0.101563 -0.138021 
+DEAL::-0.003472 0.004340 0.016493 -0.012153 -0.002604 -0.013021 -0.028646 0.039062 0.054688 -0.018229 0.005208 0.031250 0.002604 0.023438 0.007812 0.007813 -0.093750 -0.046875 -0.057292 -0.083333 
+DEAL::0.004340 -0.003472 0.016493 -0.012153 -0.013021 -0.002604 -0.018229 0.054687 0.039063 -0.028646 0.002604 0.023438 0.005208 0.031250 0.007812 0.007813 -0.093750 -0.046875 -0.083333 -0.057292 
+DEAL::-0.005208 0.004340 0.004340 0.006944 -0.007812 0.018229 0.018229 0.018229 0.018229 -0.007813 0.015625 0.000000 0.002604 -0.023438 0.002604 -0.023438 0.072917 0.015625 0.015625 -0.020833 
+DEAL::-0.010417 0.001736 0.001736 0.012153 0.027344 0.001302 -0.006510 -0.006510 0.001302 0.027344 0.015625 -0.015625 -0.002604 -0.023438 -0.002604 -0.023437 0.091146 0.031250 0.031250 -0.026042 
+DEAL::0.000000 0.000868 0.009549 0.000000 -0.049479 0.117187 0.101562 -0.070312 -0.023438 -0.002604 -0.010417 -0.010417 0.117187 -0.049479 -0.023438 -0.002604 -0.062500 -0.026042 -0.119792 -0.062500 
+DEAL::0.000868 0.004340 -0.003472 0.000868 -0.040365 0.074219 0.101563 -0.031250 -0.007813 -0.005208 0.014323 0.014323 0.074219 -0.040365 -0.007813 -0.005208 -0.101563 -0.114583 -0.138021 -0.101562 
+DEAL::-0.001736 0.006076 0.006076 -0.007813 -0.010417 -0.005208 0.002604 -0.002604 -0.010417 -0.010417 0.013021 0.041667 -0.013021 0.010417 -0.018229 0.026042 -0.057292 0.010417 0.020833 -0.020833 
+DEAL::-0.000868 -0.000868 -0.001736 -0.001736 0.006510 0.006510 0.010417 -0.018229 -0.018229 0.010417 0.006510 0.003906 0.006510 0.003906 -0.002604 0.007813 -0.065104 -0.031250 -0.044271 -0.044271 
+DEAL::0.013889 0.013889 0.008681 0.039063 0.016927 0.016927 0.009115 0.035156 0.035156 0.009115 0.005208 -0.059896 0.005208 -0.059896 0.039063 -0.067708 0.335938 0.135417 0.161458 0.161458 
+DEAL::0.006076 -0.001736 0.006076 -0.007813 -0.005208 -0.010417 -0.010417 -0.010417 -0.002604 0.002604 -0.013021 0.010417 0.013021 0.041667 -0.018229 0.026042 -0.057292 0.010417 -0.020833 0.020833 
+DEAL::
+DEAL::Child: 7
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::0.007812 0.007812 -0.015625 -0.015625 -0.070312 -0.070313 -0.070312 0.070313 0.070312 -0.070312 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.000000 0.000000 0.000000 0.140625 0.140625 
+DEAL::0.007812 -0.015625 0.007812 -0.015625 -0.070312 0.070312 0.070312 -0.070312 -0.070312 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070312 0.000000 0.140625 0.000000 0.140625 
+DEAL::-0.062500 -0.023437 -0.023437 -0.023438 0.140625 -0.070313 -0.035156 -0.035156 -0.070313 0.140625 0.140625 -0.070312 -0.035156 -0.035156 -0.035156 -0.035156 -0.210937 -0.210937 -0.210937 -0.421875 
+DEAL::0.004340 0.004340 -0.005208 0.006944 0.018229 0.018229 0.018229 -0.007812 -0.007812 0.018229 0.002604 -0.023438 0.002604 -0.023438 0.015625 0.000000 0.072917 -0.020833 0.015625 0.015625 
+DEAL::0.001736 0.001736 -0.010417 0.012153 -0.006510 -0.006510 0.001302 0.027344 0.027344 0.001302 -0.002604 -0.023438 -0.002604 -0.023438 0.015625 -0.015625 0.091146 -0.026042 0.031250 0.031250 
+DEAL::0.016493 -0.003472 0.004340 -0.012153 0.054687 -0.018229 -0.002604 -0.013021 -0.028646 0.039063 0.007812 0.007813 0.005208 0.031250 0.002604 0.023438 -0.093750 -0.057292 -0.083333 -0.046875 
+DEAL::0.016493 0.004340 -0.003472 -0.012153 0.039062 -0.028646 -0.013021 -0.002604 -0.018229 0.054688 0.007812 0.007813 0.002604 0.023438 0.005208 0.031250 -0.093750 -0.083333 -0.057292 -0.046875 
+DEAL::0.001736 -0.010417 0.001736 0.012153 0.001302 0.027344 0.027344 0.001302 -0.006510 -0.006510 -0.002604 -0.023438 0.015625 -0.015625 -0.002604 -0.023438 0.091146 0.031250 -0.026042 0.031250 
+DEAL::0.004340 -0.005208 0.004340 0.006944 0.018229 -0.007812 -0.007812 0.018229 0.018229 0.018229 0.002604 -0.023438 0.015625 0.000000 0.002604 -0.023438 0.072917 0.015625 -0.020833 0.015625 
+DEAL::-0.006944 0.000868 0.000868 0.028646 0.002604 0.026042 0.022135 0.022135 0.026042 0.002604 0.010417 -0.013021 -0.001302 -0.001302 -0.001302 -0.001302 0.049479 -0.059896 -0.059896 -0.067708 
+DEAL::-0.006944 0.005208 0.005208 0.022569 0.040365 -0.006510 -0.014323 -0.014323 -0.006510 0.040365 0.005208 0.005208 -0.033854 0.059896 -0.033854 0.059896 0.044271 -0.010417 -0.010417 -0.026042 
+DEAL::-0.003472 0.004340 0.000868 0.000868 -0.031250 0.101562 0.074219 -0.040365 -0.005208 -0.007812 -0.007813 -0.005208 0.074219 -0.040365 0.014323 0.014323 -0.101563 -0.101562 -0.138021 -0.114583 
+DEAL::0.009549 0.000868 0.000000 0.000000 -0.070313 0.101563 0.117187 -0.049479 -0.002604 -0.023438 -0.023438 -0.002604 0.117187 -0.049479 -0.010417 -0.010417 -0.062500 -0.062500 -0.119792 -0.026042 
+DEAL::-0.003472 0.000868 0.004340 0.000868 -0.007813 -0.005208 -0.040365 0.074219 0.101563 -0.031250 -0.007813 -0.005208 0.014323 0.014323 0.074219 -0.040365 -0.101562 -0.138021 -0.101562 -0.114583 
+DEAL::0.009549 0.000000 0.000868 0.000000 -0.023438 -0.002604 -0.049479 0.117188 0.101563 -0.070313 -0.023438 -0.002604 -0.010417 -0.010417 0.117188 -0.049479 -0.062500 -0.119792 -0.062500 -0.026042 
+DEAL::-0.001736 -0.000868 -0.000868 -0.001736 -0.018229 0.010417 0.006510 0.006510 0.010417 -0.018229 -0.002604 0.007813 0.006510 0.003906 0.006510 0.003906 -0.065104 -0.044271 -0.044271 -0.031250 
+DEAL::0.006076 -0.001736 0.006076 -0.007813 -0.010417 -0.010417 -0.010417 -0.005208 0.002604 -0.002604 -0.018229 0.026042 0.013021 0.041667 -0.013021 0.010417 -0.057292 0.020833 -0.020833 0.010417 
+DEAL::0.006076 0.006076 -0.001736 -0.007813 -0.002604 0.002604 -0.005208 -0.010417 -0.010417 -0.010417 -0.018229 0.026042 -0.013021 0.010417 0.013021 0.041667 -0.057292 -0.020833 0.020833 0.010417 
+DEAL::0.008681 0.013889 0.013889 0.039063 0.035156 0.009115 0.016927 0.016927 0.009115 0.035156 0.039063 -0.067708 0.005208 -0.059896 0.005208 -0.059896 0.335938 0.161458 0.161458 0.135417 
+DEAL::
+DEAL::Refinement Direction: 3
+DEAL::Child: 0
+DEAL::0.031250 0.070313 0.070313 0.070313 0.703125 -0.351563 -0.105469 -0.105469 -0.351563 0.703125 0.703125 -0.351563 -0.105469 -0.105469 -0.105469 -0.105469 0.351563 0.351563 0.351563 -0.281250 
+DEAL::0.000000 -0.015625 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 -0.035156 -0.035156 0.140625 0.140625 -0.070312 0.140625 
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+DEAL::0.003472 -0.002604 -0.002604 0.007813 -0.019531 0.003906 0.027344 0.027344 0.003906 -0.019531 -0.007812 0.015625 -0.007813 -0.007813 -0.007812 -0.007813 0.070313 -0.015625 -0.015625 0.031250 
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+DEAL::
+DEAL::Child: 1
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+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070312 0.140625 0.140625 0.140625 
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+DEAL::-0.005208 0.017361 0.046875 0.046875 0.265625 0.046875 0.019531 -0.121094 -0.164063 0.210938 0.210938 -0.164062 0.019531 -0.121094 -0.050781 -0.050781 0.343750 0.343750 0.109375 -0.101562 
+DEAL::0.046875 0.017361 -0.005208 0.046875 -0.121094 0.019531 0.046875 0.265625 0.210937 -0.164062 -0.050781 -0.050781 0.019531 -0.121094 0.210937 -0.164062 0.343750 -0.101562 0.109375 0.343750 
+DEAL::0.007812 0.003472 0.018229 0.007812 0.015625 -0.007813 -0.031250 0.101562 0.058594 -0.035156 0.019531 0.019531 -0.007813 0.015625 0.058594 -0.035156 -0.039063 0.007813 -0.062500 -0.039063 
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+DEAL::0.000000 0.000000 -0.005208 0.005208 -0.035156 -0.035156 -0.011719 0.035156 0.035156 -0.011719 -0.023437 0.023437 -0.023437 0.023437 0.000000 -0.015625 0.070313 0.000000 0.046875 0.046875 
+DEAL::0.000000 0.000000 0.005208 -0.005208 -0.035156 -0.035156 -0.023437 0.023437 0.023437 -0.023437 -0.011719 0.035156 -0.011719 0.035156 -0.015625 0.000000 0.000000 0.070313 0.046875 0.046875 
+DEAL::-0.002604 0.003472 -0.002604 0.007813 0.003906 -0.019531 -0.019531 0.003906 0.027344 0.027344 -0.007812 -0.007813 -0.007812 0.015625 -0.007812 -0.007813 0.070313 -0.015625 0.031250 -0.015625 
+DEAL::-0.002604 0.003472 0.007813 -0.002604 0.003906 -0.019531 -0.007813 0.015625 -0.007813 -0.007812 0.027344 0.027344 -0.019531 0.003906 -0.007813 -0.007812 -0.015625 0.070313 0.031250 -0.015625 
+DEAL::0.005208 0.000000 0.005208 0.005208 0.023438 -0.023437 -0.023437 0.023437 0.003906 0.003906 0.003906 0.003906 -0.023437 0.023438 0.003906 0.003906 0.023438 0.023438 0.015625 0.023438 
+DEAL::0.007813 0.003472 -0.002604 -0.002604 0.015625 -0.007812 -0.019531 0.003906 -0.007813 -0.007813 -0.007813 -0.007812 -0.019531 0.003906 0.027344 0.027344 -0.015625 -0.015625 0.031250 0.070312 
+DEAL::
+DEAL::Child: 2
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+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070312 0.140625 0.140625 0.140625 
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+DEAL::0.007812 0.018229 0.003472 0.007812 -0.035156 0.058594 0.101562 -0.031250 -0.007813 0.015625 0.019531 0.019531 0.058594 -0.035156 -0.007813 0.015625 -0.039063 -0.062500 0.007813 -0.039063 
+DEAL::0.046875 -0.005208 0.017361 0.046875 -0.164062 0.210937 0.265625 0.046875 0.019531 -0.121094 -0.050781 -0.050781 0.210938 -0.164062 0.019531 -0.121094 0.343750 0.109375 -0.101562 0.343750 
+DEAL::-0.005208 0.046875 0.017361 0.046875 0.210938 -0.164063 -0.121094 0.019531 0.046875 0.265625 0.210938 -0.164062 -0.050781 -0.050781 0.019531 -0.121094 0.343750 0.109375 0.343750 -0.101562 
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+DEAL::0.000000 -0.005208 0.000000 0.005208 -0.011719 0.035156 0.035156 -0.011719 -0.035156 -0.035156 -0.023437 0.023438 0.000000 -0.015625 -0.023438 0.023437 0.070313 0.046875 0.000000 0.046875 
+DEAL::0.000000 0.005208 0.000000 -0.005208 -0.023437 0.023438 0.023438 -0.023438 -0.035156 -0.035156 -0.011719 0.035156 -0.015625 0.000000 -0.011719 0.035156 0.000000 0.046875 0.070313 0.046875 
+DEAL::0.046875 0.046875 0.017361 -0.005208 -0.050781 -0.050781 -0.121094 0.019531 0.019531 -0.121094 -0.164063 0.210937 -0.164063 0.210937 0.046875 0.265625 -0.101562 0.109375 0.343750 0.343750 
+DEAL::0.007812 0.007812 0.003472 0.018229 0.019531 0.019531 0.015625 -0.007813 -0.007813 0.015625 -0.035156 0.058594 -0.035156 0.058594 -0.031250 0.101563 0.007813 -0.062500 -0.039062 -0.039062 
+DEAL::-0.002604 -0.002604 0.003472 0.007813 0.027344 0.027344 0.003906 -0.019531 -0.019531 0.003906 -0.007812 -0.007813 -0.007812 -0.007813 -0.007813 0.015625 0.070313 0.031250 -0.015625 -0.015625 
+DEAL::0.005208 0.005208 0.000000 0.005208 0.003906 0.003906 0.023437 -0.023437 -0.023437 0.023437 0.003906 0.003906 0.003906 0.003906 -0.023437 0.023437 0.023438 0.015625 0.023438 0.023438 
+DEAL::-0.002604 0.007813 0.003472 -0.002604 -0.007812 -0.007813 0.015625 -0.007813 -0.019531 0.003906 0.027344 0.027344 -0.007813 -0.007813 -0.019531 0.003906 -0.015625 0.031250 0.070313 -0.015625 
+DEAL::0.007813 -0.002604 0.003472 -0.002604 -0.007813 -0.007813 0.003906 -0.019531 -0.007813 0.015625 -0.007813 -0.007812 0.027344 0.027344 -0.019531 0.003906 -0.015625 0.031250 -0.015625 0.070313 
+DEAL::
+DEAL::Child: 3
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+DEAL::0.000000 0.000000 -0.015625 0.000000 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.140625 -0.070312 0.140625 0.140625 
+DEAL::0.070313 0.070313 0.070313 0.031250 -0.105469 -0.105469 -0.105469 -0.105469 -0.105469 -0.105469 -0.351562 0.703125 -0.351563 0.703125 -0.351563 0.703125 -0.281250 0.351563 0.351563 0.351563 
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+DEAL::0.005208 -0.005208 0.000000 0.000000 -0.015625 0.000000 0.035156 -0.011719 -0.023437 0.023437 0.023437 -0.023437 0.035156 -0.011719 -0.035156 -0.035156 0.046875 0.046875 0.000000 0.070313 
+DEAL::0.000000 -0.005208 0.005208 0.000000 -0.011719 0.035156 0.000000 -0.015625 0.023437 -0.023437 -0.035156 -0.035156 0.035156 -0.011719 0.023437 -0.023437 0.046875 0.070313 0.000000 0.046875 
+DEAL::0.000000 0.005208 -0.005208 0.000000 -0.023437 0.023437 -0.015625 0.000000 0.035156 -0.011719 -0.035156 -0.035156 0.023437 -0.023437 0.035156 -0.011719 0.046875 0.000000 0.070313 0.046875 
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+DEAL::-0.005208 0.000000 0.005208 0.000000 0.035156 -0.011719 -0.023437 0.023438 -0.015625 0.000000 0.035156 -0.011719 -0.035156 -0.035156 0.023438 -0.023438 0.046875 0.070313 0.046875 0.000000 
+DEAL::0.018229 0.007812 0.007812 0.003472 0.058594 -0.035156 0.019531 0.019531 -0.035156 0.058594 0.101562 -0.031250 0.015625 -0.007813 0.015625 -0.007813 -0.062500 -0.039063 -0.039063 0.007813 
+DEAL::-0.005208 0.046875 0.046875 0.017361 0.210938 -0.164063 -0.050781 -0.050781 -0.164062 0.210937 0.265625 0.046875 -0.121094 0.019531 -0.121094 0.019531 0.109375 0.343750 0.343750 -0.101562 
+DEAL::0.007812 0.018229 0.007812 0.003472 -0.035156 0.058594 0.058594 -0.035156 0.019531 0.019531 0.015625 -0.007813 0.101562 -0.031250 0.015625 -0.007813 -0.062500 -0.039063 0.007813 -0.039062 
+DEAL::0.046875 -0.005208 0.046875 0.017361 -0.164062 0.210938 0.210938 -0.164063 -0.050781 -0.050781 -0.121094 0.019531 0.265625 0.046875 -0.121094 0.019531 0.109375 0.343750 -0.101562 0.343750 
+DEAL::0.007812 0.007813 0.018229 0.003472 0.019531 0.019531 -0.035156 0.058594 0.058594 -0.035156 0.015625 -0.007813 0.015625 -0.007813 0.101563 -0.031250 -0.062500 0.007813 -0.039062 -0.039062 
+DEAL::0.046875 0.046875 -0.005208 0.017361 -0.050781 -0.050781 -0.164063 0.210938 0.210938 -0.164063 -0.121094 0.019531 -0.121094 0.019531 0.265625 0.046875 0.109375 -0.101562 0.343750 0.343750 
+DEAL::0.005208 0.005208 0.005208 0.000000 0.003906 0.003906 0.003906 0.003906 0.003906 0.003906 0.023438 -0.023438 0.023437 -0.023437 0.023438 -0.023437 0.015625 0.023437 0.023437 0.023437 
+DEAL::-0.002604 -0.002604 0.007813 0.003472 0.027344 0.027344 -0.007813 -0.007813 -0.007813 -0.007813 0.003906 -0.019531 0.003906 -0.019531 0.015625 -0.007812 0.031250 0.070313 -0.015625 -0.015625 
+DEAL::-0.002604 0.007813 -0.002604 0.003472 -0.007812 -0.007813 -0.007813 -0.007813 0.027344 0.027344 0.003906 -0.019531 0.015625 -0.007812 0.003906 -0.019531 0.031250 -0.015625 0.070313 -0.015625 
+DEAL::0.007813 -0.002604 -0.002604 0.003472 -0.007813 -0.007812 0.027344 0.027344 -0.007812 -0.007813 0.015625 -0.007813 0.003906 -0.019531 0.003906 -0.019531 0.031250 -0.015625 -0.015625 0.070313 
+DEAL::
+DEAL::Child: 4
+DEAL::0.007812 -0.015625 0.007812 -0.015625 -0.070312 0.070313 0.070313 -0.070313 -0.070313 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070313 0.000000 0.140625 0.000000 0.140625 
+DEAL::0.007812 0.007812 -0.015625 -0.015625 -0.070312 -0.070313 -0.070312 0.070312 0.070312 -0.070312 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.000000 0.000000 0.000000 0.140625 0.140625 
+DEAL::-0.062500 -0.023437 -0.023437 -0.023438 0.140625 -0.070313 -0.035156 -0.035156 -0.070312 0.140625 0.140625 -0.070312 -0.035156 -0.035156 -0.035156 -0.035156 -0.210937 -0.210937 -0.210937 -0.421875 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::0.016493 0.004340 -0.003472 -0.012153 0.039062 -0.028646 -0.013021 -0.002604 -0.018229 0.054688 0.007812 0.007813 0.002604 0.023438 0.005208 0.031250 -0.093750 -0.083333 -0.057292 -0.046875 
+DEAL::0.016493 -0.003472 0.004340 -0.012153 0.054688 -0.018229 -0.002604 -0.013021 -0.028646 0.039063 0.007812 0.007813 0.005208 0.031250 0.002604 0.023438 -0.093750 -0.057292 -0.083333 -0.046875 
+DEAL::-0.003472 0.004340 0.000868 0.000868 -0.031250 0.101562 0.074219 -0.040365 -0.005208 -0.007812 -0.007812 -0.005208 0.074219 -0.040365 0.014323 0.014323 -0.101562 -0.101562 -0.138021 -0.114583 
+DEAL::0.009549 0.000868 0.000000 0.000000 -0.070313 0.101562 0.117187 -0.049479 -0.002604 -0.023438 -0.023438 -0.002604 0.117187 -0.049479 -0.010417 -0.010417 -0.062500 -0.062500 -0.119792 -0.026042 
+DEAL::0.009549 0.000000 0.000868 0.000000 -0.023437 -0.002604 -0.049479 0.117188 0.101563 -0.070312 -0.023438 -0.002604 -0.010417 -0.010417 0.117188 -0.049479 -0.062500 -0.119792 -0.062500 -0.026042 
+DEAL::-0.003472 0.000868 0.004340 0.000868 -0.007813 -0.005208 -0.040365 0.074219 0.101563 -0.031250 -0.007813 -0.005208 0.014323 0.014323 0.074219 -0.040365 -0.101563 -0.138021 -0.101563 -0.114583 
+DEAL::0.001736 -0.010417 0.001736 0.012153 0.001302 0.027344 0.027344 0.001302 -0.006510 -0.006510 -0.002604 -0.023438 0.015625 -0.015625 -0.002604 -0.023438 0.091146 0.031250 -0.026042 0.031250 
+DEAL::0.004340 -0.005208 0.004340 0.006944 0.018229 -0.007812 -0.007812 0.018229 0.018229 0.018229 0.002604 -0.023438 0.015625 0.000000 0.002604 -0.023438 0.072917 0.015625 -0.020833 0.015625 
+DEAL::0.001736 0.001736 -0.010417 0.012153 -0.006510 -0.006510 0.001302 0.027344 0.027344 0.001302 -0.002604 -0.023437 -0.002604 -0.023438 0.015625 -0.015625 0.091146 -0.026042 0.031250 0.031250 
+DEAL::0.004340 0.004340 -0.005208 0.006944 0.018229 0.018229 0.018229 -0.007813 -0.007813 0.018229 0.002604 -0.023438 0.002604 -0.023438 0.015625 0.000000 0.072917 -0.020833 0.015625 0.015625 
+DEAL::-0.006944 0.005208 0.005208 0.022569 0.040365 -0.006510 -0.014323 -0.014323 -0.006510 0.040365 0.005208 0.005208 -0.033854 0.059896 -0.033854 0.059896 0.044271 -0.010417 -0.010417 -0.026042 
+DEAL::-0.006944 0.000868 0.000868 0.028646 0.002604 0.026042 0.022135 0.022135 0.026042 0.002604 0.010417 -0.013021 -0.001302 -0.001302 -0.001302 -0.001302 0.049479 -0.059896 -0.059896 -0.067708 
+DEAL::0.008681 0.013889 0.013889 0.039063 0.035156 0.009115 0.016927 0.016927 0.009115 0.035156 0.039063 -0.067708 0.005208 -0.059896 0.005208 -0.059896 0.335938 0.161458 0.161458 0.135417 
+DEAL::-0.001736 -0.000868 -0.000868 -0.001736 -0.018229 0.010417 0.006510 0.006510 0.010417 -0.018229 -0.002604 0.007812 0.006510 0.003906 0.006510 0.003906 -0.065104 -0.044271 -0.044271 -0.031250 
+DEAL::0.006076 0.006076 -0.001736 -0.007813 -0.002604 0.002604 -0.005208 -0.010417 -0.010417 -0.010417 -0.018229 0.026042 -0.013021 0.010417 0.013021 0.041667 -0.057292 -0.020833 0.020833 0.010417 
+DEAL::0.006076 -0.001736 0.006076 -0.007813 -0.010417 -0.010417 -0.010417 -0.005208 0.002604 -0.002604 -0.018229 0.026042 0.013021 0.041667 -0.013021 0.010417 -0.057292 0.020833 -0.020833 0.010417 
+DEAL::
+DEAL::Child: 5
+DEAL::0.007812 0.007812 -0.015625 -0.015625 -0.070313 -0.070312 -0.070312 0.070313 0.070313 -0.070312 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.000000 0.000000 0.000000 0.140625 0.140625 
+DEAL::0.007812 -0.015625 0.007812 -0.015625 -0.070312 0.070312 0.070312 -0.070312 -0.070313 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070312 0.000000 0.140625 0.000000 0.140625 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::-0.062500 -0.023437 -0.023437 -0.023438 0.140625 -0.070312 -0.035156 -0.035156 -0.070313 0.140625 0.140625 -0.070312 -0.035156 -0.035156 -0.035156 -0.035156 -0.210937 -0.210937 -0.210937 -0.421875 
+DEAL::0.016493 -0.003472 0.004340 -0.012153 0.054688 -0.018229 -0.002604 -0.013021 -0.028646 0.039063 0.007812 0.007813 0.005208 0.031250 0.002604 0.023438 -0.093750 -0.057292 -0.083333 -0.046875 
+DEAL::0.016493 0.004340 -0.003472 -0.012153 0.039062 -0.028646 -0.013021 -0.002604 -0.018229 0.054688 0.007812 0.007813 0.002604 0.023438 0.005208 0.031250 -0.093750 -0.083333 -0.057292 -0.046875 
+DEAL::0.001736 -0.010417 0.001736 0.012153 0.001302 0.027344 0.027344 0.001302 -0.006510 -0.006510 -0.002604 -0.023437 0.015625 -0.015625 -0.002604 -0.023438 0.091146 0.031250 -0.026042 0.031250 
+DEAL::0.004340 -0.005208 0.004340 0.006944 0.018229 -0.007813 -0.007812 0.018229 0.018229 0.018229 0.002604 -0.023438 0.015625 0.000000 0.002604 -0.023438 0.072917 0.015625 -0.020833 0.015625 
+DEAL::0.004340 0.004340 -0.005208 0.006944 0.018229 0.018229 0.018229 -0.007812 -0.007812 0.018229 0.002604 -0.023438 0.002604 -0.023438 0.015625 0.000000 0.072917 -0.020833 0.015625 0.015625 
+DEAL::0.001736 0.001736 -0.010417 0.012153 -0.006510 -0.006510 0.001302 0.027344 0.027344 0.001302 -0.002604 -0.023438 -0.002604 -0.023438 0.015625 -0.015625 0.091146 -0.026042 0.031250 0.031250 
+DEAL::-0.003472 0.004340 0.000868 0.000868 -0.031250 0.101563 0.074219 -0.040365 -0.005208 -0.007813 -0.007813 -0.005208 0.074219 -0.040365 0.014323 0.014323 -0.101563 -0.101562 -0.138021 -0.114583 
+DEAL::0.009549 0.000868 0.000000 0.000000 -0.070312 0.101562 0.117187 -0.049479 -0.002604 -0.023437 -0.023438 -0.002604 0.117187 -0.049479 -0.010417 -0.010417 -0.062500 -0.062500 -0.119792 -0.026042 
+DEAL::-0.003472 0.000868 0.004340 0.000868 -0.007812 -0.005208 -0.040365 0.074219 0.101563 -0.031250 -0.007813 -0.005208 0.014323 0.014323 0.074219 -0.040365 -0.101562 -0.138021 -0.101562 -0.114583 
+DEAL::0.009549 0.000000 0.000868 0.000000 -0.023438 -0.002604 -0.049479 0.117187 0.101563 -0.070312 -0.023438 -0.002604 -0.010417 -0.010417 0.117187 -0.049479 -0.062500 -0.119792 -0.062500 -0.026042 
+DEAL::-0.006944 0.000868 0.000868 0.028646 0.002604 0.026042 0.022135 0.022135 0.026042 0.002604 0.010417 -0.013021 -0.001302 -0.001302 -0.001302 -0.001302 0.049479 -0.059896 -0.059896 -0.067708 
+DEAL::-0.006944 0.005208 0.005208 0.022569 0.040365 -0.006510 -0.014323 -0.014323 -0.006510 0.040365 0.005208 0.005208 -0.033854 0.059896 -0.033854 0.059896 0.044271 -0.010417 -0.010417 -0.026042 
+DEAL::-0.001736 -0.000868 -0.000868 -0.001736 -0.018229 0.010417 0.006510 0.006510 0.010417 -0.018229 -0.002604 0.007812 0.006510 0.003906 0.006510 0.003906 -0.065104 -0.044271 -0.044271 -0.031250 
+DEAL::0.008681 0.013889 0.013889 0.039063 0.035156 0.009115 0.016927 0.016927 0.009115 0.035156 0.039063 -0.067708 0.005208 -0.059896 0.005208 -0.059896 0.335938 0.161458 0.161458 0.135417 
+DEAL::0.006076 -0.001736 0.006076 -0.007813 -0.010417 -0.010417 -0.010417 -0.005208 0.002604 -0.002604 -0.018229 0.026042 0.013021 0.041667 -0.013021 0.010417 -0.057292 0.020833 -0.020833 0.010417 
+DEAL::0.006076 0.006076 -0.001736 -0.007813 -0.002604 0.002604 -0.005208 -0.010417 -0.010417 -0.010417 -0.018229 0.026042 -0.013021 0.010417 0.013021 0.041667 -0.057292 -0.020833 0.020833 0.010417 
+DEAL::
+DEAL::Child: 6
+DEAL::-0.023438 -0.062500 -0.023438 -0.023438 -0.070312 0.140625 0.140625 -0.070312 -0.035156 -0.035156 -0.035156 -0.035156 0.140625 -0.070312 -0.035156 -0.035156 -0.210937 -0.210937 -0.421875 -0.210937 
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::0.007812 0.007812 -0.015625 -0.015625 -0.070312 -0.070312 -0.070312 0.070312 0.070312 -0.070312 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.000000 0.000000 0.000000 0.140625 0.140625 
+DEAL::-0.015625 0.007812 0.007813 -0.015625 0.070312 -0.070312 -0.070312 -0.070312 -0.070312 0.070312 0.000000 0.000000 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.140625 0.140625 0.000000 
+DEAL::0.005208 -0.006944 0.005208 0.022569 -0.006510 0.040365 0.040365 -0.006510 -0.014323 -0.014323 -0.033854 0.059896 0.005208 0.005208 -0.033854 0.059896 0.044271 -0.010417 -0.026042 -0.010417 
+DEAL::0.000868 -0.006944 0.000868 0.028646 0.026042 0.002604 0.002604 0.026042 0.022135 0.022135 -0.001302 -0.001302 0.010417 -0.013021 -0.001302 -0.001302 0.049479 -0.059896 -0.067708 -0.059896 
+DEAL::0.004340 0.004340 -0.005208 0.006944 0.018229 0.018229 0.018229 -0.007812 -0.007812 0.018229 0.002604 -0.023438 0.002604 -0.023438 0.015625 0.000000 0.072917 -0.020833 0.015625 0.015625 
+DEAL::0.001736 0.001736 -0.010417 0.012153 -0.006510 -0.006510 0.001302 0.027344 0.027344 0.001302 -0.002604 -0.023438 -0.002604 -0.023438 0.015625 -0.015625 0.091146 -0.026042 0.031250 0.031250 
+DEAL::0.004340 -0.003472 0.000868 0.000868 0.101563 -0.031250 -0.007813 -0.005208 -0.040365 0.074219 0.074219 -0.040365 -0.007813 -0.005208 0.014323 0.014323 -0.101563 -0.101562 -0.114583 -0.138021 
+DEAL::0.000868 0.009549 0.000000 0.000000 0.101563 -0.070313 -0.023438 -0.002604 -0.049479 0.117188 0.117188 -0.049479 -0.023438 -0.002604 -0.010417 -0.010417 -0.062500 -0.062500 -0.026042 -0.119792 
+DEAL::0.000000 0.009549 0.000868 0.000000 -0.002604 -0.023438 -0.070312 0.101562 0.117187 -0.049479 -0.010417 -0.010417 -0.023438 -0.002604 0.117187 -0.049479 -0.062500 -0.119792 -0.026042 -0.062500 
+DEAL::0.000868 -0.003472 0.004340 0.000868 -0.005208 -0.007813 -0.031250 0.101562 0.074219 -0.040365 0.014323 0.014323 -0.007813 -0.005208 0.074219 -0.040365 -0.101562 -0.138021 -0.114583 -0.101562 
+DEAL::-0.005208 0.004340 0.004340 0.006944 -0.007813 0.018229 0.018229 0.018229 0.018229 -0.007813 0.015625 0.000000 0.002604 -0.023438 0.002604 -0.023438 0.072917 0.015625 0.015625 -0.020833 
+DEAL::-0.010417 0.001736 0.001736 0.012153 0.027344 0.001302 -0.006510 -0.006510 0.001302 0.027344 0.015625 -0.015625 -0.002604 -0.023438 -0.002604 -0.023438 0.091146 0.031250 0.031250 -0.026042 
+DEAL::-0.003472 0.016493 0.004340 -0.012153 -0.018229 0.054688 0.039063 -0.028646 -0.013021 -0.002604 0.005208 0.031250 0.007812 0.007813 0.002604 0.023438 -0.093750 -0.057292 -0.046875 -0.083333 
+DEAL::0.004340 0.016493 -0.003472 -0.012153 -0.028646 0.039063 0.054688 -0.018229 -0.002604 -0.013021 0.002604 0.023438 0.007813 0.007813 0.005208 0.031250 -0.093750 -0.083333 -0.046875 -0.057292 
+DEAL::-0.001736 0.006076 0.006076 -0.007813 -0.010417 -0.010417 -0.002604 0.002604 -0.005208 -0.010417 0.013021 0.041667 -0.018229 0.026042 -0.013021 0.010417 -0.057292 0.020833 0.010417 -0.020833 
+DEAL::0.006076 0.006076 -0.001736 -0.007813 0.002604 -0.002604 -0.010417 -0.010417 -0.010417 -0.005208 -0.013021 0.010417 -0.018229 0.026042 0.013021 0.041667 -0.057292 -0.020833 0.010417 0.020833 
+DEAL::0.013889 0.008681 0.013889 0.039063 0.009115 0.035156 0.035156 0.009115 0.016927 0.016927 0.005208 -0.059896 0.039063 -0.067708 0.005208 -0.059896 0.335938 0.161458 0.135417 0.161458 
+DEAL::-0.000868 -0.001736 -0.000868 -0.001736 0.010417 -0.018229 -0.018229 0.010417 0.006510 0.006510 0.006510 0.003906 -0.002604 0.007813 0.006510 0.003906 -0.065104 -0.044271 -0.031250 -0.044271 
+DEAL::
+DEAL::Child: 7
+DEAL::0.000000 0.000000 0.000000 -0.015625 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 -0.035156 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070313 0.140625 0.140625 0.140625 
+DEAL::-0.023437 -0.023437 -0.062500 -0.023437 -0.035156 -0.035156 -0.070312 0.140625 0.140625 -0.070313 -0.035156 -0.035156 -0.035156 -0.035156 0.140625 -0.070312 -0.210937 -0.421875 -0.210937 -0.210937 
+DEAL::0.007812 -0.015625 0.007812 -0.015625 -0.070313 0.070312 0.070312 -0.070312 -0.070312 -0.070313 -0.070313 0.070312 0.000000 0.000000 -0.070312 0.070312 0.000000 0.140625 0.000000 0.140625 
+DEAL::-0.015625 0.007812 0.007812 -0.015625 0.070313 -0.070313 -0.070313 -0.070312 -0.070312 0.070313 0.000000 0.000000 -0.070312 0.070312 -0.070312 0.070312 0.000000 0.140625 0.140625 0.000000 
+DEAL::0.000868 0.000868 -0.006944 0.028646 0.022135 0.022135 0.026042 0.002604 0.002604 0.026042 -0.001302 -0.001302 -0.001302 -0.001302 0.010417 -0.013021 0.049479 -0.067708 -0.059896 -0.059896 
+DEAL::0.005208 0.005208 -0.006944 0.022569 -0.014323 -0.014323 -0.006510 0.040365 0.040365 -0.006510 -0.033854 0.059896 -0.033854 0.059896 0.005208 0.005208 0.044271 -0.026042 -0.010417 -0.010417 
+DEAL::0.000868 0.000000 0.009549 0.000000 0.117187 -0.049479 -0.002604 -0.023438 -0.070312 0.101562 0.117187 -0.049479 -0.010417 -0.010417 -0.023438 -0.002604 -0.062500 -0.026042 -0.062500 -0.119792 
+DEAL::0.004340 0.000868 -0.003472 0.000868 0.074219 -0.040365 -0.005208 -0.007813 -0.031250 0.101563 0.074219 -0.040365 0.014323 0.014323 -0.007813 -0.005208 -0.101562 -0.114583 -0.101562 -0.138021 
+DEAL::0.001736 -0.010417 0.001736 0.012153 0.001302 0.027344 0.027344 0.001302 -0.006510 -0.006510 -0.002604 -0.023438 0.015625 -0.015625 -0.002604 -0.023438 0.091146 0.031250 -0.026042 0.031250 
+DEAL::0.004340 -0.005208 0.004340 0.006944 0.018229 -0.007812 -0.007812 0.018229 0.018229 0.018229 0.002604 -0.023438 0.015625 0.000000 0.002604 -0.023438 0.072917 0.015625 -0.020833 0.015625 
+DEAL::-0.005208 0.004340 0.004340 0.006944 -0.007812 0.018229 0.018229 0.018229 0.018229 -0.007812 0.015625 0.000000 0.002604 -0.023438 0.002604 -0.023438 0.072917 0.015625 0.015625 -0.020833 
+DEAL::-0.010417 0.001736 0.001736 0.012153 0.027344 0.001302 -0.006510 -0.006510 0.001302 0.027344 0.015625 -0.015625 -0.002604 -0.023438 -0.002604 -0.023438 0.091146 0.031250 0.031250 -0.026042 
+DEAL::0.000000 0.000868 0.009549 0.000000 -0.049479 0.117187 0.101562 -0.070313 -0.023438 -0.002604 -0.010417 -0.010417 0.117187 -0.049479 -0.023438 -0.002604 -0.062500 -0.026042 -0.119792 -0.062500 
+DEAL::0.000868 0.004340 -0.003472 0.000868 -0.040365 0.074219 0.101563 -0.031250 -0.007813 -0.005208 0.014323 0.014323 0.074219 -0.040365 -0.007813 -0.005208 -0.101562 -0.114583 -0.138021 -0.101562 
+DEAL::-0.003472 0.004340 0.016493 -0.012153 -0.002604 -0.013021 -0.028646 0.039062 0.054688 -0.018229 0.005208 0.031250 0.002604 0.023438 0.007812 0.007813 -0.093750 -0.046875 -0.057292 -0.083333 
+DEAL::0.004340 -0.003472 0.016493 -0.012153 -0.013021 -0.002604 -0.018229 0.054688 0.039063 -0.028646 0.002604 0.023438 0.005208 0.031250 0.007813 0.007813 -0.093750 -0.046875 -0.083333 -0.057292 
+DEAL::-0.001736 0.006076 0.006076 -0.007813 -0.010417 -0.005208 0.002604 -0.002604 -0.010417 -0.010417 0.013021 0.041667 -0.013021 0.010417 -0.018229 0.026042 -0.057292 0.010417 0.020833 -0.020833 
+DEAL::0.006076 -0.001736 0.006076 -0.007813 -0.005208 -0.010417 -0.010417 -0.010417 -0.002604 0.002604 -0.013021 0.010417 0.013021 0.041667 -0.018229 0.026042 -0.057292 0.010417 -0.020833 0.020833 
+DEAL::-0.000868 -0.000868 -0.001736 -0.001736 0.006510 0.006510 0.010417 -0.018229 -0.018229 0.010417 0.006510 0.003906 0.006510 0.003906 -0.002604 0.007813 -0.065104 -0.031250 -0.044271 -0.044271 
+DEAL::0.013889 0.013889 0.008681 0.039063 0.016927 0.016927 0.009115 0.035156 0.035156 0.009115 0.005208 -0.059896 0.005208 -0.059896 0.039063 -0.067708 0.335938 0.135417 0.161458 0.161458 
+DEAL::

diff --git a/tests/fe/up_and_down_simplex.cc b/tests/fe/up_and_down_simplex.cc
new file mode 100644 (file)
index 0000000..f936958
--- /dev/null
+++ b/tests/fe/up_and_down_simplex.cc
@@ -0,0 +1,252 @@
+// ------------------------------------------------------------------------
+//
+// SPDX-License-Identifier: LGPL-2.1-or-later
+// Copyright (C) 2002 - 2024 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// Part of the source code is dual licensed under Apache-2.0 WITH
+// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
+// governing the source code and code contributions can be found in
+// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
+//
+// ------------------------------------------------------------------------
+
+// like fe/up_and_down test but use simplex elements instead
+// Restrict a vector to a coarse grid and prolongate it again,
+// repeat the procedure twice and check if the reslting vectors are the same
+// i.e. if prolongation and restriction are successful.
+
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/dofs/dof_accessor.h>
+
+#include <deal.II/fe/fe_simplex_p.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_iterator.h>
+
+#include <deal.II/lac/vector.h>
+
+#include <string>
+#include <vector>
+
+#include "../tests.h"
+
+#define PRECISION 3
+
+
+template <int dim>
+Point<dim>
+transform(const Point<dim> p)
+{
+  switch (dim)
+    {
+      case 1:
+        return p;
+      case 2:
+        return Point<dim>(p[0] * (1 + p[1]), p[1] * (1 + p[0]));
+      case 3:
+        return Point<dim>(p[0] * (1 + p[1]) * (1 + p[2]),
+                          p[1] * (1 + p[0]) * (1 + p[2]),
+                          p[2] * (1 + p[0]) * (1 + p[1]));
+      default:
+        DEAL_II_NOT_IMPLEMENTED();
+        return Point<dim>();
+    };
+}
+
+
+template <int dim>
+void
+check_element(const Triangulation<dim> &tr, const FiniteElement<dim> &fe)
+{
+  DoFHandler<dim> dof_handler(tr);
+  dof_handler.distribute_dofs(fe);
+
+  // create a mostly arbitrary
+  // function plus a trend on this
+  // grid
+  Vector<double> tmp(dof_handler.n_dofs());
+  // for (unsigned int i = 0; i < tmp.size(); ++i)
+  //   tmp(i) = i; //(i + 13*i%17);
+  for (const auto &cell : tr.cell_iterators())
+    for (const auto v : cell->vertex_indices())
+      {
+        const auto v_global = cell->vertex_index(v);
+        tmp(v_global)       = cell->vertex(v)(0) + cell->vertex(v)(1);
+        if (dim == 3)
+          tmp(v_global) = cell->vertex(v)(0) + cell->vertex(v)(2);
+      }
+
+
+  // restrict this function to the
+  // next coarser level and
+  // distribute it again to the
+  // higher level
+  Vector<double> x(tmp.size());
+  Vector<double> v(fe.dofs_per_cell);
+  for (typename DoFHandler<dim>::cell_iterator cell = dof_handler.begin();
+       cell != dof_handler.end();
+       ++cell)
+    if (cell->has_children() && cell->child(0)->is_active())
+      {
+        // first make sure that what
+        // we do is reasonable. for
+        // this, _all_ children have
+        // to be active, not only
+        // some of them
+        for (unsigned int c = 0; c < GeometryInfo<dim>::max_children_per_cell;
+             ++c)
+          AssertThrow(cell->child(c)->is_active(), ExcInternalError());
+
+        // then restrict and prolongate
+        cell->get_interpolated_dof_values(tmp, v);
+        cell->set_dof_values_by_interpolation(v, x);
+      };
+
+  // now x is a function on the fine
+  // grid that is representable on
+  // the coarse grid. so another
+  // cycle should not alter it any
+  // more:
+  Vector<double> x2(x.size());
+  for (typename DoFHandler<dim>::cell_iterator cell = dof_handler.begin();
+       cell != dof_handler.end();
+       ++cell)
+    if (cell->has_children() && cell->child(0)->is_active())
+      {
+        cell->get_interpolated_dof_values(x, v);
+        cell->set_dof_values_by_interpolation(v, x2);
+      };
+
+  // then check that this is so:
+  x2 -= x;
+  const double relative_residual = (x2.l2_norm() / x.l2_norm());
+
+  const double threshold = 1e-6;
+  deallog << ", dofs_per_cell=" << fe.dofs_per_cell
+          << "; relative residual: " << relative_residual << " "
+          << (relative_residual < threshold ? "ok" : "botched up!")
+          << std::endl;
+
+  // TODO:[WB] Why this exception with a value different from above. Output of
+  // the error should be sufficient!
+  //  Assert (relative_residual < threshold*x.l2_norm(), ExcInternalError());
+}
+
+
+template <int dim>
+void
+test()
+{
+  // make a coarse triangulation as a
+  // hypercube. if in more than 1d,
+  // distort it so that it is no more
+  // an affine image of the
+  // hypercube, to make things more
+  // difficult. then refine it twice
+  Triangulation<dim> temp, tr;
+  GridGenerator::hyper_cube(temp, 0., 1.);
+  Point<dim> (*p)(Point<dim>) = &transform<dim>;
+  GridTools::transform(p, temp);
+  GridGenerator::convert_hypercube_to_simplex_mesh(temp, tr);
+
+  tr.refine_global(2);
+
+  // now for a list of finite
+  // elements, for which we want to
+  // test. we happily waste tons of
+  // memory here, but who cares...
+  const FiniteElement<dim> *fe_list[] = {
+    // first for some scalar
+    // elements:
+
+    // FE_SimplexP
+    new FE_SimplexP<dim>(1),
+    new FE_SimplexP<dim>(2),
+    new FE_SimplexP<dim>(3),
+    new FE_SimplexDGP<dim>(1),
+    new FE_SimplexDGP<dim>(2),
+    new FE_SimplexDGP<dim>(3),
+
+    // some composed elements
+    // of increasing
+    // complexity, to check the
+    // logics by which the
+    // matrices of the composed
+    // elements are assembled
+    // from those of the base
+    // elements. note that some
+    // of the base elements are
+    // additive, some not, so
+    // the result will be an
+    // element that is mixed in
+    // this respect
+
+    new FESystem<dim>(FE_SimplexP<dim>(2), 2),
+    new FESystem<dim>(FE_SimplexP<dim>(1), 2, FE_SimplexDGP<dim>(2), 2),
+    new FESystem<dim>(FE_SimplexP<dim>(1),
+                      2,
+                      FE_SimplexDGP<dim>(2),
+                      2,
+                      FE_SimplexDGP<dim>(0),
+                      1),
+    new FESystem<dim>(FE_SimplexP<dim>(1),
+                      2,
+                      FESystem<dim>(FE_SimplexP<dim>(1),
+                                    2,
+                                    FE_SimplexDGP<dim>(2),
+                                    2,
+                                    FE_SimplexDGP<dim>(2),
+                                    1),
+                      2,
+                      FE_SimplexDGP<dim>(0),
+                      1),
+    new FESystem<dim>(FE_SimplexP<dim>(1),
+                      2,
+                      FESystem<dim>(FE_SimplexP<dim>(1),
+                                    2,
+                                    FE_SimplexDGP<dim>(2),
+                                    2,
+                                    FESystem<dim>(FE_SimplexDGP<dim>(0), 3),
+                                    1),
+                      2,
+                      FE_SimplexDGP<dim>(0),
+                      1),
+
+
+  };
+
+  for (unsigned int i = 0; i < sizeof(fe_list) / sizeof(fe_list[0]); ++i)
+    if (fe_list[i] != nullptr)
+      {
+        deallog << dim << "d, uniform grid, fe #" << i;
+        check_element(tr, *fe_list[i]);
+      }
+
+
+  for (unsigned int i = 0; i < sizeof(fe_list) / sizeof(fe_list[0]); ++i)
+    if (fe_list[i] != nullptr)
+      delete fe_list[i];
+}
+
+
+
+int
+main()
+{
+  std::ofstream logfile("output");
+  deallog << std::setprecision(PRECISION);
+  deallog << std::fixed;
+  deallog.attach(logfile);
+
+  test<2>();
+  test<3>();
+
+  return 0;
+}

diff --git a/tests/fe/up_and_down_simplex.output b/tests/fe/up_and_down_simplex.output
new file mode 100644 (file)
index 0000000..314e7c9
--- /dev/null
+++ b/tests/fe/up_and_down_simplex.output
@@ -0,0 +1,23 @@
+
+DEAL::2d, uniform grid, fe #0, dofs_per_cell=3; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #1, dofs_per_cell=6; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #2, dofs_per_cell=10; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #3, dofs_per_cell=3; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #4, dofs_per_cell=6; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #5, dofs_per_cell=10; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #6, dofs_per_cell=12; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #7, dofs_per_cell=18; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #8, dofs_per_cell=19; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #9, dofs_per_cell=55; relative residual: 0.000 ok
+DEAL::2d, uniform grid, fe #10, dofs_per_cell=49; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #0, dofs_per_cell=4; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #1, dofs_per_cell=10; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #2, dofs_per_cell=20; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #3, dofs_per_cell=4; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #4, dofs_per_cell=10; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #5, dofs_per_cell=20; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #6, dofs_per_cell=20; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #7, dofs_per_cell=28; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #8, dofs_per_cell=29; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #9, dofs_per_cell=85; relative residual: 0.000 ok
+DEAL::3d, uniform grid, fe #10, dofs_per_cell=71; relative residual: 0.000 ok

diff --git a/tests/multigrid-global-coarsening/mg_transfer_a_05.cc b/tests/multigrid-global-coarsening/mg_transfer_a_05.cc
index 81e54c34da1074ba34b3eb8b406fe0ae811f8b78..9a0c12784ef4e35dd920b4919c0eac617b443f0a 100644 (file)
--- a/tests/multigrid-global-coarsening/mg_transfer_a_05.cc
+++ b/tests/multigrid-global-coarsening/mg_transfer_a_05.cc
@@ -155,10 +155,14 @@ main(int argc, char **argv)
 
   // Functions::ConstantFunction<2, double> fu(1.);
   RightHandSideFunction<2> fu;
+  RightHandSideFunction<3> fu3;
 
   for (unsigned int i = 0; i <= 4; ++i)
     test<2, double>(i, fu, false);
 
   for (unsigned int i = 0; i <= 2; ++i)
     test<2, double>(i, fu, true);
+
+  for (unsigned int i = 1; i <= 2; ++i)
+    test<3, double>(i, fu3, true);
 }

diff --git a/tests/multigrid-global-coarsening/mg_transfer_a_05.with_p4est=true.mpirun=1.output b/tests/multigrid-global-coarsening/mg_transfer_a_05.with_p4est=true.mpirun=1.output
index 5c952a2813ba0ccbbb0b6910f9488f7610f33d17..121f421ecf81d8a1b8c5c69cdc17984b79388627 100644 (file)
--- a/tests/multigrid-global-coarsening/mg_transfer_a_05.with_p4est=true.mpirun=1.output
+++ b/tests/multigrid-global-coarsening/mg_transfer_a_05.with_p4est=true.mpirun=1.output
@@ -35,3 +35,15 @@ DEAL:0:CG<2>(2)<->CG<2>(2)::0.0000000 0.25000000 0.0000000 0.12500000 0.12500000
 DEAL:0:CG<2>(2)<->CG<2>(2)::10.451291
 DEAL:0:CG<2>(2)<->CG<2>(2)::0.0000000 0.25000000 0.0000000 0.12500000 0.12500000 0.0000000 0.50000000 0.25000000 0.37500000 0.37500000 0.25000000 0.0000000 0.12500000 0.12500000 0.0000000 0.75000000 0.50000000 0.62500000 0.62500000 0.50000000 1.0000000 0.75000000 0.87500000 0.87500000 0.75000000 0.50000000 0.62500000 0.62500000 0.50000000 0.25000000 0.0000000 0.12500000 0.12500000 0.0000000 0.25000000 0.37500000 0.37500000 0.25000000 0.0000000 0.12500000 0.12500000 0.0000000 0.37500000 0.37500000 0.25000000 1.0000000 0.75000000 1.0000000 0.87500000 0.87500000 1.0000000 0.50000000 0.75000000 0.62500000 0.62500000 0.75000000 1.0000000 0.87500000 0.87500000 1.0000000 0.25000000 0.50000000 0.37500000 0.37500000 0.50000000 0.12500000 0.25000000 0.37500000 0.50000000 0.75000000 1.0000000 0.87500000 0.87500000 1.0000000 0.62500000 0.75000000 0.87500000 1.0000000 0.62500000 0.62500000 0.75000000 
 DEAL:0:CG<2>(2)<->CG<2>(2)::-0.046875000 0.71875000 -0.18750000 0.84375000 1.2500000 0.18750000 1.3906250 0.50000000 2.7187500 3.7500000 2.5000000 -0.14062500 1.2500000 1.2500000 0.18750000 1.2968750 0.53125000 1.4375000 2.9062500 3.7500000 3.5625000 1.0312500 2.5000000 3.7500000 3.5625000 
+DEAL:0:CG<2>(1)<->CG<2>(1)::6.6283022
+DEAL:0:CG<2>(1)<->CG<2>(1)::0.0000000 0.50000000 0.0000000 0.0000000 1.0000000 0.50000000 0.50000000 0.0000000 0.0000000 0.0000000 0.50000000 0.50000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 0.50000000 0.50000000 1.0000000 1.0000000 0.0000000 0.0000000 0.50000000 0.0000000 
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+DEAL:0:CG<2>(1)<->CG<2>(1)::13.907302
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+DEAL:0:CG<2>(2)<->CG<2>(2)::15.262163
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