Enable VtkFlags::write_higher_order_cells for triangles

diff --git a/include/deal.II/numerics/data_out_dof_data.templates.h b/include/deal.II/numerics/data_out_dof_data.templates.h
index 9e56b71f62ecdfa66bb9d392dfc08b4f41bb0293..e666c5d7519d88bf292f42c4bec739e0caacb6ed 100644 (file)
--- a/include/deal.II/numerics/data_out_dof_data.templates.h
+++ b/include/deal.II/numerics/data_out_dof_data.templates.h
@@ -83,6 +83,121 @@ namespace internal
 
 
 
+    /**
+     * Generate evalution points on a simplex with arbitrary number of
+     * subdivisions.
+     */
+    template <int dim>
+    inline std::vector<Point<dim>>
+    generate_simplex_evaluation_points(const unsigned int n_subdivisions)
+    {
+      (void)n_subdivisions;
+
+      Assert(false, ExcNotImplemented());
+
+      return {};
+    }
+
+
+
+    /**
+     * Helper function to create evaluation points recursively with
+     * subdivisions=0,1,2 being the base case:
+     *                                        +
+     *                                        |\
+     *                            +           +-+
+     *                            |\          |\|\
+     *                  +         +-+         +-+-+
+     *                  |\        |\|\        |\|\|\
+     *          +       +-+       +-+-+       +-+-+-+
+     *          |\      |\|\      |\|\|\      |\|\|\|\
+     *    +     +-+     +-+-+     +-+-+-+     +-+-+-+-+
+     *
+     *    0      1        2          3            4
+     *    ^      ^                   |            |
+     *    |      |                   |            |
+     *    +--------------------------+            |
+     *           |                                |
+     *           +--------------------------------+
+     */
+    inline void
+    generate_simplex_evaluation_points_recursively(
+      const std::vector<Point<2>> &bounding_vertices,
+      const unsigned int           n_subdivisions,
+      std::vector<Point<2>> &      evaluation_points)
+    {
+      if (n_subdivisions == 0)
+        {
+          evaluation_points.push_back(bounding_vertices[0]);
+          return;
+        }
+
+      for (const auto &p : bounding_vertices)
+        evaluation_points.push_back(p);
+
+      if (n_subdivisions == 1)
+        return;
+
+      // Helper functions to create intermediate points between p0 and p1 with
+      // n_subdivisions. This function appends these new points to the vector
+      // evaluation_points but also returns the points as a vector to be able
+      // to easily access specific points on the line.
+      const auto generate_inbetween_points = [&](const Point<2> &p0,
+                                                 const Point<2> &p1) {
+        std::vector<Point<2>> line_points;
+
+        for (unsigned int i = 1; i < n_subdivisions; ++i)
+          line_points.push_back(p0 + (p1 - p0) / n_subdivisions * i);
+
+        evaluation_points.insert(evaluation_points.end(),
+                                 line_points.begin(),
+                                 line_points.end());
+
+        return line_points;
+      };
+
+      const auto line_points_0 =
+        generate_inbetween_points(bounding_vertices[0], bounding_vertices[1]);
+      const auto line_points_1 =
+        generate_inbetween_points(bounding_vertices[1], bounding_vertices[2]);
+      const auto line_points_2 =
+        generate_inbetween_points(bounding_vertices[2], bounding_vertices[0]);
+
+      if (n_subdivisions == 2)
+        return;
+
+      generate_simplex_evaluation_points_recursively(
+        // create new inner triangle (see ASCII art above)
+        {{Point<2>(line_points_0[line_points_0.size() - 2][0],
+                   line_points_1[0][1]),
+          Point<2>(line_points_0[0][0],
+                   line_points_1[line_points_1.size() - 2][1]),
+          Point<2>(line_points_0[0][0], line_points_1[0][1])}},
+        n_subdivisions - 3,
+        evaluation_points);
+    }
+
+
+
+    /**
+     * Specialization for triangles.
+     */
+    template <>
+    inline std::vector<Point<2>>
+    generate_simplex_evaluation_points(const unsigned int n_subdivisions)
+    {
+      std::vector<Point<2>> evalution_points;
+
+      generate_simplex_evaluation_points_recursively(
+        {{Point<2>(0.0, 0.0), Point<2>(1.0, 0.0), Point<2>(0.0, 1.0)}},
+        n_subdivisions,
+        evalution_points);
+
+      return evalution_points;
+    }
+
+
+
     /**
      * Set up vectors of FEValues and FEFaceValues needed inside of
      * ParallelDataBase and return the maximum number of quadrature points
@@ -140,9 +255,13 @@ namespace internal
 
           if (needs_simplex_setup)
             {
-              quadrature_simplex = std::make_unique<Quadrature<dim>>(
-                Simplex::FE_P<dim, spacedim>(n_subdivisions)
-                  .get_unit_support_points());
+              if (dim == 2)
+                quadrature_simplex = std::make_unique<Quadrature<dim>>(
+                  generate_simplex_evaluation_points<dim>(n_subdivisions));
+              else
+                quadrature_simplex = std::make_unique<Quadrature<dim>>(
+                  Simplex::FE_P<dim, spacedim>(n_subdivisions)
+                    .get_unit_support_points());
             }
 
           if (needs_hypercube_setup)

diff --git a/source/base/data_out_base.cc b/source/base/data_out_base.cc
index 66d97d7f2e2003bebe012f2ec7b04e4354134e04..0c129c598534498c879eb8aababaf28a625925cc 100644 (file)
--- a/source/base/data_out_base.cc
+++ b/source/base/data_out_base.cc
@@ -627,6 +627,11 @@ namespace
             vtk_cell_id[0] = cell_type_by_dim[dim];
             vtk_cell_id[1] = 1;
           }
+        else if (patch.reference_cell_type == ReferenceCell::Type::Tri)
+          {
+            vtk_cell_id[0] = VTK_LAGRANGE_TRIANGLE;
+            vtk_cell_id[1] = 1;
+          }
         else
           {
             Assert(false, ExcNotImplemented());
@@ -2730,36 +2735,54 @@ namespace DataOutBase
 
     for (const auto &patch : patches)
       {
-        const unsigned int n_subdivisions = patch.n_subdivisions;
-        const unsigned int n              = n_subdivisions + 1;
+        if (patch.reference_cell_type !=
+            ReferenceCell::Type::get_hypercube<dim>())
+          {
+            connectivity.resize(patch.data.n_cols());
 
-        cell_order.fill(n_subdivisions);
-        connectivity.resize(Utilities::fixed_power<dim>(n));
-
-        // Length of loops in all dimensons
-        const unsigned int n1 = (dim > 0) ? n_subdivisions : 0;
-        const unsigned int n2 = (dim > 1) ? n_subdivisions : 0;
-        const unsigned int n3 = (dim > 2) ? n_subdivisions : 0;
-        // Offsets of outer loops
-        const unsigned int d1 = 1;
-        const unsigned int d2 = n;
-        const unsigned int d3 = n * n;
-        for (unsigned int i3 = 0; i3 <= n3; ++i3)
-          for (unsigned int i2 = 0; i2 <= n2; ++i2)
-            for (unsigned int i1 = 0; i1 <= n1; ++i1)
-              {
-                const unsigned int local_index = i3 * d3 + i2 * d2 + i1 * d1;
-                const unsigned int connectivity_index =
-                  vtk_point_index_from_ijk(i1, i2, i3, cell_order);
-                connectivity[connectivity_index] = local_index;
-              }
+            for (unsigned int i = 0; i < patch.data.n_cols(); ++i)
+              connectivity[i] = i;
 
-        out.template write_high_order_cell<dim>(count++,
-                                                first_vertex_of_patch,
-                                                connectivity);
+            out.template write_high_order_cell<dim>(count++,
+                                                    first_vertex_of_patch,
+                                                    connectivity);
 
-        // finally update the number of the first vertex of this patch
-        first_vertex_of_patch += Utilities::fixed_power<dim>(n);
+            first_vertex_of_patch += patch.data.n_cols();
+          }
+        else
+          {
+            const unsigned int n_subdivisions = patch.n_subdivisions;
+            const unsigned int n              = n_subdivisions + 1;
+
+            cell_order.fill(n_subdivisions);
+            connectivity.resize(Utilities::fixed_power<dim>(n));
+
+            // Length of loops in all dimensons
+            const unsigned int n1 = (dim > 0) ? n_subdivisions : 0;
+            const unsigned int n2 = (dim > 1) ? n_subdivisions : 0;
+            const unsigned int n3 = (dim > 2) ? n_subdivisions : 0;
+            // Offsets of outer loops
+            const unsigned int d1 = 1;
+            const unsigned int d2 = n;
+            const unsigned int d3 = n * n;
+            for (unsigned int i3 = 0; i3 <= n3; ++i3)
+              for (unsigned int i2 = 0; i2 <= n2; ++i2)
+                for (unsigned int i1 = 0; i1 <= n1; ++i1)
+                  {
+                    const unsigned int local_index =
+                      i3 * d3 + i2 * d2 + i1 * d1;
+                    const unsigned int connectivity_index =
+                      vtk_point_index_from_ijk(i1, i2, i3, cell_order);
+                    connectivity[connectivity_index] = local_index;
+                  }
+
+            out.template write_high_order_cell<dim>(count++,
+                                                    first_vertex_of_patch,
+                                                    connectivity);
+
+            // finally update the number of the first vertex of this patch
+            first_vertex_of_patch += Utilities::fixed_power<dim>(n);
+          }
       }
 
     out.flush_cells();

diff --git a/tests/simplex/data_out_write_vtk_01.cc b/tests/simplex/data_out_write_vtk_01.cc
index 1e81b95402b23ebb12d5901d2c953e10519dd9da..0886b0fc426c7983e414a4cda9ebce92b423335c 100644 (file)
--- a/tests/simplex/data_out_write_vtk_01.cc
+++ b/tests/simplex/data_out_write_vtk_01.cc
@@ -54,7 +54,9 @@ public:
 
 template <int dim, int spacedim = dim>
 void
-test(const FiniteElement<dim, spacedim> &fe, const unsigned int n_components)
+test(const FiniteElement<dim, spacedim> &fe,
+     const unsigned int                  n_components,
+     const bool                          do_high_order)
 {
   Triangulation<dim, spacedim> tria;
   GridGenerator::subdivided_hyper_cube_with_simplices(tria, dim == 2 ? 4 : 2);
@@ -79,9 +81,15 @@ test(const FiniteElement<dim, spacedim> &fe, const unsigned int n_components)
 
   static unsigned int counter = 0;
 
-  for (unsigned int n_subdivisions = 1; n_subdivisions <= 2; ++n_subdivisions)
+  for (unsigned int n_subdivisions = 1;
+       n_subdivisions <= (do_high_order ? 3 : 2);
+       ++n_subdivisions)
     {
+      DataOutBase::VtkFlags flags;
+      flags.write_higher_order_cells = do_high_order;
+
       DataOut<dim> data_out;
+      data_out.set_flags(flags);
 
       data_out.attach_dof_handler(dof_handler);
       data_out.add_data_vector(solution, "solution");
@@ -90,8 +98,9 @@ test(const FiniteElement<dim, spacedim> &fe, const unsigned int n_components)
       data_out.build_patches(mapping, n_subdivisions);
 
 #if false
-  std::ofstream output("test." + std::to_string(dim) + "." + std::to_string(counter++) + ".vtk");
-  data_out.write_vtk(output);
+      std::ofstream output("test." + std::to_string(dim) + "." +
+                           std::to_string(counter++) + ".vtk");
+      data_out.write_vtk(output);
 #else
       data_out.write_vtk(deallog.get_file_stream());
 #endif
@@ -103,24 +112,39 @@ main()
 {
   initlog();
 
-  {
-    const unsigned int dim = 2;
-    test<dim>(Simplex::FE_P<dim>(2) /*=degree*/, 1);
-    test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/), dim), dim);
-    test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/),
-                            dim,
-                            Simplex::FE_P<dim>(1 /*=degree*/),
-                            1),
-              dim + 1);
-  }
-  {
-    const unsigned int dim = 3;
-    test<dim>(Simplex::FE_P<dim>(2) /*=degree*/, 1);
-    test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/), dim), dim);
-    test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/),
-                            dim,
-                            Simplex::FE_P<dim>(1 /*=degree*/),
-                            1),
-              dim + 1);
-  }
+  for (unsigned int i = 0; i < 2; ++i)
+    {
+      const bool do_high_order = (i == 1);
+
+      if (do_high_order)
+        {
+          const unsigned int dim = 2;
+          test<dim>(Simplex::FE_P<dim>(2) /*=degree*/, 1, do_high_order);
+          test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/), dim),
+                    dim,
+                    do_high_order);
+          test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/),
+                                  dim,
+                                  Simplex::FE_P<dim>(1 /*=degree*/),
+                                  1),
+                    dim + 1,
+                    do_high_order);
+        }
+
+      if (do_high_order ==
+          false /*TODO: higher-order output not working for 3D*/)
+        {
+          const unsigned int dim = 3;
+          test<dim>(Simplex::FE_P<dim>(2) /*=degree*/, 1, do_high_order);
+          test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/), dim),
+                    dim,
+                    do_high_order);
+          test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2 /*=degree*/),
+                                  dim,
+                                  Simplex::FE_P<dim>(1 /*=degree*/),
+                                  1),
+                    dim + 1,
+                    do_high_order);
+        }
+    }
 }

diff --git a/tests/simplex/data_out_write_vtk_01.with_simplex_support=on.output b/tests/simplex/data_out_write_vtk_01.with_simplex_support=on.output
index 019eb349536c686d5d3effe4319090c5bb8fad84..40bff84ef9f5a30e9df540af798ae0dc56726226 100644 (file)
--- a/tests/simplex/data_out_write_vtk_01.with_simplex_support=on.output
+++ b/tests/simplex/data_out_write_vtk_01.with_simplex_support=on.output
@@ -4,1170 +4,6 @@
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-
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-SCALARS solution_0 double 1
-LOOKUP_TABLE default
-5.57117e-14 0.0625000 -7.36861e-14 0.0156250 0.0156250 -8.25314e-13 0.0625000 -7.36861e-14 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.0625000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.250000 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 0.562500 1.00000 0.562500 1.00000 0.765625 0.765625 1.00000 -7.36861e-14 0.0625000 -1.31864e-13 0.0156250 0.0156250 1.57681e-13 0.0625000 -1.31864e-13 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.0625000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.250000 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 0.562500 1.00000 0.562500 1.00000 0.765625 0.765625 1.00000 -1.31864e-13 0.0625000 2.72472e-13 0.0156250 0.0156250 1.69792e-14 0.0625000 2.72472e-13 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.0625000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.250000 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 0.562500 1.00000 0.562500 1.00000 0.765625 0.765625 1.00000 2.72472e-13 0.0625000 -1.33077e-13 0.0156250 0.0156250 3.91329e-13 0.0625000 -1.33077e-13 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.0625000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.250000 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 0.562500 1.00000 0.562500 1.00000 0.765625 0.765625 1.00000 
-SCALARS solution_1 double 1
-LOOKUP_TABLE default
--4.51293e-14 -5.58317e-14 0.0625000 9.68227e-14 0.0156250 0.0156250 0.0625000 0.0625000 -5.58317e-14 0.0625000 0.0156250 0.0156250 -5.58317e-14 -3.57059e-13 0.0625000 -1.35346e-13 0.0156250 0.0156250 0.0625000 0.0625000 -3.57059e-13 0.0625000 0.0156250 0.0156250 -3.57059e-13 -1.01948e-13 0.0625000 2.51308e-13 0.0156250 0.0156250 0.0625000 0.0625000 -1.01948e-13 0.0625000 0.0156250 0.0156250 -1.01948e-13 2.58913e-13 0.0625000 1.44424e-13 0.0156250 0.0156250 0.0625000 0.0625000 2.58913e-13 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.250000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.250000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.250000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.250000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.562500 0.562500 0.250000 0.562500 0.390625 0.390625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.562500 0.562500 0.250000 0.562500 0.390625 0.390625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.562500 0.562500 0.250000 0.562500 0.390625 0.390625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.562500 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 1.00000 1.00000 0.562500 1.00000 0.765625 0.765625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 1.00000 1.00000 0.562500 1.00000 0.765625 0.765625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 1.00000 1.00000 0.562500 1.00000 0.765625 0.765625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 1.00000 1.00000 0.562500 1.00000 0.765625 0.765625 
-SCALARS solution_2 double 1
-LOOKUP_TABLE default
--0.00799710 0.0517471 -0.0107529 0.0218750 0.0204971 -0.00937500 0.0522153 -0.0107529 0.0517471 0.0207312 0.0204971 0.0519812 0.0517471 0.239590 0.0522153 0.145668 0.145903 0.0519812 0.239517 0.0522153 0.239590 0.145866 0.145903 0.239554 0.239590 0.552249 0.239517 0.395919 0.395883 0.239554 0.552254 0.239517 0.552249 0.395886 0.395883 0.552251 0.552249 0.988374 0.552254 0.770311 0.770314 0.552251 0.989749 0.552254 0.988374 0.771001 0.770314 0.989061 -0.0107529 0.0522153 -0.0104102 0.0207312 0.0209025 -0.0105816 0.0520174 -0.0104102 0.0522153 0.0208036 0.0209025 0.0521163 0.0522153 0.239517 0.0520174 0.145866 0.145767 0.0521163 0.239570 0.0520174 0.239517 0.145794 0.145767 0.239544 0.239517 0.552254 0.239570 0.395886 0.395912 0.239544 0.552017 0.239570 0.552254 0.395794 0.395912 0.552136 0.552254 0.989749 0.552017 0.771001 0.770883 0.552136 0.989590 0.552017 0.989749 0.770804 0.770883 0.989669 -0.0104102 0.0520174 -0.0102510 0.0208036 0.0208832 -0.0103306 0.0522539 -0.0102510 0.0520174 0.0210014 0.0208832 0.0521356 0.0520174 0.239570 0.0522539 0.145794 0.145912 0.0521356 0.239517 0.0522539 0.239570 0.145886 0.145912 0.239544 0.239570 0.552017 0.239517 0.395794 0.395767 0.239544 0.552215 0.239517 0.552017 0.395866 0.395767 0.552116 0.552017 0.989590 0.552215 0.770804 0.770903 0.552116 0.989247 0.552215 0.989590 0.770731 0.770903 0.989418 -0.0102510 0.0522539 -0.0116264 0.0210014 0.0203137 -0.0109387 0.0522490 -0.0116264 0.0522539 0.0203113 0.0203137 0.0522514 0.0522539 0.239517 0.0522490 0.145886 0.145883 0.0522514 0.239590 0.0522490 0.239517 0.145919 0.145883 0.239554 0.239517 0.552215 0.239590 0.395866 0.395903 0.239554 0.551747 0.239590 0.552215 0.395668 0.395903 0.551981 0.552215 0.989247 0.551747 0.770731 0.770497 0.551981 0.992003 0.551747 0.989247 0.771875 0.770497 0.990625 
-# vtk DataFile Version 3.0
-#This file was generated 
-ASCII
-DATASET UNSTRUCTURED_GRID
-
 POINTS 160 double
 0.00000 0.00000 0.00000
 0.500000 0.00000 0.00000
@@ -3146,60 +1982,2334 @@ POINTS 400 double
 1.00000 0.750000 0.750000
 0.750000 0.750000 1.00000
 
-CELLS 40 440
-       10      0       1       2       3       4       5       6       7       8       9
-       10      10      11      12      13      14      15      16      17      18      19
-       10      20      21      22      23      24      25      26      27      28      29
-       10      30      31      32      33      34      35      36      37      38      39
-       10      40      41      42      43      44      45      46      47      48      49
-       10      50      51      52      53      54      55      56      57      58      59
-       10      60      61      62      63      64      65      66      67      68      69
-       10      70      71      72      73      74      75      76      77      78      79
-       10      80      81      82      83      84      85      86      87      88      89
-       10      90      91      92      93      94      95      96      97      98      99
-       10      100     101     102     103     104     105     106     107     108     109
-       10      110     111     112     113     114     115     116     117     118     119
-       10      120     121     122     123     124     125     126     127     128     129
-       10      130     131     132     133     134     135     136     137     138     139
-       10      140     141     142     143     144     145     146     147     148     149
-       10      150     151     152     153     154     155     156     157     158     159
-       10      160     161     162     163     164     165     166     167     168     169
-       10      170     171     172     173     174     175     176     177     178     179
-       10      180     181     182     183     184     185     186     187     188     189
-       10      190     191     192     193     194     195     196     197     198     199
-       10      200     201     202     203     204     205     206     207     208     209
-       10      210     211     212     213     214     215     216     217     218     219
-       10      220     221     222     223     224     225     226     227     228     229
-       10      230     231     232     233     234     235     236     237     238     239
-       10      240     241     242     243     244     245     246     247     248     249
-       10      250     251     252     253     254     255     256     257     258     259
-       10      260     261     262     263     264     265     266     267     268     269
-       10      270     271     272     273     274     275     276     277     278     279
-       10      280     281     282     283     284     285     286     287     288     289
-       10      290     291     292     293     294     295     296     297     298     299
-       10      300     301     302     303     304     305     306     307     308     309
-       10      310     311     312     313     314     315     316     317     318     319
-       10      320     321     322     323     324     325     326     327     328     329
-       10      330     331     332     333     334     335     336     337     338     339
-       10      340     341     342     343     344     345     346     347     348     349
-       10      350     351     352     353     354     355     356     357     358     359
-       10      360     361     362     363     364     365     366     367     368     369
-       10      370     371     372     373     374     375     376     377     378     379
-       10      380     381     382     383     384     385     386     387     388     389
-       10      390     391     392     393     394     395     396     397     398     399
+CELLS 40 440
+       10      0       1       2       3       4       5       6       7       8       9
+       10      10      11      12      13      14      15      16      17      18      19
+       10      20      21      22      23      24      25      26      27      28      29
+       10      30      31      32      33      34      35      36      37      38      39
+       10      40      41      42      43      44      45      46      47      48      49
+       10      50      51      52      53      54      55      56      57      58      59
+       10      60      61      62      63      64      65      66      67      68      69
+       10      70      71      72      73      74      75      76      77      78      79
+       10      80      81      82      83      84      85      86      87      88      89
+       10      90      91      92      93      94      95      96      97      98      99
+       10      100     101     102     103     104     105     106     107     108     109
+       10      110     111     112     113     114     115     116     117     118     119
+       10      120     121     122     123     124     125     126     127     128     129
+       10      130     131     132     133     134     135     136     137     138     139
+       10      140     141     142     143     144     145     146     147     148     149
+       10      150     151     152     153     154     155     156     157     158     159
+       10      160     161     162     163     164     165     166     167     168     169
+       10      170     171     172     173     174     175     176     177     178     179
+       10      180     181     182     183     184     185     186     187     188     189
+       10      190     191     192     193     194     195     196     197     198     199
+       10      200     201     202     203     204     205     206     207     208     209
+       10      210     211     212     213     214     215     216     217     218     219
+       10      220     221     222     223     224     225     226     227     228     229
+       10      230     231     232     233     234     235     236     237     238     239
+       10      240     241     242     243     244     245     246     247     248     249
+       10      250     251     252     253     254     255     256     257     258     259
+       10      260     261     262     263     264     265     266     267     268     269
+       10      270     271     272     273     274     275     276     277     278     279
+       10      280     281     282     283     284     285     286     287     288     289
+       10      290     291     292     293     294     295     296     297     298     299
+       10      300     301     302     303     304     305     306     307     308     309
+       10      310     311     312     313     314     315     316     317     318     319
+       10      320     321     322     323     324     325     326     327     328     329
+       10      330     331     332     333     334     335     336     337     338     339
+       10      340     341     342     343     344     345     346     347     348     349
+       10      350     351     352     353     354     355     356     357     358     359
+       10      360     361     362     363     364     365     366     367     368     369
+       10      370     371     372     373     374     375     376     377     378     379
+       10      380     381     382     383     384     385     386     387     388     389
+       10      390     391     392     393     394     395     396     397     398     399
+
+CELL_TYPES 40
+ 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24
+POINT_DATA 400
+SCALARS solution_0 double 1
+LOOKUP_TABLE default
+2.52320e-12 0.250000 8.29592e-12 -8.81762e-12 0.0625000 0.0625000 -3.74580e-12 8.55571e-12 0.0625000 1.53004e-12 8.29592e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.250000 -8.81762e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 8.29592e-12 -8.81762e-12 0.250000 1.09453e-13 1.53004e-12 0.0625000 0.0625000 -5.01637e-13 1.96139e-12 0.0625000 0.250000 8.29592e-12 -8.81762e-12 0.250000 0.0625000 1.53004e-12 0.0625000 0.250000 0.0625000 0.0625000 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 1.00000 1.00000 0.250000 1.00000 1.00000 1.00000 0.562500 0.562500 0.562500 0.250000 1.00000 0.250000 1.00000 0.562500 0.562500 0.250000 0.562500 1.00000 0.562500 8.29592e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 8.29592e-12 0.250000 1.50595e-12 -6.97375e-12 0.0625000 0.0625000 -5.07973e-12 -1.80498e-12 0.0625000 1.02848e-11 8.29592e-12 1.09453e-13 0.250000 -6.97375e-12 -5.01637e-13 0.0625000 0.0625000 -1.80498e-12 2.70006e-12 0.0625000 0.250000 0.250000 0.250000 -6.97375e-12 0.250000 0.250000 0.250000 0.0625000 0.0625000 0.0625000 8.29592e-12 0.250000 -6.97375e-12 0.250000 0.0625000 0.0625000 -1.80498e-12 0.0625000 0.250000 0.0625000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 0.250000 0.250000 1.00000 0.562500 0.250000 0.562500 1.00000 0.562500 0.562500 -8.81762e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 -8.81762e-12 0.250000 1.09453e-13 2.21517e-12 0.0625000 0.0625000 1.96139e-12 8.13688e-13 0.0625000 -3.76789e-12 -8.81762e-12 8.68123e-12 0.250000 2.21517e-12 -1.33597e-13 0.0625000 0.0625000 8.13688e-13 -9.30839e-12 0.0625000 0.250000 0.250000 0.250000 2.21517e-12 0.250000 0.250000 0.250000 0.0625000 0.0625000 0.0625000 -8.81762e-12 0.250000 2.21517e-12 0.250000 0.0625000 0.0625000 8.13688e-13 0.0625000 0.250000 0.0625000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 0.250000 0.250000 1.00000 0.562500 0.250000 0.562500 1.00000 0.562500 0.562500 1.09453e-13 0.250000 -6.97375e-12 2.21517e-12 0.0625000 0.0625000 2.70006e-12 -3.76789e-12 0.0625000 2.34004e-12 -6.97375e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.250000 2.21517e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 -6.97375e-12 2.21517e-12 0.250000 1.04174e-11 2.34004e-12 0.0625000 0.0625000 -3.50647e-12 -6.11725e-12 0.0625000 0.250000 -6.97375e-12 2.21517e-12 0.250000 0.0625000 2.34004e-12 0.0625000 0.250000 0.0625000 0.0625000 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 1.00000 1.00000 0.250000 1.00000 1.00000 1.00000 0.562500 0.562500 0.562500 0.250000 1.00000 0.250000 1.00000 0.562500 0.562500 0.250000 0.562500 1.00000 0.562500 
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 SCALARS solution_0 double 1
 LOOKUP_TABLE default
-2.52320e-12 0.250000 8.29592e-12 -8.81762e-12 0.0625000 0.0625000 -3.74580e-12 8.55571e-12 0.0625000 1.53004e-12 8.29592e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.250000 -8.81762e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 8.29592e-12 -8.81762e-12 0.250000 1.09453e-13 1.53004e-12 0.0625000 0.0625000 -5.01637e-13 1.96139e-12 0.0625000 0.250000 8.29592e-12 -8.81762e-12 0.250000 0.0625000 1.53004e-12 0.0625000 0.250000 0.0625000 0.0625000 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 1.00000 1.00000 0.250000 1.00000 1.00000 1.00000 0.562500 0.562500 0.562500 0.250000 1.00000 0.250000 1.00000 0.562500 0.562500 0.250000 0.562500 1.00000 0.562500 8.29592e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 8.29592e-12 0.250000 1.50595e-12 -6.97375e-12 0.0625000 0.0625000 -5.07973e-12 -1.80498e-12 0.0625000 1.02848e-11 8.29592e-12 1.09453e-13 0.250000 -6.97375e-12 -5.01637e-13 0.0625000 0.0625000 -1.80498e-12 2.70006e-12 0.0625000 0.250000 0.250000 0.250000 -6.97375e-12 0.250000 0.250000 0.250000 0.0625000 0.0625000 0.0625000 8.29592e-12 0.250000 -6.97375e-12 0.250000 0.0625000 0.0625000 -1.80498e-12 0.0625000 0.250000 0.0625000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 0.250000 0.250000 1.00000 0.562500 0.250000 0.562500 1.00000 0.562500 0.562500 -8.81762e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 -8.81762e-12 0.250000 1.09453e-13 2.21517e-12 0.0625000 0.0625000 1.96139e-12 8.13688e-13 0.0625000 -3.76789e-12 -8.81762e-12 8.68123e-12 0.250000 2.21517e-12 -1.33597e-13 0.0625000 0.0625000 8.13688e-13 -9.30839e-12 0.0625000 0.250000 0.250000 0.250000 2.21517e-12 0.250000 0.250000 0.250000 0.0625000 0.0625000 0.0625000 -8.81762e-12 0.250000 2.21517e-12 0.250000 0.0625000 0.0625000 8.13688e-13 0.0625000 0.250000 0.0625000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 0.250000 0.250000 1.00000 0.562500 0.250000 0.562500 1.00000 0.562500 0.562500 1.09453e-13 0.250000 -6.97375e-12 2.21517e-12 0.0625000 0.0625000 2.70006e-12 -3.76789e-12 0.0625000 2.34004e-12 -6.97375e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.250000 2.21517e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 -6.97375e-12 2.21517e-12 0.250000 1.04174e-11 2.34004e-12 0.0625000 0.0625000 -3.50647e-12 -6.11725e-12 0.0625000 0.250000 -6.97375e-12 2.21517e-12 0.250000 0.0625000 2.34004e-12 0.0625000 0.250000 0.0625000 0.0625000 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 1.00000 1.00000 0.250000 1.00000 1.00000 1.00000 0.562500 0.562500 0.562500 0.250000 1.00000 0.250000 1.00000 0.562500 0.562500 0.250000 0.562500 1.00000 0.562500 
+5.57117e-14 0.0625000 -7.36861e-14 0.0156250 0.0156250 -8.25314e-13 0.0625000 -7.36861e-14 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.0625000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.250000 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 0.562500 1.00000 0.562500 1.00000 0.765625 0.765625 1.00000 -7.36861e-14 0.0625000 -1.31864e-13 0.0156250 0.0156250 1.57681e-13 0.0625000 -1.31864e-13 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.0625000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.250000 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 0.562500 1.00000 0.562500 1.00000 0.765625 0.765625 1.00000 -1.31864e-13 0.0625000 2.72472e-13 0.0156250 0.0156250 1.69792e-14 0.0625000 2.72472e-13 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.0625000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.250000 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 0.562500 1.00000 0.562500 1.00000 0.765625 0.765625 1.00000 2.72472e-13 0.0625000 -1.33077e-13 0.0156250 0.0156250 3.91329e-13 0.0625000 -1.33077e-13 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.0625000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.250000 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 0.562500 1.00000 0.562500 1.00000 0.765625 0.765625 1.00000 
 SCALARS solution_1 double 1
 LOOKUP_TABLE default
--6.15704e-12 2.75555e-12 0.250000 1.18796e-12 2.66194e-12 0.0625000 0.0625000 6.83915e-13 -7.22636e-13 0.0625000 0.250000 2.75555e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 2.75555e-12 1.18796e-12 -2.12860e-12 0.250000 -7.22636e-13 1.38545e-12 1.89303e-12 0.0625000 0.0625000 0.0625000 0.250000 1.18796e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 2.75555e-12 0.250000 1.18796e-12 0.250000 0.0625000 0.0625000 -7.22636e-13 0.0625000 0.250000 0.0625000 2.75555e-12 -3.07001e-12 0.250000 -3.50790e-12 4.07044e-13 0.0625000 0.0625000 1.46329e-12 -7.70037e-12 0.0625000 2.75555e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 2.75555e-12 -2.12860e-12 -3.50790e-12 0.250000 1.89303e-12 1.23869e-12 1.46329e-12 0.0625000 0.0625000 0.0625000 0.250000 -3.50790e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 2.75555e-12 0.250000 0.250000 -3.50790e-12 0.0625000 0.250000 0.0625000 1.46329e-12 0.0625000 0.0625000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 0.250000 0.250000 0.250000 1.00000 0.250000 0.250000 0.250000 0.562500 0.562500 0.562500 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 1.00000 1.00000 0.250000 0.562500 1.00000 0.562500 0.250000 0.562500 0.562500 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 0.250000 0.250000 1.00000 0.250000 0.250000 0.250000 0.562500 0.562500 0.562500 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 1.00000 0.250000 1.00000 0.562500 0.562500 0.250000 0.562500 1.00000 0.562500 1.18796e-12 -2.12860e-12 0.250000 7.67641e-12 1.38545e-12 0.0625000 0.0625000 -2.95827e-13 -2.65541e-12 0.0625000 1.18796e-12 0.250000 0.250000 0.250000 0.0625000 0.250000 0.0625000 0.0625000 0.250000 0.250000 1.18796e-12 8.84726e-12 7.67641e-12 0.250000 3.08472e-12 8.11914e-13 -2.95827e-13 0.0625000 0.0625000 0.0625000 0.250000 7.67641e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 1.18796e-12 0.250000 0.250000 7.67641e-12 0.0625000 0.250000 0.0625000 -2.95827e-13 0.0625000 0.0625000 -2.12860e-12 -3.50790e-12 0.250000 7.67641e-12 1.23869e-12 0.0625000 0.0625000 -2.65541e-12 1.03559e-12 0.0625000 0.250000 -3.50790e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 -3.50790e-12 7.67641e-12 -1.02481e-12 0.250000 1.03559e-12 -1.81834e-12 2.34645e-12 0.0625000 0.0625000 0.0625000 0.250000 7.67641e-12 0.250000 0.250000 0.0625000 0.0625000 0.250000 0.250000 0.0625000 0.250000 -3.50790e-12 0.250000 7.67641e-12 0.250000 0.0625000 0.0625000 1.03559e-12 0.0625000 0.250000 0.0625000 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 0.250000 0.250000 1.00000 0.250000 0.250000 0.250000 0.562500 0.562500 0.562500 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 1.00000 0.250000 1.00000 0.562500 0.562500 0.250000 0.562500 1.00000 0.562500 0.250000 0.250000 1.00000 0.250000 0.250000 0.562500 0.562500 0.250000 0.250000 0.562500 0.250000 1.00000 1.00000 1.00000 0.562500 1.00000 0.562500 0.562500 1.00000 1.00000 0.250000 0.250000 0.250000 1.00000 0.250000 0.250000 0.250000 0.562500 0.562500 0.562500 1.00000 0.250000 1.00000 1.00000 0.562500 0.562500 1.00000 1.00000 0.562500 1.00000 0.250000 1.00000 1.00000 0.250000 0.562500 1.00000 0.562500 0.250000 0.562500 0.562500 
+-4.51293e-14 -5.58317e-14 0.0625000 9.68227e-14 0.0156250 0.0156250 0.0625000 0.0625000 -5.58317e-14 0.0625000 0.0156250 0.0156250 -5.58317e-14 -3.57059e-13 0.0625000 -1.35346e-13 0.0156250 0.0156250 0.0625000 0.0625000 -3.57059e-13 0.0625000 0.0156250 0.0156250 -3.57059e-13 -1.01948e-13 0.0625000 2.51308e-13 0.0156250 0.0156250 0.0625000 0.0625000 -1.01948e-13 0.0625000 0.0156250 0.0156250 -1.01948e-13 2.58913e-13 0.0625000 1.44424e-13 0.0156250 0.0156250 0.0625000 0.0625000 2.58913e-13 0.0625000 0.0156250 0.0156250 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.250000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.250000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.250000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.0625000 0.0625000 0.250000 0.0625000 0.140625 0.140625 0.250000 0.250000 0.0625000 0.250000 0.140625 0.140625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.562500 0.562500 0.250000 0.562500 0.390625 0.390625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.562500 0.562500 0.250000 0.562500 0.390625 0.390625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.562500 0.562500 0.250000 0.562500 0.390625 0.390625 0.250000 0.250000 0.562500 0.250000 0.390625 0.390625 0.562500 0.562500 0.250000 0.562500 0.390625 0.390625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 1.00000 1.00000 0.562500 1.00000 0.765625 0.765625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 1.00000 1.00000 0.562500 1.00000 0.765625 0.765625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 1.00000 1.00000 0.562500 1.00000 0.765625 0.765625 0.562500 0.562500 1.00000 0.562500 0.765625 0.765625 1.00000 1.00000 0.562500 1.00000 0.765625 0.765625 
 SCALARS solution_2 double 1
 LOOKUP_TABLE default
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-SCALARS solution_3 double 1
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+SCALARS solution_0 double 1
 LOOKUP_TABLE default
--0.0119048 0.202381 -0.0476190 -0.0476190 0.0952381 0.0773810 -0.0297619 -0.0297619 0.0773810 -0.0476190 -0.0476190 0.202381 0.238095 0.202381 0.0773810 0.220238 0.0952381 0.0773810 0.202381 0.220238 0.202381 -0.0476190 0.238095 0.202381 0.0773810 0.0952381 0.220238 0.202381 0.0773810 0.220238 -0.0476190 -0.0476190 0.202381 -0.0119048 -0.0476190 0.0773810 0.0773810 -0.0297619 -0.0297619 0.0952381 0.202381 -0.0476190 -0.0476190 0.202381 0.0773810 -0.0476190 0.0773810 0.202381 0.0773810 0.0773810 0.202381 0.988095 0.952381 0.952381 0.595238 0.970238 0.577381 0.577381 0.970238 0.952381 0.202381 0.952381 0.238095 0.202381 0.577381 0.595238 0.220238 0.202381 0.577381 0.220238 0.202381 0.238095 0.952381 0.202381 0.220238 0.595238 0.577381 0.202381 0.220238 0.577381 0.952381 0.952381 0.988095 0.202381 0.952381 0.970238 0.970238 0.577381 0.577381 0.595238 0.202381 0.952381 0.202381 0.952381 0.577381 0.577381 0.202381 0.577381 0.952381 0.577381 -0.0476190 0.238095 0.202381 0.202381 0.0952381 0.220238 0.0773810 0.0773810 0.220238 0.202381 -0.0476190 0.202381 -0.0119048 -0.0476190 0.0773810 0.0952381 -0.0297619 -0.0476190 0.0773810 -0.0297619 -0.0476190 -0.0119048 0.202381 -0.0476190 -0.0297619 0.0952381 0.0773810 -0.0476190 -0.0297619 0.0773810 0.202381 0.202381 0.238095 -0.0476190 0.202381 0.220238 0.220238 0.0773810 0.0773810 0.0952381 -0.0476190 0.202381 -0.0476190 0.202381 0.0773810 0.0773810 -0.0476190 0.0773810 0.202381 0.0773810 0.238095 0.952381 0.202381 0.202381 0.595238 0.577381 0.220238 0.220238 0.577381 0.202381 0.202381 0.952381 0.988095 0.952381 0.577381 0.970238 0.595238 0.577381 0.952381 0.970238 0.952381 0.202381 0.988095 0.952381 0.577381 0.595238 0.970238 0.952381 0.577381 0.970238 0.202381 0.202381 0.952381 0.238095 0.202381 0.577381 0.577381 0.220238 0.220238 0.595238 0.952381 0.202381 0.202381 0.952381 0.577381 0.202381 0.577381 0.952381 0.577381 0.577381 -0.0476190 0.238095 0.202381 0.202381 0.0952381 0.220238 0.0773810 0.0773810 0.220238 0.202381 -0.0476190 0.202381 -0.0119048 -0.0476190 0.0773810 0.0952381 -0.0297619 -0.0476190 0.0773810 -0.0297619 -0.0476190 -0.0119048 0.202381 -0.0476190 -0.0297619 0.0952381 0.0773810 -0.0476190 -0.0297619 0.0773810 0.202381 0.202381 0.238095 -0.0476190 0.202381 0.220238 0.220238 0.0773810 0.0773810 0.0952381 -0.0476190 0.202381 -0.0476190 0.202381 0.0773810 0.0773810 -0.0476190 0.0773810 0.202381 0.0773810 0.238095 0.952381 0.202381 0.202381 0.595238 0.577381 0.220238 0.220238 0.577381 0.202381 0.202381 0.952381 0.988095 0.952381 0.577381 0.970238 0.595238 0.577381 0.952381 0.970238 0.952381 0.202381 0.988095 0.952381 0.577381 0.595238 0.970238 0.952381 0.577381 0.970238 0.202381 0.202381 0.952381 0.238095 0.202381 0.577381 0.577381 0.220238 0.220238 0.595238 0.952381 0.202381 0.202381 0.952381 0.577381 0.202381 0.577381 0.952381 0.577381 0.577381 -0.0119048 0.202381 -0.0476190 -0.0476190 0.0952381 0.0773810 -0.0297619 -0.0297619 0.0773810 -0.0476190 -0.0476190 0.202381 0.238095 0.202381 0.0773810 0.220238 0.0952381 0.0773810 0.202381 0.220238 0.202381 -0.0476190 0.238095 0.202381 0.0773810 0.0952381 0.220238 0.202381 0.0773810 0.220238 -0.0476190 -0.0476190 0.202381 -0.0119048 -0.0476190 0.0773810 0.0773810 -0.0297619 -0.0297619 0.0952381 0.202381 -0.0476190 -0.0476190 0.202381 0.0773810 -0.0476190 0.0773810 0.202381 0.0773810 0.0773810 0.202381 0.988095 0.952381 0.952381 0.595238 0.970238 0.577381 0.577381 0.970238 0.952381 0.202381 0.952381 0.238095 0.202381 0.577381 0.595238 0.220238 0.202381 0.577381 0.220238 0.202381 0.238095 0.952381 0.202381 0.220238 0.595238 0.577381 0.202381 0.220238 0.577381 0.952381 0.952381 0.988095 0.202381 0.952381 0.970238 0.970238 0.577381 0.577381 0.595238 0.202381 0.952381 0.202381 0.952381 0.577381 0.577381 0.202381 0.577381 0.952381 0.577381 
+5.57117e-14 0.0625000 -7.36861e-14 0.00694444 0.0277778 0.0277778 0.00694444 -7.56178e-13 -7.13045e-13 0.00694444 0.0625000 -7.36861e-14 0.0625000 0.0277778 0.00694444 0.00694444 0.0277778 0.0625000 0.0625000 0.0277778 0.0625000 0.250000 0.0625000 0.111111 0.173611 0.173611 0.111111 0.0625000 0.0625000 0.111111 0.250000 0.0625000 0.250000 0.173611 0.111111 0.111111 0.173611 0.250000 0.250000 0.173611 0.250000 0.562500 0.250000 0.340278 0.444444 0.444444 0.340278 0.250000 0.250000 0.340278 0.562500 0.250000 0.562500 0.444444 0.340278 0.340278 0.444444 0.562500 0.562500 0.444444 0.562500 1.00000 0.562500 0.694444 0.840278 0.840278 0.694444 0.562500 0.562500 0.694444 1.00000 0.562500 1.00000 0.840278 0.694444 0.694444 0.840278 1.00000 1.00000 0.840278 -7.36861e-14 0.0625000 -1.31864e-13 0.00694444 0.0277778 0.0277778 0.00694444 1.19045e-13 1.38437e-13 0.00694444 0.0625000 -1.31864e-13 0.0625000 0.0277778 0.00694444 0.00694444 0.0277778 0.0625000 0.0625000 0.0277778 0.0625000 0.250000 0.0625000 0.111111 0.173611 0.173611 0.111111 0.0625000 0.0625000 0.111111 0.250000 0.0625000 0.250000 0.173611 0.111111 0.111111 0.173611 0.250000 0.250000 0.173611 0.250000 0.562500 0.250000 0.340278 0.444444 0.444444 0.340278 0.250000 0.250000 0.340278 0.562500 0.250000 0.562500 0.444444 0.340278 0.340278 0.444444 0.562500 0.562500 0.444444 0.562500 1.00000 0.562500 0.694444 0.840278 0.840278 0.694444 0.562500 0.562500 0.694444 1.00000 0.562500 1.00000 0.840278 0.694444 0.694444 0.840278 1.00000 1.00000 0.840278 -1.31864e-13 0.0625000 2.72472e-13 0.00694444 0.0277778 0.0277778 0.00694444 9.02935e-14 -4.44852e-14 0.00694444 0.0625000 2.72472e-13 0.0625000 0.0277778 0.00694444 0.00694444 0.0277778 0.0625000 0.0625000 0.0277778 0.0625000 0.250000 0.0625000 0.111111 0.173611 0.173611 0.111111 0.0625000 0.0625000 0.111111 0.250000 0.0625000 0.250000 0.173611 0.111111 0.111111 0.173611 0.250000 0.250000 0.173611 0.250000 0.562500 0.250000 0.340278 0.444444 0.444444 0.340278 0.250000 0.250000 0.340278 0.562500 0.250000 0.562500 0.444444 0.340278 0.340278 0.444444 0.562500 0.562500 0.444444 0.562500 1.00000 0.562500 0.694444 0.840278 0.840278 0.694444 0.562500 0.562500 0.694444 1.00000 0.562500 1.00000 0.840278 0.694444 0.694444 0.840278 1.00000 1.00000 0.840278 2.72472e-13 0.0625000 -1.33077e-13 0.00694444 0.0277778 0.0277778 0.00694444 2.88000e-13 4.23183e-13 0.00694444 0.0625000 -1.33077e-13 0.0625000 0.0277778 0.00694444 0.00694444 0.0277778 0.0625000 0.0625000 0.0277778 0.0625000 0.250000 0.0625000 0.111111 0.173611 0.173611 0.111111 0.0625000 0.0625000 0.111111 0.250000 0.0625000 0.250000 0.173611 0.111111 0.111111 0.173611 0.250000 0.250000 0.173611 0.250000 0.562500 0.250000 0.340278 0.444444 0.444444 0.340278 0.250000 0.250000 0.340278 0.562500 0.250000 0.562500 0.444444 0.340278 0.340278 0.444444 0.562500 0.562500 0.444444 0.562500 1.00000 0.562500 0.694444 0.840278 0.840278 0.694444 0.562500 0.562500 0.694444 1.00000 0.562500 1.00000 0.840278 0.694444 0.694444 0.840278 1.00000 1.00000 0.840278 
+SCALARS solution_1 double 1
+LOOKUP_TABLE default
+-4.51293e-14 -5.58317e-14 0.0625000 8.22394e-14 7.86720e-14 0.00694444 0.0277778 0.0277778 0.00694444 0.00694444 0.0625000 0.0625000 -5.58317e-14 0.0625000 0.0625000 0.0277778 0.00694444 0.00694444 0.0277778 0.0277778 -5.58317e-14 -3.57059e-13 0.0625000 -9.30416e-14 -1.93451e-13 0.00694444 0.0277778 0.0277778 0.00694444 0.00694444 0.0625000 0.0625000 -3.57059e-13 0.0625000 0.0625000 0.0277778 0.00694444 0.00694444 0.0277778 0.0277778 -3.57059e-13 -1.01948e-13 0.0625000 1.55366e-13 2.40403e-13 0.00694444 0.0277778 0.0277778 0.00694444 0.00694444 0.0625000 0.0625000 -1.01948e-13 0.0625000 0.0625000 0.0277778 0.00694444 0.00694444 0.0277778 0.0277778 -1.01948e-13 2.58913e-13 0.0625000 7.69531e-14 1.97240e-13 0.00694444 0.0277778 0.0277778 0.00694444 0.00694444 0.0625000 0.0625000 2.58913e-13 0.0625000 0.0625000 0.0277778 0.00694444 0.00694444 0.0277778 0.0277778 0.0625000 0.0625000 0.250000 0.0625000 0.0625000 0.111111 0.173611 0.173611 0.111111 0.111111 0.250000 0.250000 0.0625000 0.250000 0.250000 0.173611 0.111111 0.111111 0.173611 0.173611 0.0625000 0.0625000 0.250000 0.0625000 0.0625000 0.111111 0.173611 0.173611 0.111111 0.111111 0.250000 0.250000 0.0625000 0.250000 0.250000 0.173611 0.111111 0.111111 0.173611 0.173611 0.0625000 0.0625000 0.250000 0.0625000 0.0625000 0.111111 0.173611 0.173611 0.111111 0.111111 0.250000 0.250000 0.0625000 0.250000 0.250000 0.173611 0.111111 0.111111 0.173611 0.173611 0.0625000 0.0625000 0.250000 0.0625000 0.0625000 0.111111 0.173611 0.173611 0.111111 0.111111 0.250000 0.250000 0.0625000 0.250000 0.250000 0.173611 0.111111 0.111111 0.173611 0.173611 0.250000 0.250000 0.562500 0.250000 0.250000 0.340278 0.444444 0.444444 0.340278 0.340278 0.562500 0.562500 0.250000 0.562500 0.562500 0.444444 0.340278 0.340278 0.444444 0.444444 0.250000 0.250000 0.562500 0.250000 0.250000 0.340278 0.444444 0.444444 0.340278 0.340278 0.562500 0.562500 0.250000 0.562500 0.562500 0.444444 0.340278 0.340278 0.444444 0.444444 0.250000 0.250000 0.562500 0.250000 0.250000 0.340278 0.444444 0.444444 0.340278 0.340278 0.562500 0.562500 0.250000 0.562500 0.562500 0.444444 0.340278 0.340278 0.444444 0.444444 0.250000 0.250000 0.562500 0.250000 0.250000 0.340278 0.444444 0.444444 0.340278 0.340278 0.562500 0.562500 0.250000 0.562500 0.562500 0.444444 0.340278 0.340278 0.444444 0.444444 0.562500 0.562500 1.00000 0.562500 0.562500 0.694444 0.840278 0.840278 0.694444 0.694444 1.00000 1.00000 0.562500 1.00000 1.00000 0.840278 0.694444 0.694444 0.840278 0.840278 0.562500 0.562500 1.00000 0.562500 0.562500 0.694444 0.840278 0.840278 0.694444 0.694444 1.00000 1.00000 0.562500 1.00000 1.00000 0.840278 0.694444 0.694444 0.840278 0.840278 0.562500 0.562500 1.00000 0.562500 0.562500 0.694444 0.840278 0.840278 0.694444 0.694444 1.00000 1.00000 0.562500 1.00000 1.00000 0.840278 0.694444 0.694444 0.840278 0.840278 0.562500 0.562500 1.00000 0.562500 0.562500 0.694444 0.840278 0.840278 0.694444 0.694444 1.00000 1.00000 0.562500 1.00000 1.00000 0.840278 0.694444 0.694444 0.840278 0.840278 
+SCALARS solution_2 double 1
+LOOKUP_TABLE default
+-0.00799710 0.0517471 -0.0107529 0.0119176 0.0318324 0.0309138 0.0100804 -0.00983430 -0.00891570 0.0109990 0.0522153 -0.0107529 0.0517471 0.0312259 0.0102365 0.0100804 0.0309138 0.0519032 0.0520592 0.0310698 0.0517471 0.239590 0.0522153 0.114361 0.176976 0.177132 0.114673 0.0520592 0.0519032 0.114517 0.239517 0.0522153 0.239590 0.177083 0.114649 0.114673 0.177132 0.239566 0.239542 0.177107 0.239590 0.552249 0.239517 0.343810 0.448029 0.448005 0.343761 0.239542 0.239566 0.343785 0.552254 0.239517 0.552249 0.448008 0.343763 0.343761 0.448005 0.552251 0.552252 0.448007 0.552249 0.988374 0.552254 0.697624 0.842999 0.843000 0.697627 0.552252 0.552251 0.697625 0.989749 0.552254 0.988374 0.843917 0.698086 0.697627 0.843000 0.988832 0.989291 0.843459 -0.0107529 0.0522153 -0.0104102 0.0102365 0.0312259 0.0313401 0.0104649 -0.0105245 -0.0106387 0.0103507 0.0520174 -0.0104102 0.0522153 0.0312082 0.0103990 0.0104649 0.0313401 0.0521493 0.0520833 0.0312741 0.0522153 0.239517 0.0520174 0.114649 0.177083 0.177017 0.114517 0.0520833 0.0521493 0.114583 0.239570 0.0520174 0.239517 0.177053 0.114535 0.114517 0.177017 0.239535 0.239553 0.177035 0.239517 0.552254 0.239570 0.343763 0.448008 0.448026 0.343798 0.239553 0.239535 0.343781 0.552017 0.239570 0.552254 0.447868 0.343719 0.343798 0.448026 0.552175 0.552096 0.447947 0.552254 0.989749 0.552017 0.698086 0.843917 0.843838 0.697928 0.552096 0.552175 0.698007 0.989590 0.552017 0.989749 0.843732 0.697875 0.697928 0.843838 0.989696 0.989643 0.843785 -0.0104102 0.0520174 -0.0102510 0.0103990 0.0312082 0.0312613 0.0105051 -0.0103041 -0.0103571 0.0104521 0.0522539 -0.0102510 0.0520174 0.0314189 0.0105840 0.0105051 0.0312613 0.0520962 0.0521750 0.0313401 0.0520174 0.239570 0.0522539 0.114535 0.177053 0.177132 0.114693 0.0521750 0.0520962 0.114614 0.239517 0.0522539 0.239570 0.177096 0.114675 0.114693 0.177132 0.239553 0.239535 0.177114 0.239570 0.552017 0.239517 0.343719 0.447868 0.447851 0.343684 0.239535 0.239553 0.343702 0.552215 0.239517 0.552017 0.447983 0.343750 0.343684 0.447851 0.552083 0.552149 0.447917 0.552017 0.989590 0.552215 0.697875 0.843732 0.843798 0.698007 0.552149 0.552083 0.697941 0.989247 0.552215 0.989590 0.843570 0.697893 0.698007 0.843798 0.989476 0.989361 0.843684 -0.0102510 0.0522539 -0.0116264 0.0105840 0.0314189 0.0309604 0.00966699 -0.0111680 -0.0107095 0.0101255 0.0522490 -0.0116264 0.0522539 0.0309572 0.00966538 0.00966699 0.0309604 0.0522523 0.0522506 0.0309588 0.0522539 0.239517 0.0522490 0.114675 0.177096 0.177095 0.114672 0.0522506 0.0522523 0.114673 0.239590 0.0522490 0.239517 0.177143 0.114696 0.114672 0.177095 0.239542 0.239566 0.177119 0.239517 0.552215 0.239590 0.343750 0.447983 0.448007 0.343798 0.239566 0.239542 0.343774 0.551747 0.239590 0.552215 0.447695 0.343642 0.343798 0.448007 0.552059 0.551903 0.447851 0.552215 0.989247 0.551747 0.697893 0.843570 0.843414 0.697580 0.551903 0.552059 0.697737 0.992003 0.551747 0.989247 0.845251 0.698499 0.697580 0.843414 0.990166 0.991084 0.844332 

diff --git a/tests/simplex/data_out_write_vtk_02.cc b/tests/simplex/data_out_write_vtk_02.cc
new file mode 100644 (file)
index 0000000..5e799a8
--- /dev/null
+++ b/tests/simplex/data_out_write_vtk_02.cc
@@ -0,0 +1,164 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+
+// Test DataOut::write_vtk() for simplex meshes.
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/mapping_fe.h>
+
+#include <deal.II/grid/grid_in.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include <deal.II/simplex/fe_lib.h>
+#include <deal.II/simplex/grid_generator.h>
+#include <deal.II/simplex/quadrature_lib.h>
+
+#include "../tests.h"
+
+#include "./simplex_grids.h"
+
+using namespace dealii;
+
+template <int dim>
+class RightHandSideFunction : public Function<dim>
+{
+public:
+  RightHandSideFunction(const unsigned int n_components)
+    : Function<dim>(n_components)
+  {}
+
+  virtual double
+  value(const Point<dim> &p, const unsigned int component = 0) const
+  {
+    return p[component % dim] * p[component % dim];
+  }
+};
+
+template <int dim, int spacedim = dim>
+void
+test(const FiniteElement<dim, spacedim> &fe_0,
+     const FiniteElement<dim, spacedim> &fe_1,
+     const unsigned int                  n_components,
+     const bool                          do_high_order)
+{
+  const unsigned int degree = fe_0.tensor_degree();
+
+  hp::FECollection<dim, spacedim> fe(fe_0, fe_1);
+
+  hp::QCollection<dim> quadrature(Simplex::QGauss<dim>(degree + 1),
+                                  QGauss<dim>(degree + 1));
+
+  hp::MappingCollection<dim, spacedim> mapping(
+    MappingFE<dim, spacedim>(Simplex::FE_P<dim, spacedim>(1)),
+    MappingQGeneric<dim, spacedim>(1));
+
+  Triangulation<dim, spacedim> tria;
+  GridGenerator::subdivided_hyper_cube_with_simplices_mix(tria,
+                                                          dim == 2 ? 4 : 2);
+
+  DoFHandler<dim> dof_handler(tria);
+
+  for (const auto &cell : dof_handler.active_cell_iterators())
+    {
+      if (cell->is_locally_owned() == false)
+        continue;
+
+      if (cell->reference_cell_type() == ReferenceCell::Type::Tri)
+        cell->set_active_fe_index(0);
+      else if (cell->reference_cell_type() == ReferenceCell::Type::Quad)
+        cell->set_active_fe_index(1);
+      else
+        Assert(false, ExcNotImplemented());
+    }
+
+  dof_handler.distribute_dofs(fe);
+
+  Vector<double> solution(dof_handler.n_dofs());
+
+  AffineConstraints<double> dummy;
+  dummy.close();
+
+  VectorTools::project(mapping,
+                       dof_handler,
+                       dummy,
+                       quadrature,
+                       RightHandSideFunction<dim>(n_components),
+                       solution);
+
+  static unsigned int counter = 0;
+
+  for (unsigned int n_subdivisions = 1;
+       n_subdivisions <= (do_high_order ? 4 : 2);
+       ++n_subdivisions)
+    {
+      DataOutBase::VtkFlags flags;
+      flags.write_higher_order_cells = do_high_order;
+
+      DataOut<dim> data_out;
+      data_out.set_flags(flags);
+
+      data_out.attach_dof_handler(dof_handler);
+      data_out.add_data_vector(solution, "solution");
+
+
+      data_out.build_patches(mapping, n_subdivisions);
+
+#if false
+      std::ofstream output("test." + std::to_string(dim) + "." +
+                           std::to_string(counter++) + ".vtk");
+      data_out.write_vtk(output);
+#else
+      data_out.write_vtk(deallog.get_file_stream());
+#endif
+    }
+}
+
+int
+main()
+{
+  initlog();
+
+  for (unsigned int i = 0; i < 2; ++i)
+    {
+      const bool do_high_order = (i == 1);
+
+      if (true)
+        {
+          const unsigned int dim = 2;
+          test<dim>(Simplex::FE_P<dim>(2), FE_Q<dim>(2), 1, do_high_order);
+
+          continue; // TODO
+
+          test<dim>(FESystem<dim>(Simplex::FE_P<dim>(2), dim),
+                    FESystem<dim>(FE_Q<dim>(2), dim),
+                    dim,
+                    do_high_order);
+          test<dim>(
+            FESystem<dim>(Simplex::FE_P<dim>(2), dim, Simplex::FE_P<dim>(1), 1),
+            FESystem<dim>(FE_Q<dim>(2), dim, FE_Q<dim>(1), 1),
+            dim + 1,
+            do_high_order);
+        }
+    }
+}

diff --git a/tests/simplex/data_out_write_vtk_02.with_simplex_support=on.output b/tests/simplex/data_out_write_vtk_02.with_simplex_support=on.output
new file mode 100644 (file)
index 0000000..1cd377b
--- /dev/null
+++ b/tests/simplex/data_out_write_vtk_02.with_simplex_support=on.output
@@ -0,0 +1,1571 @@
+
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