From: Wenyu Lei <wenyu.lei@sissa.it>
Date: Thu, 14 Jan 2021 00:15:20 +0000 (+0100)
Subject: added a test for compute_point_locations in simplex meshes
X-Git-Tag: v9.3.0-rc1~610^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=d8725052d2da7791b015a69fe00e519a1e23d16c;p=dealii.git

added a test for compute_point_locations in simplex meshes
---

diff --git a/tests/simplex/compute_point_locations_01.cc b/tests/simplex/compute_point_locations_01.cc
new file mode 100644
index 0000000000..66dc56cb39
--- /dev/null
+++ b/tests/simplex/compute_point_locations_01.cc
@@ -0,0 +1,105 @@
+// 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.
+//
+// ---------------------------------------------------------------------
+
+#include <deal.II/fe/fe_tools.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_fe.h>
+
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/grid/grid_tools_cache.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"
+
+// Create a simplex mesh in the unit cube. Check points distribute to each cell
+// via GridTools::compute_point_locations
+
+using namespace dealii;
+
+template <int dim>
+void
+test_in_unit_cube(const std::vector<Point<dim>> &points)
+{
+  Triangulation<dim> tria;
+  GridGenerator::subdivided_hyper_cube_with_simplices(tria, 1);
+
+  MappingFE<dim> mapping(Simplex::FE_P<dim>(1));
+
+  const auto tria_cache =
+    std::make_unique<GridTools::Cache<dim>>(tria, mapping);
+
+  const auto point_locations =
+    GridTools::compute_point_locations(*tria_cache, points);
+
+  const auto cells   = std::get<0>(point_locations);
+  const auto qpoints = std::get<1>(point_locations);
+  const auto indices = std::get<2>(point_locations);
+
+  deallog << "Print out results in " << dim << "D: " << std::endl;
+  for (unsigned int i = 0; i < cells.size(); ++i)
+    {
+      deallog << "At cell " << i << ":" << std::endl;
+      for (unsigned int j = 0; j < qpoints[i].size(); ++j)
+        {
+          deallog << "    qpoints " << j << ": " << std::endl;
+          deallog << "        reference position  : (" << qpoints[i][j] << ")"
+                  << std::endl;
+          deallog << "        physical position   : (" << points[indices[i][j]]
+                  << ")" << std::endl;
+          deallog << "        FE mapping position : ("
+                  << mapping.transform_unit_to_real_cell(cells[i],
+                                                         qpoints[i][j])
+                  << ")" << std::endl;
+        }
+    }
+  deallog << std::endl;
+}
+
+int
+main()
+{
+  initlog();
+
+  {
+    unsigned int          n = 3;
+    std::vector<Point<2>> test_points((n + 1) * (n + 1));
+    unsigned int          global_index = 0;
+    for (unsigned int i = 0; i < n + 1; ++i)
+      for (unsigned int j = 0; j < n + 1; ++j)
+        {
+          test_points[global_index][0] = (1.0 / n) * i;
+          test_points[global_index][1] = (1.0 / n) * j;
+          ++global_index;
+        }
+    test_in_unit_cube(test_points);
+  }
+
+  {
+    unsigned int          n = 3;
+    std::vector<Point<3>> test_points((n + 1) * (n + 1) * (n + 1));
+    unsigned int          global_index = 0;
+    for (unsigned int i = 0; i < n + 1; ++i)
+      for (unsigned int j = 0; j < n + 1; ++j)
+        for (unsigned int k = 0; k < n + 1; ++k)
+          {
+            test_points[global_index][0] = (1.0 / n) * i;
+            test_points[global_index][1] = (1.0 / n) * j;
+            test_points[global_index][2] = (1.0 / n) * k;
+            ++global_index;
+          }
+    test_in_unit_cube(test_points);
+  }
+}
diff --git a/tests/simplex/compute_point_locations_01.output b/tests/simplex/compute_point_locations_01.output
new file mode 100644
index 0000000000..087ff3025f
--- /dev/null
+++ b/tests/simplex/compute_point_locations_01.output
@@ -0,0 +1,332 @@
+
+DEAL::Print out results in 2D: 
+DEAL::At cell 0:
+DEAL::    qpoints 0: 
+DEAL::        reference position  : (0.00000 0.00000)
+DEAL::        physical position   : (0.00000 0.00000)
+DEAL::        FE mapping position : (0.00000 0.00000)
+DEAL::    qpoints 1: 
+DEAL::        reference position  : (0.00000 0.333333)
+DEAL::        physical position   : (0.00000 0.333333)
+DEAL::        FE mapping position : (0.00000 0.333333)
+DEAL::    qpoints 2: 
+DEAL::        reference position  : (0.00000 0.666667)
+DEAL::        physical position   : (0.00000 0.666667)
+DEAL::        FE mapping position : (0.00000 0.666667)
+DEAL::    qpoints 3: 
+DEAL::        reference position  : (0.00000 1.00000)
+DEAL::        physical position   : (0.00000 1.00000)
+DEAL::        FE mapping position : (0.00000 1.00000)
+DEAL::    qpoints 4: 
+DEAL::        reference position  : (0.333333 0.00000)
+DEAL::        physical position   : (0.333333 0.00000)
+DEAL::        FE mapping position : (0.333333 0.00000)
+DEAL::    qpoints 5: 
+DEAL::        reference position  : (0.333333 0.333333)
+DEAL::        physical position   : (0.333333 0.333333)
+DEAL::        FE mapping position : (0.333333 0.333333)
+DEAL::    qpoints 6: 
+DEAL::        reference position  : (0.333333 0.666667)
+DEAL::        physical position   : (0.333333 0.666667)
+DEAL::        FE mapping position : (0.333333 0.666667)
+DEAL::    qpoints 7: 
+DEAL::        reference position  : (0.666667 0.00000)
+DEAL::        physical position   : (0.666667 0.00000)
+DEAL::        FE mapping position : (0.666667 0.00000)
+DEAL::    qpoints 8: 
+DEAL::        reference position  : (0.666667 0.333333)
+DEAL::        physical position   : (0.666667 0.333333)
+DEAL::        FE mapping position : (0.666667 0.333333)
+DEAL::    qpoints 9: 
+DEAL::        reference position  : (1.00000 0.00000)
+DEAL::        physical position   : (1.00000 0.00000)
+DEAL::        FE mapping position : (1.00000 0.00000)
+DEAL::At cell 1:
+DEAL::    qpoints 0: 
+DEAL::        reference position  : (0.666667 0.00000)
+DEAL::        physical position   : (0.333333 1.00000)
+DEAL::        FE mapping position : (0.333333 1.00000)
+DEAL::    qpoints 1: 
+DEAL::        reference position  : (0.333333 0.333333)
+DEAL::        physical position   : (0.666667 0.666667)
+DEAL::        FE mapping position : (0.666667 0.666667)
+DEAL::    qpoints 2: 
+DEAL::        reference position  : (0.333333 0.00000)
+DEAL::        physical position   : (0.666667 1.00000)
+DEAL::        FE mapping position : (0.666667 1.00000)
+DEAL::    qpoints 3: 
+DEAL::        reference position  : (0.00000 0.666667)
+DEAL::        physical position   : (1.00000 0.333333)
+DEAL::        FE mapping position : (1.00000 0.333333)
+DEAL::    qpoints 4: 
+DEAL::        reference position  : (0.00000 0.333333)
+DEAL::        physical position   : (1.00000 0.666667)
+DEAL::        FE mapping position : (1.00000 0.666667)
+DEAL::    qpoints 5: 
+DEAL::        reference position  : (0.00000 0.00000)
+DEAL::        physical position   : (1.00000 1.00000)
+DEAL::        FE mapping position : (1.00000 1.00000)
+DEAL::
+DEAL::Print out results in 3D: 
+DEAL::At cell 0:
+DEAL::    qpoints 0: 
+DEAL::        reference position  : (0.00000 0.00000 0.00000)
+DEAL::        physical position   : (0.00000 0.00000 0.00000)
+DEAL::        FE mapping position : (0.00000 0.00000 0.00000)
+DEAL::    qpoints 1: 
+DEAL::        reference position  : (0.00000 0.00000 0.333333)
+DEAL::        physical position   : (0.00000 0.00000 0.333333)
+DEAL::        FE mapping position : (0.00000 0.00000 0.333333)
+DEAL::    qpoints 2: 
+DEAL::        reference position  : (0.00000 0.00000 0.666667)
+DEAL::        physical position   : (0.00000 0.00000 0.666667)
+DEAL::        FE mapping position : (0.00000 0.00000 0.666667)
+DEAL::    qpoints 3: 
+DEAL::        reference position  : (0.00000 0.00000 1.00000)
+DEAL::        physical position   : (0.00000 0.00000 1.00000)
+DEAL::        FE mapping position : (0.00000 0.00000 1.00000)
+DEAL::    qpoints 4: 
+DEAL::        reference position  : (0.00000 0.333333 0.00000)
+DEAL::        physical position   : (0.00000 0.333333 0.00000)
+DEAL::        FE mapping position : (0.00000 0.333333 0.00000)
+DEAL::    qpoints 5: 
+DEAL::        reference position  : (0.00000 0.333333 0.333333)
+DEAL::        physical position   : (0.00000 0.333333 0.333333)
+DEAL::        FE mapping position : (0.00000 0.333333 0.333333)
+DEAL::    qpoints 6: 
+DEAL::        reference position  : (0.00000 0.333333 0.666667)
+DEAL::        physical position   : (0.00000 0.333333 0.666667)
+DEAL::        FE mapping position : (0.00000 0.333333 0.666667)
+DEAL::    qpoints 7: 
+DEAL::        reference position  : (0.00000 0.666667 0.00000)
+DEAL::        physical position   : (0.00000 0.666667 0.00000)
+DEAL::        FE mapping position : (0.00000 0.666667 0.00000)
+DEAL::    qpoints 8: 
+DEAL::        reference position  : (0.00000 0.666667 0.333333)
+DEAL::        physical position   : (0.00000 0.666667 0.333333)
+DEAL::        FE mapping position : (0.00000 0.666667 0.333333)
+DEAL::    qpoints 9: 
+DEAL::        reference position  : (0.00000 1.00000 0.00000)
+DEAL::        physical position   : (0.00000 1.00000 0.00000)
+DEAL::        FE mapping position : (0.00000 1.00000 0.00000)
+DEAL::    qpoints 10: 
+DEAL::        reference position  : (0.333333 0.00000 0.00000)
+DEAL::        physical position   : (0.333333 0.00000 0.00000)
+DEAL::        FE mapping position : (0.333333 0.00000 0.00000)
+DEAL::    qpoints 11: 
+DEAL::        reference position  : (0.333333 0.00000 0.333333)
+DEAL::        physical position   : (0.333333 0.00000 0.333333)
+DEAL::        FE mapping position : (0.333333 0.00000 0.333333)
+DEAL::    qpoints 12: 
+DEAL::        reference position  : (0.333333 0.00000 0.666667)
+DEAL::        physical position   : (0.333333 0.00000 0.666667)
+DEAL::        FE mapping position : (0.333333 0.00000 0.666667)
+DEAL::    qpoints 13: 
+DEAL::        reference position  : (0.333333 0.333333 0.00000)
+DEAL::        physical position   : (0.333333 0.333333 0.00000)
+DEAL::        FE mapping position : (0.333333 0.333333 0.00000)
+DEAL::    qpoints 14: 
+DEAL::        reference position  : (0.333333 0.333333 0.333333)
+DEAL::        physical position   : (0.333333 0.333333 0.333333)
+DEAL::        FE mapping position : (0.333333 0.333333 0.333333)
+DEAL::    qpoints 15: 
+DEAL::        reference position  : (0.333333 0.666667 0.00000)
+DEAL::        physical position   : (0.333333 0.666667 0.00000)
+DEAL::        FE mapping position : (0.333333 0.666667 0.00000)
+DEAL::    qpoints 16: 
+DEAL::        reference position  : (0.666667 0.00000 0.00000)
+DEAL::        physical position   : (0.666667 0.00000 0.00000)
+DEAL::        FE mapping position : (0.666667 0.00000 0.00000)
+DEAL::    qpoints 17: 
+DEAL::        reference position  : (0.666667 0.00000 0.333333)
+DEAL::        physical position   : (0.666667 0.00000 0.333333)
+DEAL::        FE mapping position : (0.666667 0.00000 0.333333)
+DEAL::    qpoints 18: 
+DEAL::        reference position  : (0.666667 0.333333 0.00000)
+DEAL::        physical position   : (0.666667 0.333333 0.00000)
+DEAL::        FE mapping position : (0.666667 0.333333 0.00000)
+DEAL::    qpoints 19: 
+DEAL::        reference position  : (1.00000 0.00000 0.00000)
+DEAL::        physical position   : (1.00000 0.00000 0.00000)
+DEAL::        FE mapping position : (1.00000 0.00000 0.00000)
+DEAL::At cell 1:
+DEAL::    qpoints 0: 
+DEAL::        reference position  : (0.666667 0.00000 0.333333)
+DEAL::        physical position   : (0.00000 0.333333 1.00000)
+DEAL::        FE mapping position : (0.00000 0.333333 1.00000)
+DEAL::    qpoints 1: 
+DEAL::        reference position  : (0.333333 0.00000 0.333333)
+DEAL::        physical position   : (0.00000 0.666667 0.666667)
+DEAL::        FE mapping position : (0.00000 0.666667 0.666667)
+DEAL::    qpoints 2: 
+DEAL::        reference position  : (0.333333 0.00000 0.666667)
+DEAL::        physical position   : (0.00000 0.666667 1.00000)
+DEAL::        FE mapping position : (0.00000 0.666667 1.00000)
+DEAL::    qpoints 3: 
+DEAL::        reference position  : (0.00000 0.00000 0.333333)
+DEAL::        physical position   : (0.00000 1.00000 0.333333)
+DEAL::        FE mapping position : (0.00000 1.00000 0.333333)
+DEAL::    qpoints 4: 
+DEAL::        reference position  : (0.00000 0.00000 0.666667)
+DEAL::        physical position   : (0.00000 1.00000 0.666667)
+DEAL::        FE mapping position : (0.00000 1.00000 0.666667)
+DEAL::    qpoints 5: 
+DEAL::        reference position  : (0.00000 0.00000 1.00000)
+DEAL::        physical position   : (0.00000 1.00000 1.00000)
+DEAL::        FE mapping position : (0.00000 1.00000 1.00000)
+DEAL::    qpoints 6: 
+DEAL::        reference position  : (0.333333 0.333333 -5.55112e-17)
+DEAL::        physical position   : (0.333333 0.666667 0.666667)
+DEAL::        FE mapping position : (0.333333 0.666667 0.666667)
+DEAL::    qpoints 7: 
+DEAL::        reference position  : (0.333333 0.333333 0.333333)
+DEAL::        physical position   : (0.333333 0.666667 1.00000)
+DEAL::        FE mapping position : (0.333333 0.666667 1.00000)
+DEAL::    qpoints 8: 
+DEAL::        reference position  : (0.00000 0.333333 0.333333)
+DEAL::        physical position   : (0.333333 1.00000 0.666667)
+DEAL::        FE mapping position : (0.333333 1.00000 0.666667)
+DEAL::    qpoints 9: 
+DEAL::        reference position  : (0.00000 0.333333 0.666667)
+DEAL::        physical position   : (0.333333 1.00000 1.00000)
+DEAL::        FE mapping position : (0.333333 1.00000 1.00000)
+DEAL::    qpoints 10: 
+DEAL::        reference position  : (0.00000 0.666667 0.333333)
+DEAL::        physical position   : (0.666667 1.00000 1.00000)
+DEAL::        FE mapping position : (0.666667 1.00000 1.00000)
+DEAL::At cell 2:
+DEAL::    qpoints 0: 
+DEAL::        reference position  : (0.666667 0.333333 0.00000)
+DEAL::        physical position   : (0.333333 0.00000 1.00000)
+DEAL::        FE mapping position : (0.333333 0.00000 1.00000)
+DEAL::    qpoints 1: 
+DEAL::        reference position  : (0.666667 0.00000 0.333333)
+DEAL::        physical position   : (0.333333 0.333333 1.00000)
+DEAL::        FE mapping position : (0.333333 0.333333 1.00000)
+DEAL::    qpoints 2: 
+DEAL::        reference position  : (0.333333 0.333333 0.00000)
+DEAL::        physical position   : (0.666667 0.00000 0.666667)
+DEAL::        FE mapping position : (0.666667 0.00000 0.666667)
+DEAL::    qpoints 3: 
+DEAL::        reference position  : (0.333333 0.666667 0.00000)
+DEAL::        physical position   : (0.666667 0.00000 1.00000)
+DEAL::        FE mapping position : (0.666667 0.00000 1.00000)
+DEAL::    qpoints 4: 
+DEAL::        reference position  : (0.333333 -5.55112e-17 0.333333)
+DEAL::        physical position   : (0.666667 0.333333 0.666667)
+DEAL::        FE mapping position : (0.666667 0.333333 0.666667)
+DEAL::    qpoints 5: 
+DEAL::        reference position  : (0.333333 0.333333 0.333333)
+DEAL::        physical position   : (0.666667 0.333333 1.00000)
+DEAL::        FE mapping position : (0.666667 0.333333 1.00000)
+DEAL::    qpoints 6: 
+DEAL::        reference position  : (0.333333 0.00000 0.666667)
+DEAL::        physical position   : (0.666667 0.666667 1.00000)
+DEAL::        FE mapping position : (0.666667 0.666667 1.00000)
+DEAL::    qpoints 7: 
+DEAL::        reference position  : (0.00000 0.333333 0.00000)
+DEAL::        physical position   : (1.00000 0.00000 0.333333)
+DEAL::        FE mapping position : (1.00000 0.00000 0.333333)
+DEAL::    qpoints 8: 
+DEAL::        reference position  : (0.00000 0.666667 0.00000)
+DEAL::        physical position   : (1.00000 0.00000 0.666667)
+DEAL::        FE mapping position : (1.00000 0.00000 0.666667)
+DEAL::    qpoints 9: 
+DEAL::        reference position  : (0.00000 1.00000 0.00000)
+DEAL::        physical position   : (1.00000 0.00000 1.00000)
+DEAL::        FE mapping position : (1.00000 0.00000 1.00000)
+DEAL::    qpoints 10: 
+DEAL::        reference position  : (0.00000 0.333333 0.333333)
+DEAL::        physical position   : (1.00000 0.333333 0.666667)
+DEAL::        FE mapping position : (1.00000 0.333333 0.666667)
+DEAL::    qpoints 11: 
+DEAL::        reference position  : (0.00000 0.666667 0.333333)
+DEAL::        physical position   : (1.00000 0.333333 1.00000)
+DEAL::        FE mapping position : (1.00000 0.333333 1.00000)
+DEAL::    qpoints 12: 
+DEAL::        reference position  : (0.00000 0.333333 0.666667)
+DEAL::        physical position   : (1.00000 0.666667 1.00000)
+DEAL::        FE mapping position : (1.00000 0.666667 1.00000)
+DEAL::At cell 3:
+DEAL::    qpoints 0: 
+DEAL::        reference position  : (0.166667 0.500000 0.166667)
+DEAL::        physical position   : (0.333333 0.333333 0.666667)
+DEAL::        FE mapping position : (0.333333 0.333333 0.666667)
+DEAL::    qpoints 1: 
+DEAL::        reference position  : (0.500000 0.166667 0.166667)
+DEAL::        physical position   : (0.333333 0.666667 0.333333)
+DEAL::        FE mapping position : (0.333333 0.666667 0.333333)
+DEAL::    qpoints 2: 
+DEAL::        reference position  : (0.166667 0.166667 0.166667)
+DEAL::        physical position   : (0.666667 0.333333 0.333333)
+DEAL::        FE mapping position : (0.666667 0.333333 0.333333)
+DEAL::    qpoints 3: 
+DEAL::        reference position  : (0.166667 0.166667 0.500000)
+DEAL::        physical position   : (0.666667 0.666667 0.666667)
+DEAL::        FE mapping position : (0.666667 0.666667 0.666667)
+DEAL::At cell 4:
+DEAL::    qpoints 0: 
+DEAL::        reference position  : (0.00000 0.333333 0.00000)
+DEAL::        physical position   : (0.333333 1.00000 0.00000)
+DEAL::        FE mapping position : (0.333333 1.00000 0.00000)
+DEAL::    qpoints 1: 
+DEAL::        reference position  : (0.00000 0.00000 0.333333)
+DEAL::        physical position   : (0.333333 1.00000 0.333333)
+DEAL::        FE mapping position : (0.333333 1.00000 0.333333)
+DEAL::    qpoints 2: 
+DEAL::        reference position  : (0.333333 0.333333 0.00000)
+DEAL::        physical position   : (0.666667 0.666667 0.00000)
+DEAL::        FE mapping position : (0.666667 0.666667 0.00000)
+DEAL::    qpoints 3: 
+DEAL::        reference position  : (0.333333 -5.55112e-17 0.333333)
+DEAL::        physical position   : (0.666667 0.666667 0.333333)
+DEAL::        FE mapping position : (0.666667 0.666667 0.333333)
+DEAL::    qpoints 4: 
+DEAL::        reference position  : (0.00000 0.666667 0.00000)
+DEAL::        physical position   : (0.666667 1.00000 0.00000)
+DEAL::        FE mapping position : (0.666667 1.00000 0.00000)
+DEAL::    qpoints 5: 
+DEAL::        reference position  : (0.00000 0.333333 0.333333)
+DEAL::        physical position   : (0.666667 1.00000 0.333333)
+DEAL::        FE mapping position : (0.666667 1.00000 0.333333)
+DEAL::    qpoints 6: 
+DEAL::        reference position  : (0.00000 0.00000 0.666667)
+DEAL::        physical position   : (0.666667 1.00000 0.666667)
+DEAL::        FE mapping position : (0.666667 1.00000 0.666667)
+DEAL::    qpoints 7: 
+DEAL::        reference position  : (0.666667 0.333333 0.00000)
+DEAL::        physical position   : (1.00000 0.333333 0.00000)
+DEAL::        FE mapping position : (1.00000 0.333333 0.00000)
+DEAL::    qpoints 8: 
+DEAL::        reference position  : (0.666667 0.00000 0.333333)
+DEAL::        physical position   : (1.00000 0.333333 0.333333)
+DEAL::        FE mapping position : (1.00000 0.333333 0.333333)
+DEAL::    qpoints 9: 
+DEAL::        reference position  : (0.333333 0.666667 0.00000)
+DEAL::        physical position   : (1.00000 0.666667 0.00000)
+DEAL::        FE mapping position : (1.00000 0.666667 0.00000)
+DEAL::    qpoints 10: 
+DEAL::        reference position  : (0.333333 0.333333 0.333333)
+DEAL::        physical position   : (1.00000 0.666667 0.333333)
+DEAL::        FE mapping position : (1.00000 0.666667 0.333333)
+DEAL::    qpoints 11: 
+DEAL::        reference position  : (0.333333 0.00000 0.666667)
+DEAL::        physical position   : (1.00000 0.666667 0.666667)
+DEAL::        FE mapping position : (1.00000 0.666667 0.666667)
+DEAL::    qpoints 12: 
+DEAL::        reference position  : (0.00000 1.00000 0.00000)
+DEAL::        physical position   : (1.00000 1.00000 0.00000)
+DEAL::        FE mapping position : (1.00000 1.00000 0.00000)
+DEAL::    qpoints 13: 
+DEAL::        reference position  : (0.00000 0.666667 0.333333)
+DEAL::        physical position   : (1.00000 1.00000 0.333333)
+DEAL::        FE mapping position : (1.00000 1.00000 0.333333)
+DEAL::    qpoints 14: 
+DEAL::        reference position  : (0.00000 0.333333 0.666667)
+DEAL::        physical position   : (1.00000 1.00000 0.666667)
+DEAL::        FE mapping position : (1.00000 1.00000 0.666667)
+DEAL::    qpoints 15: 
+DEAL::        reference position  : (0.00000 0.00000 1.00000)
+DEAL::        physical position   : (1.00000 1.00000 1.00000)
+DEAL::        FE mapping position : (1.00000 1.00000 1.00000)
+DEAL::