From 859ff2d1a87522a3ddcc421603d76da51c61418d Mon Sep 17 00:00:00 2001
From: Wolfgang Bangerth <bangerth@math.tamu.edu>
Date: Fri, 4 Mar 2016 11:53:04 -0600
Subject: [PATCH] Add tests for ChartManifold.

These tests implement a ChartManifold with an identity pull-back/push-forward,
thereby creating a flat manifold. The pre-image that the pull-back projects
onto has a higher dimension, however, adding a tiny wrinkle to the system.
---
 tests/manifold/chart_manifold_01_embedded.cc  |  114 +
 .../chart_manifold_01_embedded.output         |   20 +
 tests/manifold/chart_manifold_02_embedded.cc  |  121 +
 .../chart_manifold_02_embedded.output         |   22 +
 tests/manifold/chart_manifold_03_embedded.cc  |  149 +
 .../chart_manifold_03_embedded.output         |   34 +
 tests/manifold/chart_manifold_04_embedded.cc  |  141 +
 .../chart_manifold_04_embedded.output         | 5703 +++++++++++++++++
 8 files changed, 6304 insertions(+)
 create mode 100644 tests/manifold/chart_manifold_01_embedded.cc
 create mode 100644 tests/manifold/chart_manifold_01_embedded.output
 create mode 100644 tests/manifold/chart_manifold_02_embedded.cc
 create mode 100644 tests/manifold/chart_manifold_02_embedded.output
 create mode 100644 tests/manifold/chart_manifold_03_embedded.cc
 create mode 100644 tests/manifold/chart_manifold_03_embedded.output
 create mode 100644 tests/manifold/chart_manifold_04_embedded.cc
 create mode 100644 tests/manifold/chart_manifold_04_embedded.output

diff --git a/tests/manifold/chart_manifold_01_embedded.cc b/tests/manifold/chart_manifold_01_embedded.cc
new file mode 100644
index 0000000000..28b8959e75
--- /dev/null
+++ b/tests/manifold/chart_manifold_01_embedded.cc
@@ -0,0 +1,114 @@
+//----------------------------  manifold_id_01.cc  ---------------------------
+//    Copyright (C) 2011 - 2016 by the mathLab team.
+//
+//    This file is subject to LGPL and may not be  distributed
+//    without copyright and license information. Please refer
+//    to the file deal.II/doc/license.html for the  text  and
+//    further information on this license.
+//
+//----------------------------  flat_manifold_01.cc  ---------------------------
+
+
+// Test that the flat manifold does what it should, where the
+// flat manifold is implemented as a ChartManifold with identity
+// pull-back and push-forward
+//
+// make the chart higher dimensional
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+
+// all include files you need here
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/grid/grid_out.h>
+
+
+template <int dim, int spacedim>
+class MyFlatManifold : public ChartManifold<dim,spacedim,spacedim+1>
+{
+public:
+  virtual
+  Point<spacedim+1>
+  pull_back(const Point<spacedim> &space_point) const
+  {
+    Point<spacedim+1> p;
+    for (unsigned int d=0; d<spacedim; ++d)
+      p[d] = space_point[d];
+    return p;
+  }
+
+
+  virtual
+  Point<spacedim>
+  push_forward(const Point<spacedim+1> &chart_point) const
+  {
+    Point<spacedim> p;
+    for (unsigned int d=0; d<spacedim; ++d)
+      p[d] = chart_point[d];
+    return p;
+  }
+
+  virtual
+  DerivativeForm<1,spacedim+1,spacedim>
+  push_forward_gradient(const Point<spacedim+1> &chart_point) const
+  {
+    DerivativeForm<1,spacedim+1,spacedim> x;
+    for (unsigned int d=0; d<spacedim; ++d)
+      x[d][d] = 1;
+    return x;
+  }
+};
+
+// Helper function
+template <int dim, int spacedim>
+void test(unsigned int ref=1)
+{
+  deallog << "Testing dim=" << dim
+          << ", spacedim="<< spacedim << std::endl;
+
+  MyFlatManifold<dim,spacedim> flat_manifold;
+  Triangulation<dim,spacedim> tria;
+  tria.set_manifold (0, flat_manifold);
+  GridGenerator::hyper_cube (tria);
+  tria.refine_global(1);
+
+  typename Triangulation<dim,spacedim>::active_cell_iterator
+  cell;
+
+  for (cell=tria.begin_active(); cell!=tria.end(); ++cell)
+    {
+      cell->set_all_manifold_ids (0);
+
+      // check that FlatManifold returns the middle of the cell.
+      deallog << "Cell: " << cell << std::endl;
+      if (cell->get_manifold().get_new_point_on_cell(cell).distance(cell->center()) > 1e-6)
+        {
+          deallog << "Default manifold: " << cell->get_manifold().get_new_point_on_cell(cell) << std::endl;
+          deallog << "Center of cell  : " << cell->center() << std::endl;
+        }
+      else
+        {
+          deallog << "OK!" << std::endl;
+        }
+    }
+}
+
+int main ()
+{
+  std::ofstream logfile("output");
+  deallog.attach(logfile);
+  deallog.threshold_double(1.e-10);
+
+  test<1,1>();
+  test<1,2>();
+  test<2,2>();
+
+  return 0;
+}
+
diff --git a/tests/manifold/chart_manifold_01_embedded.output b/tests/manifold/chart_manifold_01_embedded.output
new file mode 100644
index 0000000000..f7492c4daa
--- /dev/null
+++ b/tests/manifold/chart_manifold_01_embedded.output
@@ -0,0 +1,20 @@
+
+DEAL::Testing dim=1, spacedim=1
+DEAL::Cell: 1.0
+DEAL::OK!
+DEAL::Cell: 1.1
+DEAL::OK!
+DEAL::Testing dim=1, spacedim=2
+DEAL::Cell: 1.0
+DEAL::OK!
+DEAL::Cell: 1.1
+DEAL::OK!
+DEAL::Testing dim=2, spacedim=2
+DEAL::Cell: 1.0
+DEAL::OK!
+DEAL::Cell: 1.1
+DEAL::OK!
+DEAL::Cell: 1.2
+DEAL::OK!
+DEAL::Cell: 1.3
+DEAL::OK!
diff --git a/tests/manifold/chart_manifold_02_embedded.cc b/tests/manifold/chart_manifold_02_embedded.cc
new file mode 100644
index 0000000000..bf3372768a
--- /dev/null
+++ b/tests/manifold/chart_manifold_02_embedded.cc
@@ -0,0 +1,121 @@
+//----------------------------  manifold_id_01.cc  ---------------------------
+//    Copyright (C) 2011 - 2016 by the mathLab team.
+//
+//    This file is subject to LGPL and may not be  distributed
+//    without copyright and license information. Please refer
+//    to the file deal.II/doc/license.html for the  text  and
+//    further information on this license.
+//
+//----------------------------  flat_manifold_02.cc  ---------------------------
+
+
+// Test that the flat manifold does what it should. This time on faces, where the
+// flat manifold is implemented as a ChartManifold with identity
+// pull-back and push-forward
+//
+// make the chart higher dimensional
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+
+// all include files you need here
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/grid/grid_out.h>
+
+
+
+
+template <int dim, int spacedim>
+class MyFlatManifold : public ChartManifold<dim,spacedim,spacedim+1>
+{
+public:
+  virtual
+  Point<spacedim+1>
+  pull_back(const Point<spacedim> &space_point) const
+  {
+    Point<spacedim+1> p;
+    for (unsigned int d=0; d<spacedim; ++d)
+      p[d] = space_point[d];
+    return p;
+  }
+
+
+  virtual
+  Point<spacedim>
+  push_forward(const Point<spacedim+1> &chart_point) const
+  {
+    Point<spacedim> p;
+    for (unsigned int d=0; d<spacedim; ++d)
+      p[d] = chart_point[d];
+    return p;
+  }
+
+  virtual
+  DerivativeForm<1,spacedim+1,spacedim>
+  push_forward_gradient(const Point<spacedim+1> &chart_point) const
+  {
+    DerivativeForm<1,spacedim+1,spacedim> x;
+    for (unsigned int d=0; d<spacedim; ++d)
+      x[d][d] = 1;
+    return x;
+  }
+};
+
+
+
+// Helper function
+template <int dim, int spacedim>
+void test(unsigned int ref=1)
+{
+  deallog << "Testing dim=" << dim
+          << ", spacedim="<< spacedim << std::endl;
+
+  MyFlatManifold<dim,spacedim> flat_manifold;
+  Triangulation<dim,spacedim> tria;
+  tria.set_manifold (0, flat_manifold);
+  GridGenerator::hyper_cube (tria);
+  tria.refine_global(1);
+
+  typename Triangulation<dim,spacedim>::active_cell_iterator
+  cell;
+
+  for (cell=tria.begin_active(); cell!=tria.end(); ++cell)
+    {
+      cell->set_all_manifold_ids (0);
+
+      // check that FlatManifold returns the middle of the cell.
+      deallog << "Cell: " << cell << std::endl;
+      for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
+        {
+          const typename Triangulation<dim,spacedim>::face_iterator &face = cell->face(f);
+          if (face->get_manifold().get_new_point_on_face(face).distance(face->center()) > 1e-6)
+            {
+              deallog << "Face            : " << face << std::endl;
+              deallog << "Default manifold: " << cell->get_manifold().get_new_point_on_cell(cell) << std::endl;
+              deallog << "Center of cell  : " << cell->center() << std::endl;
+            }
+          else
+            {
+              deallog << "Face " << face << " is OK!" << std::endl;
+            }
+        }
+    }
+}
+
+int main ()
+{
+  std::ofstream logfile("output");
+  deallog.attach(logfile);
+  deallog.threshold_double(1.e-10);
+
+  test<2,2>();
+
+  return 0;
+}
+
diff --git a/tests/manifold/chart_manifold_02_embedded.output b/tests/manifold/chart_manifold_02_embedded.output
new file mode 100644
index 0000000000..8913de9c45
--- /dev/null
+++ b/tests/manifold/chart_manifold_02_embedded.output
@@ -0,0 +1,22 @@
+
+DEAL::Testing dim=2, spacedim=2
+DEAL::Cell: 1.0
+DEAL::Face 6 is OK!
+DEAL::Face 12 is OK!
+DEAL::Face 4 is OK!
+DEAL::Face 14 is OK!
+DEAL::Cell: 1.1
+DEAL::Face 12 is OK!
+DEAL::Face 8 is OK!
+DEAL::Face 5 is OK!
+DEAL::Face 15 is OK!
+DEAL::Cell: 1.2
+DEAL::Face 7 is OK!
+DEAL::Face 13 is OK!
+DEAL::Face 14 is OK!
+DEAL::Face 10 is OK!
+DEAL::Cell: 1.3
+DEAL::Face 13 is OK!
+DEAL::Face 9 is OK!
+DEAL::Face 15 is OK!
+DEAL::Face 11 is OK!
diff --git a/tests/manifold/chart_manifold_03_embedded.cc b/tests/manifold/chart_manifold_03_embedded.cc
new file mode 100644
index 0000000000..fb46426f1f
--- /dev/null
+++ b/tests/manifold/chart_manifold_03_embedded.cc
@@ -0,0 +1,149 @@
+//----------------------------  manifold_id_01.cc  ---------------------------
+//    Copyright (C) 2011 - 2016 by the mathLab team.
+//
+//    This file is subject to LGPL and may not be  distributed
+//    without copyright and license information. Please refer
+//    to the file deal.II/doc/license.html for the  text  and
+//    further information on this license.
+//
+//----------------------------  flat_manifold_03.cc  ---------------------------
+
+
+// Test periodicity of FlatManifold, where the
+// flat manifold is implemented as a ChartManifold with identity
+// pull-back and push-forward
+//
+// make the chart higher dimensional
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+
+
+// all include files you need here
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/grid/grid_out.h>
+
+
+template <int dim, int spacedim>
+class MyFlatManifold : public ChartManifold<dim,spacedim,spacedim+1>
+{
+public:
+  MyFlatManifold (const Point<spacedim+1> &periodicity)
+    :
+    ChartManifold<dim,spacedim,spacedim+1> (periodicity)
+  {}
+
+
+  virtual
+  Point<spacedim+1>
+  pull_back(const Point<spacedim> &space_point) const
+  {
+    Point<spacedim+1> p;
+    for (unsigned int d=0; d<spacedim; ++d)
+      p[d] = space_point[d];
+    return p;
+  }
+
+
+  virtual
+  Point<spacedim>
+  push_forward(const Point<spacedim+1> &chart_point) const
+  {
+    Point<spacedim> p;
+    for (unsigned int d=0; d<spacedim; ++d)
+      p[d] = chart_point[d];
+    return p;
+  }
+
+  virtual
+  DerivativeForm<1,spacedim+1,spacedim>
+  push_forward_gradient(const Point<spacedim+1> &chart_point) const
+  {
+    DerivativeForm<1,spacedim+1,spacedim> x;
+    for (unsigned int d=0; d<spacedim; ++d)
+      x[d][d] = 1;
+    return x;
+  }
+};
+
+
+
+// Helper function
+template <int dim, int spacedim>
+void test(unsigned int ref=1)
+{
+  deallog << "Testing dim=" << dim
+          << ", spacedim="<< spacedim << std::endl;
+
+  Point<spacedim+1> periodicity;
+  periodicity[0] = 5.0;
+
+  MyFlatManifold<dim,spacedim> manifold(periodicity);
+
+  Quadrature<spacedim> quad;
+  std::vector<std::vector<Point<spacedim> > >ps(10,std::vector<Point<spacedim> >(2));
+  Point<spacedim> middle;
+  std::vector<double > ws(2, 0.5);
+
+  // Case 1: both points are close to left boundary of periodicity
+  ps[0][0][0] = 1;
+  ps[0][1][0] = 2;
+  // Case 2: same, with different order
+  ps[1][0][0] = 2;
+  ps[1][1][0] = 1;
+
+  // Case 3: one is close to left, one to right
+  ps[2][0][0] = 1;
+  ps[2][1][0] = 4;
+  // Case 4: same, opposite order
+  ps[3][0][0] = 4;
+  ps[3][1][0] = 1;
+
+  // Case 5: both close to right
+  ps[4][0][0] = 3;
+  ps[4][1][0] = 4;
+  // Case 6: same, opposite order
+  ps[5][0][0] = 4;
+  ps[5][1][0] = 3;
+
+  // Case 7: both close to middle
+  ps[6][0][0] = 2;
+  ps[6][1][0] = 3;
+  // Case 8: same, opposite order
+  ps[7][0][0] = 3;
+  ps[7][1][0] = 2;
+
+  // Case 9: Corner cases
+  ps[8][0][0] = -1e-10;
+  ps[8][1][0] = 5+1e-10;
+  // Case 10: same, opposite order
+  ps[9][0][0] = 5+1e-10;
+  ps[9][1][0] = -1e-10;
+
+  for (unsigned int i=0; i<ps.size(); ++i)
+    {
+      quad = Quadrature<spacedim>(ps[i],ws);
+      middle = manifold.get_new_point(quad);
+      deallog << "P0: " << ps[i][0] << " , P1: " << ps[i][1] << " , Middle: " << middle << std::endl;
+    }
+
+}
+
+int main ()
+{
+  std::ofstream logfile("output");
+  deallog.attach(logfile);
+  deallog.threshold_double(1.e-8);
+
+  test<1,1>();
+  test<1,2>();
+  test<2,2>();
+
+  return 0;
+}
+
diff --git a/tests/manifold/chart_manifold_03_embedded.output b/tests/manifold/chart_manifold_03_embedded.output
new file mode 100644
index 0000000000..6e53c91d7c
--- /dev/null
+++ b/tests/manifold/chart_manifold_03_embedded.output
@@ -0,0 +1,34 @@
+
+DEAL::Testing dim=1, spacedim=1
+DEAL::P0: 1.00000 , P1: 2.00000 , Middle: 1.50000
+DEAL::P0: 2.00000 , P1: 1.00000 , Middle: 1.50000
+DEAL::P0: 1.00000 , P1: 4.00000 , Middle: 0.00000
+DEAL::P0: 4.00000 , P1: 1.00000 , Middle: 0.00000
+DEAL::P0: 3.00000 , P1: 4.00000 , Middle: 3.50000
+DEAL::P0: 4.00000 , P1: 3.00000 , Middle: 3.50000
+DEAL::P0: 2.00000 , P1: 3.00000 , Middle: 2.50000
+DEAL::P0: 3.00000 , P1: 2.00000 , Middle: 2.50000
+DEAL::P0: -1.00000e-10 , P1: 5.00000 , Middle: 4.13702e-18
+DEAL::P0: 5.00000 , P1: -1.00000e-10 , Middle: 4.13702e-18
+DEAL::Testing dim=1, spacedim=2
+DEAL::P0: 1.00000 0.00000 , P1: 2.00000 0.00000 , Middle: 1.50000 0.00000
+DEAL::P0: 2.00000 0.00000 , P1: 1.00000 0.00000 , Middle: 1.50000 0.00000
+DEAL::P0: 1.00000 0.00000 , P1: 4.00000 0.00000 , Middle: 0.00000 0.00000
+DEAL::P0: 4.00000 0.00000 , P1: 1.00000 0.00000 , Middle: 0.00000 0.00000
+DEAL::P0: 3.00000 0.00000 , P1: 4.00000 0.00000 , Middle: 3.50000 0.00000
+DEAL::P0: 4.00000 0.00000 , P1: 3.00000 0.00000 , Middle: 3.50000 0.00000
+DEAL::P0: 2.00000 0.00000 , P1: 3.00000 0.00000 , Middle: 2.50000 0.00000
+DEAL::P0: 3.00000 0.00000 , P1: 2.00000 0.00000 , Middle: 2.50000 0.00000
+DEAL::P0: -1.00000e-10 0.00000 , P1: 5.00000 0.00000 , Middle: 4.13702e-18 0.00000
+DEAL::P0: 5.00000 0.00000 , P1: -1.00000e-10 0.00000 , Middle: 4.13702e-18 0.00000
+DEAL::Testing dim=2, spacedim=2
+DEAL::P0: 1.00000 0.00000 , P1: 2.00000 0.00000 , Middle: 1.50000 0.00000
+DEAL::P0: 2.00000 0.00000 , P1: 1.00000 0.00000 , Middle: 1.50000 0.00000
+DEAL::P0: 1.00000 0.00000 , P1: 4.00000 0.00000 , Middle: 0.00000 0.00000
+DEAL::P0: 4.00000 0.00000 , P1: 1.00000 0.00000 , Middle: 0.00000 0.00000
+DEAL::P0: 3.00000 0.00000 , P1: 4.00000 0.00000 , Middle: 3.50000 0.00000
+DEAL::P0: 4.00000 0.00000 , P1: 3.00000 0.00000 , Middle: 3.50000 0.00000
+DEAL::P0: 2.00000 0.00000 , P1: 3.00000 0.00000 , Middle: 2.50000 0.00000
+DEAL::P0: 3.00000 0.00000 , P1: 2.00000 0.00000 , Middle: 2.50000 0.00000
+DEAL::P0: -1.00000e-10 0.00000 , P1: 5.00000 0.00000 , Middle: 4.13702e-18 0.00000
+DEAL::P0: 5.00000 0.00000 , P1: -1.00000e-10 0.00000 , Middle: 4.13702e-18 0.00000
diff --git a/tests/manifold/chart_manifold_04_embedded.cc b/tests/manifold/chart_manifold_04_embedded.cc
new file mode 100644
index 0000000000..905a0d6fc3
--- /dev/null
+++ b/tests/manifold/chart_manifold_04_embedded.cc
@@ -0,0 +1,141 @@
+//----------------------------  manifold_id_01.cc  ---------------------------
+//    Copyright (C) 2011 - 2016 by the mathLab team.
+//
+//    This file is subject to LGPL and may not be  distributed
+//    without copyright and license information. Please refer
+//    to the file deal.II/doc/license.html for the  text  and
+//    further information on this license.
+//
+//----------------------------  flat_manifold_01.cc  ---------------------------
+
+
+// Test interior mapping of flat manifold, where the
+// flat manifold is implemented as a ChartManifold with identity
+// pull-back and push-forward
+//
+// make the chart higher dimensional
+
+#include "../tests.h"
+#include <fstream>
+#include <deal.II/base/logstream.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_values.h>
+
+
+// all include files you need here
+#include <deal.II/grid/tria.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_boundary_lib.h>
+#include <deal.II/grid/grid_out.h>
+
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/fe/mapping_q.h>
+
+
+template <int dim, int spacedim>
+class MyFlatManifold : public ChartManifold<dim,spacedim,spacedim+1>
+{
+public:
+  virtual
+  Point<spacedim+1>
+  pull_back(const Point<spacedim> &space_point) const
+  {
+    Point<spacedim+1> p;
+    for (unsigned int d=0; d<spacedim; ++d)
+      p[d] = space_point[d];
+    return p;
+  }
+
+
+  virtual
+  Point<spacedim>
+  push_forward(const Point<spacedim+1> &chart_point) const
+  {
+    Point<spacedim> p;
+    for (unsigned int d=0; d<spacedim; ++d)
+      p[d] = chart_point[d];
+    return p;
+  }
+
+  virtual
+  DerivativeForm<1,spacedim+1,spacedim>
+  push_forward_gradient(const Point<spacedim+1> &chart_point) const
+  {
+    DerivativeForm<1,spacedim+1,spacedim> x;
+    for (unsigned int d=0; d<spacedim; ++d)
+      x[d][d] = 1;
+    return x;
+  }
+};
+
+
+// Helper function
+template <int dim, int spacedim>
+void test(unsigned int ref, const MappingQ<dim> &mapping)
+{
+  deallog << "Testing dim=" << dim
+          << ", spacedim="<< spacedim << std::endl;
+
+  MyFlatManifold<dim,spacedim> flat_manifold;
+  Triangulation<dim,spacedim> tria;
+  tria.set_manifold (0, flat_manifold);
+  GridGenerator::hyper_cube (tria);
+  tria.refine_global(ref);
+
+  typename Triangulation<dim,spacedim>::active_cell_iterator
+  cell;
+
+  QGauss<dim> quadrature(4);
+  FE_Q<dim> fe(2);
+
+  FEValues<dim> fe_values (mapping, fe, quadrature,
+                           update_gradients | update_values | update_quadrature_points  |
+                           update_JxW_values);
+
+  for (cell=tria.begin_active(); cell!=tria.end(); ++cell)
+    {
+      cell->set_all_manifold_ids (0);
+
+      // check that FlatManifold returns the middle of the cell.
+      deallog << "Cell: " << cell << std::endl;
+
+      fe_values.reinit(cell);
+
+      deallog << "  center: " << cell->center() << std::endl;
+      for (unsigned int q=0; q<quadrature.size(); ++q)
+        {
+
+          deallog << "  JxW(" << q << "): " << fe_values.JxW(q) << std::endl;
+          deallog << "  p("<<q<<"): " << fe_values.quadrature_point(q) << std::endl;
+          for (unsigned int i=0; i<fe_values.dofs_per_cell; ++i)
+            deallog << "  shape " << i << "," <<q<<": " << fe_values.shape_value(i,q)
+                    << " " << fe_values.shape_grad(i,q) << std::endl;
+
+        }
+
+      if (cell->get_manifold().get_new_point_on_cell(cell).distance(cell->center()) > 1e-6)
+        {
+          deallog << "Default manifold: " << cell->get_manifold().get_new_point_on_cell(cell) << std::endl;
+          deallog << "Center of cell  : " << cell->center() << std::endl;
+        }
+    }
+
+  deallog << "OK" <<std::endl<<std::endl;
+
+}
+
+int main ()
+{
+  std::ofstream logfile("output");
+  deallog.attach(logfile);
+  deallog.threshold_double(1.e-10);
+
+  test<2,2>(2, MappingQ<2>(4, false));
+  test<2,2>(2, MappingQ<2>(4, true));
+
+
+  return 0;
+}
+
diff --git a/tests/manifold/chart_manifold_04_embedded.output b/tests/manifold/chart_manifold_04_embedded.output
new file mode 100644
index 0000000000..51b0e0a50c
--- /dev/null
+++ b/tests/manifold/chart_manifold_04_embedded.output
@@ -0,0 +1,5703 @@
+
+DEAL::Testing dim=2, spacedim=2
+DEAL::Cell: 2.0
+DEAL::  center: 0.125000 0.125000
+DEAL::  JxW(0): 0.00189067
+DEAL::  p(0): 0.0173580 0.0173580
+DEAL::  shape 0,0: 0.642155 -8.72593 -8.72593
+DEAL::  shape 1,0: -0.0479127 -2.31516 0.651062
+DEAL::  shape 2,0: -0.0479127 0.651062 -2.31516
+DEAL::  shape 3,0: 0.00357488 0.172740 0.172740
+DEAL::  shape 4,0: 0.207103 -2.81422 11.0411
+DEAL::  shape 5,0: -0.0154525 -0.746669 -0.823801
+DEAL::  shape 6,0: 0.207103 11.0411 -2.81422
+DEAL::  shape 7,0: -0.0154525 -0.823801 -0.746669
+DEAL::  shape 8,0: 0.0667934 3.56089 3.56089
+DEAL::  JxW(1): 0.00354456
+DEAL::  p(1): 0.0825024 0.0173580
+DEAL::  shape 0,1: 0.182534 -5.38492 -2.48036
+DEAL::  shape 1,1: -0.0899086 1.02584 1.22172
+DEAL::  shape 2,1: -0.0136193 0.401782 -0.658089
+DEAL::  shape 3,1: 0.00670829 -0.0765406 0.324147
+DEAL::  shape 4,1: 0.0588695 -1.73671 3.13845
+DEAL::  shape 5,1: -0.0289967 0.330848 -1.54587
+DEAL::  shape 6,1: 0.708721 4.35908 -9.63045
+DEAL::  shape 7,1: -0.0528793 -0.325241 -2.55515
+DEAL::  shape 8,1: 0.228571 1.40586 12.1856
+DEAL::  JxW(2): 0.00354456
+DEAL::  p(2): 0.167498 0.0173580
+DEAL::  shape 0,2: -0.0899086 -1.02584 1.22172
+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
+DEAL::  shape 2,2: 0.00670829 0.0765406 0.324147
+DEAL::  shape 3,2: -0.0136193 -0.401782 -0.658089
+DEAL::  shape 4,2: -0.0289967 -0.330848 -1.54587
+DEAL::  shape 5,2: 0.0588695 1.73671 3.13845
+DEAL::  shape 6,2: 0.708721 -4.35908 -9.63045
+DEAL::  shape 7,2: -0.0528793 0.325241 -2.55515
+DEAL::  shape 8,2: 0.228571 -1.40586 12.1856
+DEAL::  JxW(3): 0.00189067
+DEAL::  p(3): 0.232642 0.0173580
+DEAL::  shape 0,3: -0.0479127 2.31516 0.651062
+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
+DEAL::  shape 2,3: 0.00357488 -0.172740 0.172740
+DEAL::  shape 3,3: -0.0479127 -0.651062 -2.31516
+DEAL::  shape 4,3: -0.0154525 0.746669 -0.823801
+DEAL::  shape 5,3: 0.207103 2.81422 11.0411
+DEAL::  shape 6,3: 0.207103 -11.0411 -2.81422
+DEAL::  shape 7,3: -0.0154525 0.823801 -0.746669
+DEAL::  shape 8,3: 0.0667934 -3.56089 3.56089
+DEAL::  JxW(4): 0.00354456
+DEAL::  p(4): 0.0173580 0.0825024
+DEAL::  shape 0,4: 0.182534 -2.48036 -5.38492
+DEAL::  shape 1,4: -0.0136193 -0.658089 0.401782
+DEAL::  shape 2,4: -0.0899086 1.22172 1.02584
+DEAL::  shape 3,4: 0.00670829 0.324147 -0.0765406
+DEAL::  shape 4,4: 0.708721 -9.63045 4.35908
+DEAL::  shape 5,4: -0.0528793 -2.55515 -0.325241
+DEAL::  shape 6,4: 0.0588695 3.13845 -1.73671
+DEAL::  shape 7,4: -0.0289967 -1.54587 0.330848
+DEAL::  shape 8,4: 0.228571 12.1856 1.40586
+DEAL::  JxW(5): 0.00664521
+DEAL::  p(5): 0.0825024 0.0825024
+DEAL::  shape 0,5: 0.0518856 -1.53067 -1.53067
+DEAL::  shape 1,5: -0.0255567 0.291598 0.753947
+DEAL::  shape 2,5: -0.0255567 0.753947 0.291598
+DEAL::  shape 3,5: 0.0125882 -0.143629 -0.143629
+DEAL::  shape 4,5: 0.201455 -5.94312 1.23908
+DEAL::  shape 5,5: -0.0992284 1.13218 -0.610317
+DEAL::  shape 6,5: 0.201455 1.23908 -5.94312
+DEAL::  shape 7,5: -0.0992284 -0.610317 1.13218
+DEAL::  shape 8,5: 0.782186 4.81094 4.81094
+DEAL::  JxW(6): 0.00664521
+DEAL::  p(6): 0.167498 0.0825024
+DEAL::  shape 0,6: -0.0255567 -0.291598 0.753947
+DEAL::  shape 1,6: 0.0518856 1.53067 -1.53067
+DEAL::  shape 2,6: 0.0125882 0.143629 -0.143629
+DEAL::  shape 3,6: -0.0255567 -0.753947 0.291598
+DEAL::  shape 4,6: -0.0992284 -1.13218 -0.610317
+DEAL::  shape 5,6: 0.201455 5.94312 1.23908
+DEAL::  shape 6,6: 0.201455 -1.23908 -5.94312
+DEAL::  shape 7,6: -0.0992284 0.610317 1.13218
+DEAL::  shape 8,6: 0.782186 -4.81094 4.81094
+DEAL::  JxW(7): 0.00354456
+DEAL::  p(7): 0.232642 0.0825024
+DEAL::  shape 0,7: -0.0136193 0.658089 0.401782
+DEAL::  shape 1,7: 0.182534 2.48036 -5.38492
+DEAL::  shape 2,7: 0.00670829 -0.324147 -0.0765406
+DEAL::  shape 3,7: -0.0899086 -1.22172 1.02584
+DEAL::  shape 4,7: -0.0528793 2.55515 -0.325241
+DEAL::  shape 5,7: 0.708721 9.63045 4.35908
+DEAL::  shape 6,7: 0.0588695 -3.13845 -1.73671
+DEAL::  shape 7,7: -0.0289967 1.54587 0.330848
+DEAL::  shape 8,7: 0.228571 -12.1856 1.40586
+DEAL::  JxW(8): 0.00354456
+DEAL::  p(8): 0.0173580 0.167498
+DEAL::  shape 0,8: -0.0899086 1.22172 -1.02584
+DEAL::  shape 1,8: 0.00670829 0.324147 0.0765406
+DEAL::  shape 2,8: 0.182534 -2.48036 5.38492
+DEAL::  shape 3,8: -0.0136193 -0.658089 -0.401782
+DEAL::  shape 4,8: 0.708721 -9.63045 -4.35908
+DEAL::  shape 5,8: -0.0528793 -2.55515 0.325241
+DEAL::  shape 6,8: -0.0289967 -1.54587 -0.330848
+DEAL::  shape 7,8: 0.0588695 3.13845 1.73671
+DEAL::  shape 8,8: 0.228571 12.1856 -1.40586
+DEAL::  JxW(9): 0.00664521
+DEAL::  p(9): 0.0825024 0.167498
+DEAL::  shape 0,9: -0.0255567 0.753947 -0.291598
+DEAL::  shape 1,9: 0.0125882 -0.143629 0.143629
+DEAL::  shape 2,9: 0.0518856 -1.53067 1.53067
+DEAL::  shape 3,9: -0.0255567 0.291598 -0.753947
+DEAL::  shape 4,9: 0.201455 -5.94312 -1.23908
+DEAL::  shape 5,9: -0.0992284 1.13218 0.610317
+DEAL::  shape 6,9: -0.0992284 -0.610317 -1.13218
+DEAL::  shape 7,9: 0.201455 1.23908 5.94312
+DEAL::  shape 8,9: 0.782186 4.81094 -4.81094
+DEAL::  JxW(10): 0.00664521
+DEAL::  p(10): 0.167498 0.167498
+DEAL::  shape 0,10: 0.0125882 0.143629 0.143629
+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
+DEAL::  shape 2,10: -0.0255567 -0.291598 -0.753947
+DEAL::  shape 3,10: 0.0518856 1.53067 1.53067
+DEAL::  shape 4,10: -0.0992284 -1.13218 0.610317
+DEAL::  shape 5,10: 0.201455 5.94312 -1.23908
+DEAL::  shape 6,10: -0.0992284 0.610317 -1.13218
+DEAL::  shape 7,10: 0.201455 -1.23908 5.94312
+DEAL::  shape 8,10: 0.782186 -4.81094 -4.81094
+DEAL::  JxW(11): 0.00354456
+DEAL::  p(11): 0.232642 0.167498
+DEAL::  shape 0,11: 0.00670829 -0.324147 0.0765406
+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
+DEAL::  shape 2,11: -0.0136193 0.658089 -0.401782
+DEAL::  shape 3,11: 0.182534 2.48036 5.38492
+DEAL::  shape 4,11: -0.0528793 2.55515 0.325241
+DEAL::  shape 5,11: 0.708721 9.63045 -4.35908
+DEAL::  shape 6,11: -0.0289967 1.54587 -0.330848
+DEAL::  shape 7,11: 0.0588695 -3.13845 1.73671
+DEAL::  shape 8,11: 0.228571 -12.1856 -1.40586
+DEAL::  JxW(12): 0.00189067
+DEAL::  p(12): 0.0173580 0.232642
+DEAL::  shape 0,12: -0.0479127 0.651062 2.31516
+DEAL::  shape 1,12: 0.00357488 0.172740 -0.172740
+DEAL::  shape 2,12: 0.642155 -8.72593 8.72593
+DEAL::  shape 3,12: -0.0479127 -2.31516 -0.651062
+DEAL::  shape 4,12: 0.207103 -2.81422 -11.0411
+DEAL::  shape 5,12: -0.0154525 -0.746669 0.823801
+DEAL::  shape 6,12: -0.0154525 -0.823801 0.746669
+DEAL::  shape 7,12: 0.207103 11.0411 2.81422
+DEAL::  shape 8,12: 0.0667934 3.56089 -3.56089
+DEAL::  JxW(13): 0.00354456
+DEAL::  p(13): 0.0825024 0.232642
+DEAL::  shape 0,13: -0.0136193 0.401782 0.658089
+DEAL::  shape 1,13: 0.00670829 -0.0765406 -0.324147
+DEAL::  shape 2,13: 0.182534 -5.38492 2.48036
+DEAL::  shape 3,13: -0.0899086 1.02584 -1.22172
+DEAL::  shape 4,13: 0.0588695 -1.73671 -3.13845
+DEAL::  shape 5,13: -0.0289967 0.330848 1.54587
+DEAL::  shape 6,13: -0.0528793 -0.325241 2.55515
+DEAL::  shape 7,13: 0.708721 4.35908 9.63045
+DEAL::  shape 8,13: 0.228571 1.40586 -12.1856
+DEAL::  JxW(14): 0.00354456
+DEAL::  p(14): 0.167498 0.232642
+DEAL::  shape 0,14: 0.00670829 0.0765406 -0.324147
+DEAL::  shape 1,14: -0.0136193 -0.401782 0.658089
+DEAL::  shape 2,14: -0.0899086 -1.02584 -1.22172
+DEAL::  shape 3,14: 0.182534 5.38492 2.48036
+DEAL::  shape 4,14: -0.0289967 -0.330848 1.54587
+DEAL::  shape 5,14: 0.0588695 1.73671 -3.13845
+DEAL::  shape 6,14: -0.0528793 0.325241 2.55515
+DEAL::  shape 7,14: 0.708721 -4.35908 9.63045
+DEAL::  shape 8,14: 0.228571 -1.40586 -12.1856
+DEAL::  JxW(15): 0.00189067
+DEAL::  p(15): 0.232642 0.232642
+DEAL::  shape 0,15: 0.00357488 -0.172740 -0.172740
+DEAL::  shape 1,15: -0.0479127 -0.651062 2.31516
+DEAL::  shape 2,15: -0.0479127 2.31516 -0.651062
+DEAL::  shape 3,15: 0.642155 8.72593 8.72593
+DEAL::  shape 4,15: -0.0154525 0.746669 0.823801
+DEAL::  shape 5,15: 0.207103 2.81422 -11.0411
+DEAL::  shape 6,15: -0.0154525 0.823801 0.746669
+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
+DEAL::  shape 8,15: 0.0667934 -3.56089 -3.56089
+DEAL::Cell: 2.1
+DEAL::  center: 0.375000 0.125000
+DEAL::  JxW(0): 0.00189067
+DEAL::  p(0): 0.267358 0.0173580
+DEAL::  shape 0,0: 0.642155 -8.72593 -8.72593
+DEAL::  shape 1,0: -0.0479127 -2.31516 0.651062
+DEAL::  shape 2,0: -0.0479127 0.651062 -2.31516
+DEAL::  shape 3,0: 0.00357488 0.172740 0.172740
+DEAL::  shape 4,0: 0.207103 -2.81422 11.0411
+DEAL::  shape 5,0: -0.0154525 -0.746669 -0.823801
+DEAL::  shape 6,0: 0.207103 11.0411 -2.81422
+DEAL::  shape 7,0: -0.0154525 -0.823801 -0.746669
+DEAL::  shape 8,0: 0.0667934 3.56089 3.56089
+DEAL::  JxW(1): 0.00354456
+DEAL::  p(1): 0.332502 0.0173580
+DEAL::  shape 0,1: 0.182534 -5.38492 -2.48036
+DEAL::  shape 1,1: -0.0899086 1.02584 1.22172
+DEAL::  shape 2,1: -0.0136193 0.401782 -0.658089
+DEAL::  shape 3,1: 0.00670829 -0.0765406 0.324147
+DEAL::  shape 4,1: 0.0588695 -1.73671 3.13845
+DEAL::  shape 5,1: -0.0289967 0.330848 -1.54587
+DEAL::  shape 6,1: 0.708721 4.35908 -9.63045
+DEAL::  shape 7,1: -0.0528793 -0.325241 -2.55515
+DEAL::  shape 8,1: 0.228571 1.40586 12.1856
+DEAL::  JxW(2): 0.00354456
+DEAL::  p(2): 0.417498 0.0173580
+DEAL::  shape 0,2: -0.0899086 -1.02584 1.22172
+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
+DEAL::  shape 2,2: 0.00670829 0.0765406 0.324147
+DEAL::  shape 3,2: -0.0136193 -0.401782 -0.658089
+DEAL::  shape 4,2: -0.0289967 -0.330848 -1.54587
+DEAL::  shape 5,2: 0.0588695 1.73671 3.13845
+DEAL::  shape 6,2: 0.708721 -4.35908 -9.63045
+DEAL::  shape 7,2: -0.0528793 0.325241 -2.55515
+DEAL::  shape 8,2: 0.228571 -1.40586 12.1856
+DEAL::  JxW(3): 0.00189067
+DEAL::  p(3): 0.482642 0.0173580
+DEAL::  shape 0,3: -0.0479127 2.31516 0.651062
+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
+DEAL::  shape 2,3: 0.00357488 -0.172740 0.172740
+DEAL::  shape 3,3: -0.0479127 -0.651062 -2.31516
+DEAL::  shape 4,3: -0.0154525 0.746669 -0.823801
+DEAL::  shape 5,3: 0.207103 2.81422 11.0411
+DEAL::  shape 6,3: 0.207103 -11.0411 -2.81422
+DEAL::  shape 7,3: -0.0154525 0.823801 -0.746669
+DEAL::  shape 8,3: 0.0667934 -3.56089 3.56089
+DEAL::  JxW(4): 0.00354456
+DEAL::  p(4): 0.267358 0.0825024
+DEAL::  shape 0,4: 0.182534 -2.48036 -5.38492
+DEAL::  shape 1,4: -0.0136193 -0.658089 0.401782
+DEAL::  shape 2,4: -0.0899086 1.22172 1.02584
+DEAL::  shape 3,4: 0.00670829 0.324147 -0.0765406
+DEAL::  shape 4,4: 0.708721 -9.63045 4.35908
+DEAL::  shape 5,4: -0.0528793 -2.55515 -0.325241
+DEAL::  shape 6,4: 0.0588695 3.13845 -1.73671
+DEAL::  shape 7,4: -0.0289967 -1.54587 0.330848
+DEAL::  shape 8,4: 0.228571 12.1856 1.40586
+DEAL::  JxW(5): 0.00664521
+DEAL::  p(5): 0.332502 0.0825024
+DEAL::  shape 0,5: 0.0518856 -1.53067 -1.53067
+DEAL::  shape 1,5: -0.0255567 0.291598 0.753947
+DEAL::  shape 2,5: -0.0255567 0.753947 0.291598
+DEAL::  shape 3,5: 0.0125882 -0.143629 -0.143629
+DEAL::  shape 4,5: 0.201455 -5.94312 1.23908
+DEAL::  shape 5,5: -0.0992284 1.13218 -0.610317
+DEAL::  shape 6,5: 0.201455 1.23908 -5.94312
+DEAL::  shape 7,5: -0.0992284 -0.610317 1.13218
+DEAL::  shape 8,5: 0.782186 4.81094 4.81094
+DEAL::  JxW(6): 0.00664521
+DEAL::  p(6): 0.417498 0.0825024
+DEAL::  shape 0,6: -0.0255567 -0.291598 0.753947
+DEAL::  shape 1,6: 0.0518856 1.53067 -1.53067
+DEAL::  shape 2,6: 0.0125882 0.143629 -0.143629
+DEAL::  shape 3,6: -0.0255567 -0.753947 0.291598
+DEAL::  shape 4,6: -0.0992284 -1.13218 -0.610317
+DEAL::  shape 5,6: 0.201455 5.94312 1.23908
+DEAL::  shape 6,6: 0.201455 -1.23908 -5.94312
+DEAL::  shape 7,6: -0.0992284 0.610317 1.13218
+DEAL::  shape 8,6: 0.782186 -4.81094 4.81094
+DEAL::  JxW(7): 0.00354456
+DEAL::  p(7): 0.482642 0.0825024
+DEAL::  shape 0,7: -0.0136193 0.658089 0.401782
+DEAL::  shape 1,7: 0.182534 2.48036 -5.38492
+DEAL::  shape 2,7: 0.00670829 -0.324147 -0.0765406
+DEAL::  shape 3,7: -0.0899086 -1.22172 1.02584
+DEAL::  shape 4,7: -0.0528793 2.55515 -0.325241
+DEAL::  shape 5,7: 0.708721 9.63045 4.35908
+DEAL::  shape 6,7: 0.0588695 -3.13845 -1.73671
+DEAL::  shape 7,7: -0.0289967 1.54587 0.330848
+DEAL::  shape 8,7: 0.228571 -12.1856 1.40586
+DEAL::  JxW(8): 0.00354456
+DEAL::  p(8): 0.267358 0.167498
+DEAL::  shape 0,8: -0.0899086 1.22172 -1.02584
+DEAL::  shape 1,8: 0.00670829 0.324147 0.0765406
+DEAL::  shape 2,8: 0.182534 -2.48036 5.38492
+DEAL::  shape 3,8: -0.0136193 -0.658089 -0.401782
+DEAL::  shape 4,8: 0.708721 -9.63045 -4.35908
+DEAL::  shape 5,8: -0.0528793 -2.55515 0.325241
+DEAL::  shape 6,8: -0.0289967 -1.54587 -0.330848
+DEAL::  shape 7,8: 0.0588695 3.13845 1.73671
+DEAL::  shape 8,8: 0.228571 12.1856 -1.40586
+DEAL::  JxW(9): 0.00664521
+DEAL::  p(9): 0.332502 0.167498
+DEAL::  shape 0,9: -0.0255567 0.753947 -0.291598
+DEAL::  shape 1,9: 0.0125882 -0.143629 0.143629
+DEAL::  shape 2,9: 0.0518856 -1.53067 1.53067
+DEAL::  shape 3,9: -0.0255567 0.291598 -0.753947
+DEAL::  shape 4,9: 0.201455 -5.94312 -1.23908
+DEAL::  shape 5,9: -0.0992284 1.13218 0.610317
+DEAL::  shape 6,9: -0.0992284 -0.610317 -1.13218
+DEAL::  shape 7,9: 0.201455 1.23908 5.94312
+DEAL::  shape 8,9: 0.782186 4.81094 -4.81094
+DEAL::  JxW(10): 0.00664521
+DEAL::  p(10): 0.417498 0.167498
+DEAL::  shape 0,10: 0.0125882 0.143629 0.143629
+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
+DEAL::  shape 2,10: -0.0255567 -0.291598 -0.753947
+DEAL::  shape 3,10: 0.0518856 1.53067 1.53067
+DEAL::  shape 4,10: -0.0992284 -1.13218 0.610317
+DEAL::  shape 5,10: 0.201455 5.94312 -1.23908
+DEAL::  shape 6,10: -0.0992284 0.610317 -1.13218
+DEAL::  shape 7,10: 0.201455 -1.23908 5.94312
+DEAL::  shape 8,10: 0.782186 -4.81094 -4.81094
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  shape 6,11: -0.0289967 1.54587 -0.330848
+DEAL::  shape 7,11: 0.0588695 -3.13845 1.73671
+DEAL::  shape 8,11: 0.228571 -12.1856 -1.40586
+DEAL::  JxW(12): 0.00189067
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+DEAL::  JxW(13): 0.00354456
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+DEAL::  JxW(14): 0.00354456
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+DEAL::Cell: 2.2
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  JxW(3): 0.00189067
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  shape 3,7: -0.0899086 -1.22172 1.02584
+DEAL::  shape 4,7: -0.0528793 2.55515 -0.325241
+DEAL::  shape 5,7: 0.708721 9.63045 4.35908
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+DEAL::  shape 7,7: -0.0289967 1.54587 0.330848
+DEAL::  shape 8,7: 0.228571 -12.1856 1.40586
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+DEAL::  shape 1,9: 0.0125882 -0.143629 0.143629
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
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+DEAL::Cell: 2.4
+DEAL::  center: 0.625000 0.125000
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  JxW(3): 0.00189067
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  JxW(4): 0.00354456
+DEAL::  p(4): 0.767358 0.0825024
+DEAL::  shape 0,4: 0.182534 -2.48036 -5.38492
+DEAL::  shape 1,4: -0.0136193 -0.658089 0.401782
+DEAL::  shape 2,4: -0.0899086 1.22172 1.02584
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+DEAL::  shape 5,4: -0.0528793 -2.55515 -0.325241
+DEAL::  shape 6,4: 0.0588695 3.13845 -1.73671
+DEAL::  shape 7,4: -0.0289967 -1.54587 0.330848
+DEAL::  shape 8,4: 0.228571 12.1856 1.40586
+DEAL::  JxW(5): 0.00664521
+DEAL::  p(5): 0.832502 0.0825024
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+DEAL::  shape 1,5: -0.0255567 0.291598 0.753947
+DEAL::  shape 2,5: -0.0255567 0.753947 0.291598
+DEAL::  shape 3,5: 0.0125882 -0.143629 -0.143629
+DEAL::  shape 4,5: 0.201455 -5.94312 1.23908
+DEAL::  shape 5,5: -0.0992284 1.13218 -0.610317
+DEAL::  shape 6,5: 0.201455 1.23908 -5.94312
+DEAL::  shape 7,5: -0.0992284 -0.610317 1.13218
+DEAL::  shape 8,5: 0.782186 4.81094 4.81094
+DEAL::  JxW(6): 0.00664521
+DEAL::  p(6): 0.917498 0.0825024
+DEAL::  shape 0,6: -0.0255567 -0.291598 0.753947
+DEAL::  shape 1,6: 0.0518856 1.53067 -1.53067
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+DEAL::  shape 3,6: -0.0255567 -0.753947 0.291598
+DEAL::  shape 4,6: -0.0992284 -1.13218 -0.610317
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+DEAL::  shape 6,6: 0.201455 -1.23908 -5.94312
+DEAL::  shape 7,6: -0.0992284 0.610317 1.13218
+DEAL::  shape 8,6: 0.782186 -4.81094 4.81094
+DEAL::  JxW(7): 0.00354456
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+DEAL::  shape 0,7: -0.0136193 0.658089 0.401782
+DEAL::  shape 1,7: 0.182534 2.48036 -5.38492
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+DEAL::  shape 4,7: -0.0528793 2.55515 -0.325241
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+DEAL::  shape 7,7: -0.0289967 1.54587 0.330848
+DEAL::  shape 8,7: 0.228571 -12.1856 1.40586
+DEAL::  JxW(8): 0.00354456
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+DEAL::  shape 8,8: 0.228571 12.1856 -1.40586
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+DEAL::  shape 1,9: 0.0125882 -0.143629 0.143629
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+DEAL::  shape 8,9: 0.782186 4.81094 -4.81094
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+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
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+DEAL::  shape 3,10: 0.0518856 1.53067 1.53067
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  shape 4,11: -0.0528793 2.55515 0.325241
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+DEAL::  JxW(13): 0.00354456
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+DEAL::  shape 8,13: 0.228571 1.40586 -12.1856
+DEAL::  JxW(14): 0.00354456
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+DEAL::  shape 1,14: -0.0136193 -0.401782 0.658089
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+DEAL::  JxW(15): 0.00189067
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+DEAL::  shape 1,15: -0.0479127 -0.651062 2.31516
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+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
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+DEAL::Cell: 2.6
+DEAL::  center: 0.625000 0.375000
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  JxW(3): 0.00189067
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::Cell: 2.7
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+DEAL::  JxW(3): 0.00189067
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+DEAL::  shape 0,3: -0.0479127 2.31516 0.651062
+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  shape 1,4: -0.0136193 -0.658089 0.401782
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+DEAL::  shape 6,13: -0.0528793 -0.325241 2.55515
+DEAL::  shape 7,13: 0.708721 4.35908 9.63045
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+DEAL::  JxW(15): 0.00189067
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+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
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+DEAL::Cell: 2.9
+DEAL::  center: 0.375000 0.625000
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+DEAL::  shape 6,1: 0.708721 4.35908 -9.63045
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  shape 1,5: -0.0255567 0.291598 0.753947
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+DEAL::  shape 3,10: 0.0518856 1.53067 1.53067
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+DEAL::  shape 6,10: -0.0992284 0.610317 -1.13218
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  shape 1,14: -0.0136193 -0.401782 0.658089
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+DEAL::Cell: 2.11
+DEAL::  center: 0.375000 0.875000
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  JxW(3): 0.00189067
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  JxW(7): 0.00354456
+DEAL::  p(7): 0.732642 0.582502
+DEAL::  shape 0,7: -0.0136193 0.658089 0.401782
+DEAL::  shape 1,7: 0.182534 2.48036 -5.38492
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+DEAL::  shape 3,7: -0.0899086 -1.22172 1.02584
+DEAL::  shape 4,7: -0.0528793 2.55515 -0.325241
+DEAL::  shape 5,7: 0.708721 9.63045 4.35908
+DEAL::  shape 6,7: 0.0588695 -3.13845 -1.73671
+DEAL::  shape 7,7: -0.0289967 1.54587 0.330848
+DEAL::  shape 8,7: 0.228571 -12.1856 1.40586
+DEAL::  JxW(8): 0.00354456
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+DEAL::  shape 8,8: 0.228571 12.1856 -1.40586
+DEAL::  JxW(9): 0.00664521
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+DEAL::  shape 1,9: 0.0125882 -0.143629 0.143629
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+DEAL::  shape 5,9: -0.0992284 1.13218 0.610317
+DEAL::  shape 6,9: -0.0992284 -0.610317 -1.13218
+DEAL::  shape 7,9: 0.201455 1.23908 5.94312
+DEAL::  shape 8,9: 0.782186 4.81094 -4.81094
+DEAL::  JxW(10): 0.00664521
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+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  shape 8,11: 0.228571 -12.1856 -1.40586
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+DEAL::  shape 6,12: -0.0154525 -0.823801 0.746669
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+DEAL::  JxW(13): 0.00354456
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+DEAL::  shape 6,14: -0.0528793 0.325241 2.55515
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+DEAL::  JxW(15): 0.00189067
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+DEAL::Cell: 2.13
+DEAL::  center: 0.875000 0.625000
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  shape 7,3: -0.0154525 0.823801 -0.746669
+DEAL::  shape 8,3: 0.0667934 -3.56089 3.56089
+DEAL::  JxW(4): 0.00354456
+DEAL::  p(4): 0.517358 0.832502
+DEAL::  shape 0,4: 0.182534 -2.48036 -5.38492
+DEAL::  shape 1,4: -0.0136193 -0.658089 0.401782
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+DEAL::  shape 7,4: -0.0289967 -1.54587 0.330848
+DEAL::  shape 8,4: 0.228571 12.1856 1.40586
+DEAL::  JxW(5): 0.00664521
+DEAL::  p(5): 0.582502 0.832502
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+DEAL::  shape 1,5: -0.0255567 0.291598 0.753947
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+DEAL::  shape 5,5: -0.0992284 1.13218 -0.610317
+DEAL::  shape 6,5: 0.201455 1.23908 -5.94312
+DEAL::  shape 7,5: -0.0992284 -0.610317 1.13218
+DEAL::  shape 8,5: 0.782186 4.81094 4.81094
+DEAL::  JxW(6): 0.00664521
+DEAL::  p(6): 0.667498 0.832502
+DEAL::  shape 0,6: -0.0255567 -0.291598 0.753947
+DEAL::  shape 1,6: 0.0518856 1.53067 -1.53067
+DEAL::  shape 2,6: 0.0125882 0.143629 -0.143629
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+DEAL::  shape 4,6: -0.0992284 -1.13218 -0.610317
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+DEAL::  shape 6,6: 0.201455 -1.23908 -5.94312
+DEAL::  shape 7,6: -0.0992284 0.610317 1.13218
+DEAL::  shape 8,6: 0.782186 -4.81094 4.81094
+DEAL::  JxW(7): 0.00354456
+DEAL::  p(7): 0.732642 0.832502
+DEAL::  shape 0,7: -0.0136193 0.658089 0.401782
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+DEAL::  shape 4,7: -0.0528793 2.55515 -0.325241
+DEAL::  shape 5,7: 0.708721 9.63045 4.35908
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+DEAL::  shape 7,7: -0.0289967 1.54587 0.330848
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+DEAL::  JxW(8): 0.00354456
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+DEAL::  shape 1,8: 0.00670829 0.324147 0.0765406
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+DEAL::  JxW(9): 0.00664521
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+DEAL::  shape 1,9: 0.0125882 -0.143629 0.143629
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+DEAL::  shape 6,9: -0.0992284 -0.610317 -1.13218
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+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
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+DEAL::  shape 3,10: 0.0518856 1.53067 1.53067
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+DEAL::  shape 6,10: -0.0992284 0.610317 -1.13218
+DEAL::  shape 7,10: 0.201455 -1.23908 5.94312
+DEAL::  shape 8,10: 0.782186 -4.81094 -4.81094
+DEAL::  JxW(11): 0.00354456
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  shape 5,11: 0.708721 9.63045 -4.35908
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+DEAL::  shape 7,11: 0.0588695 -3.13845 1.73671
+DEAL::  shape 8,11: 0.228571 -12.1856 -1.40586
+DEAL::  JxW(12): 0.00189067
+DEAL::  p(12): 0.517358 0.982642
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+DEAL::  shape 1,12: 0.00357488 0.172740 -0.172740
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+DEAL::  shape 3,12: -0.0479127 -2.31516 -0.651062
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+DEAL::  shape 6,12: -0.0154525 -0.823801 0.746669
+DEAL::  shape 7,12: 0.207103 11.0411 2.81422
+DEAL::  shape 8,12: 0.0667934 3.56089 -3.56089
+DEAL::  JxW(13): 0.00354456
+DEAL::  p(13): 0.582502 0.982642
+DEAL::  shape 0,13: -0.0136193 0.401782 0.658089
+DEAL::  shape 1,13: 0.00670829 -0.0765406 -0.324147
+DEAL::  shape 2,13: 0.182534 -5.38492 2.48036
+DEAL::  shape 3,13: -0.0899086 1.02584 -1.22172
+DEAL::  shape 4,13: 0.0588695 -1.73671 -3.13845
+DEAL::  shape 5,13: -0.0289967 0.330848 1.54587
+DEAL::  shape 6,13: -0.0528793 -0.325241 2.55515
+DEAL::  shape 7,13: 0.708721 4.35908 9.63045
+DEAL::  shape 8,13: 0.228571 1.40586 -12.1856
+DEAL::  JxW(14): 0.00354456
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+DEAL::  shape 6,14: -0.0528793 0.325241 2.55515
+DEAL::  shape 7,14: 0.708721 -4.35908 9.63045
+DEAL::  shape 8,14: 0.228571 -1.40586 -12.1856
+DEAL::  JxW(15): 0.00189067
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+DEAL::  shape 1,15: -0.0479127 -0.651062 2.31516
+DEAL::  shape 2,15: -0.0479127 2.31516 -0.651062
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+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
+DEAL::  shape 8,15: 0.0667934 -3.56089 -3.56089
+DEAL::Cell: 2.15
+DEAL::  center: 0.875000 0.875000
+DEAL::  JxW(0): 0.00189067
+DEAL::  p(0): 0.767358 0.767358
+DEAL::  shape 0,0: 0.642155 -8.72593 -8.72593
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+DEAL::  shape 2,0: -0.0479127 0.651062 -2.31516
+DEAL::  shape 3,0: 0.00357488 0.172740 0.172740
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+DEAL::  shape 5,0: -0.0154525 -0.746669 -0.823801
+DEAL::  shape 6,0: 0.207103 11.0411 -2.81422
+DEAL::  shape 7,0: -0.0154525 -0.823801 -0.746669
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+DEAL::  JxW(1): 0.00354456
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+DEAL::  shape 1,1: -0.0899086 1.02584 1.22172
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+DEAL::  shape 7,1: -0.0528793 -0.325241 -2.55515
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 0,2: -0.0899086 -1.02584 1.22172
+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  shape 7,2: -0.0528793 0.325241 -2.55515
+DEAL::  shape 8,2: 0.228571 -1.40586 12.1856
+DEAL::  JxW(3): 0.00189067
+DEAL::  p(3): 0.982642 0.767358
+DEAL::  shape 0,3: -0.0479127 2.31516 0.651062
+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  JxW(4): 0.00354456
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+DEAL::  JxW(5): 0.00664521
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+DEAL::  shape 6,5: 0.201455 1.23908 -5.94312
+DEAL::  shape 7,5: -0.0992284 -0.610317 1.13218
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+DEAL::  JxW(6): 0.00664521
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+DEAL::  shape 1,6: 0.0518856 1.53067 -1.53067
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+DEAL::  JxW(7): 0.00354456
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+DEAL::  JxW(8): 0.00354456
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+DEAL::  shape 8,9: 0.782186 4.81094 -4.81094
+DEAL::  JxW(10): 0.00664521
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+DEAL::  JxW(11): 0.00354456
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+DEAL::  shape 6,12: -0.0154525 -0.823801 0.746669
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+DEAL::  JxW(13): 0.00354456
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+DEAL::  shape 8,13: 0.228571 1.40586 -12.1856
+DEAL::  JxW(14): 0.00354456
+DEAL::  p(14): 0.917498 0.982642
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+DEAL::  shape 8,14: 0.228571 -1.40586 -12.1856
+DEAL::  JxW(15): 0.00189067
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+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
+DEAL::  shape 8,15: 0.0667934 -3.56089 -3.56089
+DEAL::OK
+DEAL::
+DEAL::Testing dim=2, spacedim=2
+DEAL::Cell: 2.0
+DEAL::  center: 0.125000 0.125000
+DEAL::  JxW(0): 0.00189067
+DEAL::  p(0): 0.0173580 0.0173580
+DEAL::  shape 0,0: 0.642155 -8.72593 -8.72593
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+DEAL::  shape 2,0: -0.0479127 0.651062 -2.31516
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+DEAL::  shape 1,1: -0.0899086 1.02584 1.22172
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+DEAL::  shape 6,1: 0.708721 4.35908 -9.63045
+DEAL::  shape 7,1: -0.0528793 -0.325241 -2.55515
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  JxW(3): 0.00189067
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+DEAL::  shape 0,3: -0.0479127 2.31516 0.651062
+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  shape 1,4: -0.0136193 -0.658089 0.401782
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+DEAL::  shape 1,5: -0.0255567 0.291598 0.753947
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+DEAL::Cell: 2.1
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+DEAL::  shape 6,13: -0.0528793 -0.325241 2.55515
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+DEAL::  shape 6,15: -0.0154525 0.823801 0.746669
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+DEAL::Cell: 2.2
+DEAL::  center: 0.125000 0.375000
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+DEAL::  p(0): 0.0173580 0.267358
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+DEAL::  shape 1,1: -0.0899086 1.02584 1.22172
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  JxW(10): 0.00664521
+DEAL::  p(10): 0.417498 0.417498
+DEAL::  shape 0,10: 0.0125882 0.143629 0.143629
+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
+DEAL::  shape 2,10: -0.0255567 -0.291598 -0.753947
+DEAL::  shape 3,10: 0.0518856 1.53067 1.53067
+DEAL::  shape 4,10: -0.0992284 -1.13218 0.610317
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+DEAL::  shape 6,10: -0.0992284 0.610317 -1.13218
+DEAL::  shape 7,10: 0.201455 -1.23908 5.94312
+DEAL::  shape 8,10: 0.782186 -4.81094 -4.81094
+DEAL::  JxW(11): 0.00354456
+DEAL::  p(11): 0.482642 0.417498
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
+DEAL::  shape 2,11: -0.0136193 0.658089 -0.401782
+DEAL::  shape 3,11: 0.182534 2.48036 5.38492
+DEAL::  shape 4,11: -0.0528793 2.55515 0.325241
+DEAL::  shape 5,11: 0.708721 9.63045 -4.35908
+DEAL::  shape 6,11: -0.0289967 1.54587 -0.330848
+DEAL::  shape 7,11: 0.0588695 -3.13845 1.73671
+DEAL::  shape 8,11: 0.228571 -12.1856 -1.40586
+DEAL::  JxW(12): 0.00189067
+DEAL::  p(12): 0.267358 0.482642
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+DEAL::  shape 1,12: 0.00357488 0.172740 -0.172740
+DEAL::  shape 2,12: 0.642155 -8.72593 8.72593
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+DEAL::  shape 6,12: -0.0154525 -0.823801 0.746669
+DEAL::  shape 7,12: 0.207103 11.0411 2.81422
+DEAL::  shape 8,12: 0.0667934 3.56089 -3.56089
+DEAL::  JxW(13): 0.00354456
+DEAL::  p(13): 0.332502 0.482642
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+DEAL::  shape 3,13: -0.0899086 1.02584 -1.22172
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+DEAL::  shape 5,13: -0.0289967 0.330848 1.54587
+DEAL::  shape 6,13: -0.0528793 -0.325241 2.55515
+DEAL::  shape 7,13: 0.708721 4.35908 9.63045
+DEAL::  shape 8,13: 0.228571 1.40586 -12.1856
+DEAL::  JxW(14): 0.00354456
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+DEAL::  shape 1,14: -0.0136193 -0.401782 0.658089
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+DEAL::  shape 6,14: -0.0528793 0.325241 2.55515
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+DEAL::  shape 8,14: 0.228571 -1.40586 -12.1856
+DEAL::  JxW(15): 0.00189067
+DEAL::  p(15): 0.482642 0.482642
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+DEAL::  shape 1,15: -0.0479127 -0.651062 2.31516
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+DEAL::  shape 6,15: -0.0154525 0.823801 0.746669
+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
+DEAL::  shape 8,15: 0.0667934 -3.56089 -3.56089
+DEAL::Cell: 2.4
+DEAL::  center: 0.625000 0.125000
+DEAL::  JxW(0): 0.00189067
+DEAL::  p(0): 0.517358 0.0173580
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+DEAL::  shape 7,0: -0.0154525 -0.823801 -0.746669
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+DEAL::  shape 1,1: -0.0899086 1.02584 1.22172
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+DEAL::  shape 6,1: 0.708721 4.35908 -9.63045
+DEAL::  shape 7,1: -0.0528793 -0.325241 -2.55515
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  shape 7,2: -0.0528793 0.325241 -2.55515
+DEAL::  shape 8,2: 0.228571 -1.40586 12.1856
+DEAL::  JxW(3): 0.00189067
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+DEAL::  shape 0,3: -0.0479127 2.31516 0.651062
+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  JxW(4): 0.00354456
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+DEAL::  JxW(5): 0.00664521
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+DEAL::Cell: 2.5
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+DEAL::  shape 8,6: 0.782186 -4.81094 4.81094
+DEAL::  JxW(7): 0.00354456
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+DEAL::  shape 0,7: -0.0136193 0.658089 0.401782
+DEAL::  shape 1,7: 0.182534 2.48036 -5.38492
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+DEAL::  shape 4,7: -0.0528793 2.55515 -0.325241
+DEAL::  shape 5,7: 0.708721 9.63045 4.35908
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+DEAL::  shape 7,7: -0.0289967 1.54587 0.330848
+DEAL::  shape 8,7: 0.228571 -12.1856 1.40586
+DEAL::  JxW(8): 0.00354456
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+DEAL::  shape 8,8: 0.228571 12.1856 -1.40586
+DEAL::  JxW(9): 0.00664521
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+DEAL::  shape 1,9: 0.0125882 -0.143629 0.143629
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+DEAL::  shape 6,9: -0.0992284 -0.610317 -1.13218
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+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  JxW(15): 0.00189067
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+DEAL::  shape 1,15: -0.0479127 -0.651062 2.31516
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+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
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+DEAL::  center: 0.625000 0.375000
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  shape 6,3: 0.207103 -11.0411 -2.81422
+DEAL::  shape 7,3: -0.0154525 0.823801 -0.746669
+DEAL::  shape 8,3: 0.0667934 -3.56089 3.56089
+DEAL::  JxW(4): 0.00354456
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+DEAL::  shape 1,4: -0.0136193 -0.658089 0.401782
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+DEAL::  shape 7,4: -0.0289967 -1.54587 0.330848
+DEAL::  shape 8,4: 0.228571 12.1856 1.40586
+DEAL::  JxW(5): 0.00664521
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+DEAL::  shape 1,5: -0.0255567 0.291598 0.753947
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+DEAL::  shape 5,5: -0.0992284 1.13218 -0.610317
+DEAL::  shape 6,5: 0.201455 1.23908 -5.94312
+DEAL::  shape 7,5: -0.0992284 -0.610317 1.13218
+DEAL::  shape 8,5: 0.782186 4.81094 4.81094
+DEAL::  JxW(6): 0.00664521
+DEAL::  p(6): 0.917498 0.332502
+DEAL::  shape 0,6: -0.0255567 -0.291598 0.753947
+DEAL::  shape 1,6: 0.0518856 1.53067 -1.53067
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+DEAL::  shape 1,7: 0.182534 2.48036 -5.38492
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+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  shape 1,12: 0.00357488 0.172740 -0.172740
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::Cell: 2.9
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+DEAL::  shape 1,1: -0.0899086 1.02584 1.22172
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+DEAL::  shape 6,1: 0.708721 4.35908 -9.63045
+DEAL::  shape 7,1: -0.0528793 -0.325241 -2.55515
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 0,2: -0.0899086 -1.02584 1.22172
+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  shape 7,2: -0.0528793 0.325241 -2.55515
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+DEAL::  JxW(3): 0.00189067
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+DEAL::  shape 0,3: -0.0479127 2.31516 0.651062
+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  shape 1,4: -0.0136193 -0.658089 0.401782
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+DEAL::  shape 7,4: -0.0289967 -1.54587 0.330848
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+DEAL::  shape 1,5: -0.0255567 0.291598 0.753947
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+DEAL::  shape 5,5: -0.0992284 1.13218 -0.610317
+DEAL::  shape 6,5: 0.201455 1.23908 -5.94312
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+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
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+DEAL::Cell: 2.11
+DEAL::  center: 0.375000 0.875000
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+DEAL::  JxW(2): 0.00354456
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  JxW(10): 0.00664521
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+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
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+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  shape 8,11: 0.228571 -12.1856 -1.40586
+DEAL::  JxW(12): 0.00189067
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+DEAL::  JxW(13): 0.00354456
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+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
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+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
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+DEAL::  shape 6,6: 0.201455 -1.23908 -5.94312
+DEAL::  shape 7,6: -0.0992284 0.610317 1.13218
+DEAL::  shape 8,6: 0.782186 -4.81094 4.81094
+DEAL::  JxW(7): 0.00354456
+DEAL::  p(7): 0.732642 0.832502
+DEAL::  shape 0,7: -0.0136193 0.658089 0.401782
+DEAL::  shape 1,7: 0.182534 2.48036 -5.38492
+DEAL::  shape 2,7: 0.00670829 -0.324147 -0.0765406
+DEAL::  shape 3,7: -0.0899086 -1.22172 1.02584
+DEAL::  shape 4,7: -0.0528793 2.55515 -0.325241
+DEAL::  shape 5,7: 0.708721 9.63045 4.35908
+DEAL::  shape 6,7: 0.0588695 -3.13845 -1.73671
+DEAL::  shape 7,7: -0.0289967 1.54587 0.330848
+DEAL::  shape 8,7: 0.228571 -12.1856 1.40586
+DEAL::  JxW(8): 0.00354456
+DEAL::  p(8): 0.517358 0.917498
+DEAL::  shape 0,8: -0.0899086 1.22172 -1.02584
+DEAL::  shape 1,8: 0.00670829 0.324147 0.0765406
+DEAL::  shape 2,8: 0.182534 -2.48036 5.38492
+DEAL::  shape 3,8: -0.0136193 -0.658089 -0.401782
+DEAL::  shape 4,8: 0.708721 -9.63045 -4.35908
+DEAL::  shape 5,8: -0.0528793 -2.55515 0.325241
+DEAL::  shape 6,8: -0.0289967 -1.54587 -0.330848
+DEAL::  shape 7,8: 0.0588695 3.13845 1.73671
+DEAL::  shape 8,8: 0.228571 12.1856 -1.40586
+DEAL::  JxW(9): 0.00664521
+DEAL::  p(9): 0.582502 0.917498
+DEAL::  shape 0,9: -0.0255567 0.753947 -0.291598
+DEAL::  shape 1,9: 0.0125882 -0.143629 0.143629
+DEAL::  shape 2,9: 0.0518856 -1.53067 1.53067
+DEAL::  shape 3,9: -0.0255567 0.291598 -0.753947
+DEAL::  shape 4,9: 0.201455 -5.94312 -1.23908
+DEAL::  shape 5,9: -0.0992284 1.13218 0.610317
+DEAL::  shape 6,9: -0.0992284 -0.610317 -1.13218
+DEAL::  shape 7,9: 0.201455 1.23908 5.94312
+DEAL::  shape 8,9: 0.782186 4.81094 -4.81094
+DEAL::  JxW(10): 0.00664521
+DEAL::  p(10): 0.667498 0.917498
+DEAL::  shape 0,10: 0.0125882 0.143629 0.143629
+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
+DEAL::  shape 2,10: -0.0255567 -0.291598 -0.753947
+DEAL::  shape 3,10: 0.0518856 1.53067 1.53067
+DEAL::  shape 4,10: -0.0992284 -1.13218 0.610317
+DEAL::  shape 5,10: 0.201455 5.94312 -1.23908
+DEAL::  shape 6,10: -0.0992284 0.610317 -1.13218
+DEAL::  shape 7,10: 0.201455 -1.23908 5.94312
+DEAL::  shape 8,10: 0.782186 -4.81094 -4.81094
+DEAL::  JxW(11): 0.00354456
+DEAL::  p(11): 0.732642 0.917498
+DEAL::  shape 0,11: 0.00670829 -0.324147 0.0765406
+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
+DEAL::  shape 2,11: -0.0136193 0.658089 -0.401782
+DEAL::  shape 3,11: 0.182534 2.48036 5.38492
+DEAL::  shape 4,11: -0.0528793 2.55515 0.325241
+DEAL::  shape 5,11: 0.708721 9.63045 -4.35908
+DEAL::  shape 6,11: -0.0289967 1.54587 -0.330848
+DEAL::  shape 7,11: 0.0588695 -3.13845 1.73671
+DEAL::  shape 8,11: 0.228571 -12.1856 -1.40586
+DEAL::  JxW(12): 0.00189067
+DEAL::  p(12): 0.517358 0.982642
+DEAL::  shape 0,12: -0.0479127 0.651062 2.31516
+DEAL::  shape 1,12: 0.00357488 0.172740 -0.172740
+DEAL::  shape 2,12: 0.642155 -8.72593 8.72593
+DEAL::  shape 3,12: -0.0479127 -2.31516 -0.651062
+DEAL::  shape 4,12: 0.207103 -2.81422 -11.0411
+DEAL::  shape 5,12: -0.0154525 -0.746669 0.823801
+DEAL::  shape 6,12: -0.0154525 -0.823801 0.746669
+DEAL::  shape 7,12: 0.207103 11.0411 2.81422
+DEAL::  shape 8,12: 0.0667934 3.56089 -3.56089
+DEAL::  JxW(13): 0.00354456
+DEAL::  p(13): 0.582502 0.982642
+DEAL::  shape 0,13: -0.0136193 0.401782 0.658089
+DEAL::  shape 1,13: 0.00670829 -0.0765406 -0.324147
+DEAL::  shape 2,13: 0.182534 -5.38492 2.48036
+DEAL::  shape 3,13: -0.0899086 1.02584 -1.22172
+DEAL::  shape 4,13: 0.0588695 -1.73671 -3.13845
+DEAL::  shape 5,13: -0.0289967 0.330848 1.54587
+DEAL::  shape 6,13: -0.0528793 -0.325241 2.55515
+DEAL::  shape 7,13: 0.708721 4.35908 9.63045
+DEAL::  shape 8,13: 0.228571 1.40586 -12.1856
+DEAL::  JxW(14): 0.00354456
+DEAL::  p(14): 0.667498 0.982642
+DEAL::  shape 0,14: 0.00670829 0.0765406 -0.324147
+DEAL::  shape 1,14: -0.0136193 -0.401782 0.658089
+DEAL::  shape 2,14: -0.0899086 -1.02584 -1.22172
+DEAL::  shape 3,14: 0.182534 5.38492 2.48036
+DEAL::  shape 4,14: -0.0289967 -0.330848 1.54587
+DEAL::  shape 5,14: 0.0588695 1.73671 -3.13845
+DEAL::  shape 6,14: -0.0528793 0.325241 2.55515
+DEAL::  shape 7,14: 0.708721 -4.35908 9.63045
+DEAL::  shape 8,14: 0.228571 -1.40586 -12.1856
+DEAL::  JxW(15): 0.00189067
+DEAL::  p(15): 0.732642 0.982642
+DEAL::  shape 0,15: 0.00357488 -0.172740 -0.172740
+DEAL::  shape 1,15: -0.0479127 -0.651062 2.31516
+DEAL::  shape 2,15: -0.0479127 2.31516 -0.651062
+DEAL::  shape 3,15: 0.642155 8.72593 8.72593
+DEAL::  shape 4,15: -0.0154525 0.746669 0.823801
+DEAL::  shape 5,15: 0.207103 2.81422 -11.0411
+DEAL::  shape 6,15: -0.0154525 0.823801 0.746669
+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
+DEAL::  shape 8,15: 0.0667934 -3.56089 -3.56089
+DEAL::Cell: 2.15
+DEAL::  center: 0.875000 0.875000
+DEAL::  JxW(0): 0.00189067
+DEAL::  p(0): 0.767358 0.767358
+DEAL::  shape 0,0: 0.642155 -8.72593 -8.72593
+DEAL::  shape 1,0: -0.0479127 -2.31516 0.651062
+DEAL::  shape 2,0: -0.0479127 0.651062 -2.31516
+DEAL::  shape 3,0: 0.00357488 0.172740 0.172740
+DEAL::  shape 4,0: 0.207103 -2.81422 11.0411
+DEAL::  shape 5,0: -0.0154525 -0.746669 -0.823801
+DEAL::  shape 6,0: 0.207103 11.0411 -2.81422
+DEAL::  shape 7,0: -0.0154525 -0.823801 -0.746669
+DEAL::  shape 8,0: 0.0667934 3.56089 3.56089
+DEAL::  JxW(1): 0.00354456
+DEAL::  p(1): 0.832502 0.767358
+DEAL::  shape 0,1: 0.182534 -5.38492 -2.48036
+DEAL::  shape 1,1: -0.0899086 1.02584 1.22172
+DEAL::  shape 2,1: -0.0136193 0.401782 -0.658089
+DEAL::  shape 3,1: 0.00670829 -0.0765406 0.324147
+DEAL::  shape 4,1: 0.0588695 -1.73671 3.13845
+DEAL::  shape 5,1: -0.0289967 0.330848 -1.54587
+DEAL::  shape 6,1: 0.708721 4.35908 -9.63045
+DEAL::  shape 7,1: -0.0528793 -0.325241 -2.55515
+DEAL::  shape 8,1: 0.228571 1.40586 12.1856
+DEAL::  JxW(2): 0.00354456
+DEAL::  p(2): 0.917498 0.767358
+DEAL::  shape 0,2: -0.0899086 -1.02584 1.22172
+DEAL::  shape 1,2: 0.182534 5.38492 -2.48036
+DEAL::  shape 2,2: 0.00670829 0.0765406 0.324147
+DEAL::  shape 3,2: -0.0136193 -0.401782 -0.658089
+DEAL::  shape 4,2: -0.0289967 -0.330848 -1.54587
+DEAL::  shape 5,2: 0.0588695 1.73671 3.13845
+DEAL::  shape 6,2: 0.708721 -4.35908 -9.63045
+DEAL::  shape 7,2: -0.0528793 0.325241 -2.55515
+DEAL::  shape 8,2: 0.228571 -1.40586 12.1856
+DEAL::  JxW(3): 0.00189067
+DEAL::  p(3): 0.982642 0.767358
+DEAL::  shape 0,3: -0.0479127 2.31516 0.651062
+DEAL::  shape 1,3: 0.642155 8.72593 -8.72593
+DEAL::  shape 2,3: 0.00357488 -0.172740 0.172740
+DEAL::  shape 3,3: -0.0479127 -0.651062 -2.31516
+DEAL::  shape 4,3: -0.0154525 0.746669 -0.823801
+DEAL::  shape 5,3: 0.207103 2.81422 11.0411
+DEAL::  shape 6,3: 0.207103 -11.0411 -2.81422
+DEAL::  shape 7,3: -0.0154525 0.823801 -0.746669
+DEAL::  shape 8,3: 0.0667934 -3.56089 3.56089
+DEAL::  JxW(4): 0.00354456
+DEAL::  p(4): 0.767358 0.832502
+DEAL::  shape 0,4: 0.182534 -2.48036 -5.38492
+DEAL::  shape 1,4: -0.0136193 -0.658089 0.401782
+DEAL::  shape 2,4: -0.0899086 1.22172 1.02584
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+DEAL::  shape 5,4: -0.0528793 -2.55515 -0.325241
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+DEAL::  shape 7,4: -0.0289967 -1.54587 0.330848
+DEAL::  shape 8,4: 0.228571 12.1856 1.40586
+DEAL::  JxW(5): 0.00664521
+DEAL::  p(5): 0.832502 0.832502
+DEAL::  shape 0,5: 0.0518856 -1.53067 -1.53067
+DEAL::  shape 1,5: -0.0255567 0.291598 0.753947
+DEAL::  shape 2,5: -0.0255567 0.753947 0.291598
+DEAL::  shape 3,5: 0.0125882 -0.143629 -0.143629
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+DEAL::  shape 5,5: -0.0992284 1.13218 -0.610317
+DEAL::  shape 6,5: 0.201455 1.23908 -5.94312
+DEAL::  shape 7,5: -0.0992284 -0.610317 1.13218
+DEAL::  shape 8,5: 0.782186 4.81094 4.81094
+DEAL::  JxW(6): 0.00664521
+DEAL::  p(6): 0.917498 0.832502
+DEAL::  shape 0,6: -0.0255567 -0.291598 0.753947
+DEAL::  shape 1,6: 0.0518856 1.53067 -1.53067
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+DEAL::  shape 3,6: -0.0255567 -0.753947 0.291598
+DEAL::  shape 4,6: -0.0992284 -1.13218 -0.610317
+DEAL::  shape 5,6: 0.201455 5.94312 1.23908
+DEAL::  shape 6,6: 0.201455 -1.23908 -5.94312
+DEAL::  shape 7,6: -0.0992284 0.610317 1.13218
+DEAL::  shape 8,6: 0.782186 -4.81094 4.81094
+DEAL::  JxW(7): 0.00354456
+DEAL::  p(7): 0.982642 0.832502
+DEAL::  shape 0,7: -0.0136193 0.658089 0.401782
+DEAL::  shape 1,7: 0.182534 2.48036 -5.38492
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+DEAL::  shape 4,7: -0.0528793 2.55515 -0.325241
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+DEAL::  shape 6,7: 0.0588695 -3.13845 -1.73671
+DEAL::  shape 7,7: -0.0289967 1.54587 0.330848
+DEAL::  shape 8,7: 0.228571 -12.1856 1.40586
+DEAL::  JxW(8): 0.00354456
+DEAL::  p(8): 0.767358 0.917498
+DEAL::  shape 0,8: -0.0899086 1.22172 -1.02584
+DEAL::  shape 1,8: 0.00670829 0.324147 0.0765406
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+DEAL::  shape 5,8: -0.0528793 -2.55515 0.325241
+DEAL::  shape 6,8: -0.0289967 -1.54587 -0.330848
+DEAL::  shape 7,8: 0.0588695 3.13845 1.73671
+DEAL::  shape 8,8: 0.228571 12.1856 -1.40586
+DEAL::  JxW(9): 0.00664521
+DEAL::  p(9): 0.832502 0.917498
+DEAL::  shape 0,9: -0.0255567 0.753947 -0.291598
+DEAL::  shape 1,9: 0.0125882 -0.143629 0.143629
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+DEAL::  shape 3,9: -0.0255567 0.291598 -0.753947
+DEAL::  shape 4,9: 0.201455 -5.94312 -1.23908
+DEAL::  shape 5,9: -0.0992284 1.13218 0.610317
+DEAL::  shape 6,9: -0.0992284 -0.610317 -1.13218
+DEAL::  shape 7,9: 0.201455 1.23908 5.94312
+DEAL::  shape 8,9: 0.782186 4.81094 -4.81094
+DEAL::  JxW(10): 0.00664521
+DEAL::  p(10): 0.917498 0.917498
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+DEAL::  shape 1,10: -0.0255567 -0.753947 -0.291598
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+DEAL::  shape 3,10: 0.0518856 1.53067 1.53067
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+DEAL::  shape 5,10: 0.201455 5.94312 -1.23908
+DEAL::  shape 6,10: -0.0992284 0.610317 -1.13218
+DEAL::  shape 7,10: 0.201455 -1.23908 5.94312
+DEAL::  shape 8,10: 0.782186 -4.81094 -4.81094
+DEAL::  JxW(11): 0.00354456
+DEAL::  p(11): 0.982642 0.917498
+DEAL::  shape 0,11: 0.00670829 -0.324147 0.0765406
+DEAL::  shape 1,11: -0.0899086 -1.22172 -1.02584
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+DEAL::  shape 3,11: 0.182534 2.48036 5.38492
+DEAL::  shape 4,11: -0.0528793 2.55515 0.325241
+DEAL::  shape 5,11: 0.708721 9.63045 -4.35908
+DEAL::  shape 6,11: -0.0289967 1.54587 -0.330848
+DEAL::  shape 7,11: 0.0588695 -3.13845 1.73671
+DEAL::  shape 8,11: 0.228571 -12.1856 -1.40586
+DEAL::  JxW(12): 0.00189067
+DEAL::  p(12): 0.767358 0.982642
+DEAL::  shape 0,12: -0.0479127 0.651062 2.31516
+DEAL::  shape 1,12: 0.00357488 0.172740 -0.172740
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+DEAL::  shape 3,12: -0.0479127 -2.31516 -0.651062
+DEAL::  shape 4,12: 0.207103 -2.81422 -11.0411
+DEAL::  shape 5,12: -0.0154525 -0.746669 0.823801
+DEAL::  shape 6,12: -0.0154525 -0.823801 0.746669
+DEAL::  shape 7,12: 0.207103 11.0411 2.81422
+DEAL::  shape 8,12: 0.0667934 3.56089 -3.56089
+DEAL::  JxW(13): 0.00354456
+DEAL::  p(13): 0.832502 0.982642
+DEAL::  shape 0,13: -0.0136193 0.401782 0.658089
+DEAL::  shape 1,13: 0.00670829 -0.0765406 -0.324147
+DEAL::  shape 2,13: 0.182534 -5.38492 2.48036
+DEAL::  shape 3,13: -0.0899086 1.02584 -1.22172
+DEAL::  shape 4,13: 0.0588695 -1.73671 -3.13845
+DEAL::  shape 5,13: -0.0289967 0.330848 1.54587
+DEAL::  shape 6,13: -0.0528793 -0.325241 2.55515
+DEAL::  shape 7,13: 0.708721 4.35908 9.63045
+DEAL::  shape 8,13: 0.228571 1.40586 -12.1856
+DEAL::  JxW(14): 0.00354456
+DEAL::  p(14): 0.917498 0.982642
+DEAL::  shape 0,14: 0.00670829 0.0765406 -0.324147
+DEAL::  shape 1,14: -0.0136193 -0.401782 0.658089
+DEAL::  shape 2,14: -0.0899086 -1.02584 -1.22172
+DEAL::  shape 3,14: 0.182534 5.38492 2.48036
+DEAL::  shape 4,14: -0.0289967 -0.330848 1.54587
+DEAL::  shape 5,14: 0.0588695 1.73671 -3.13845
+DEAL::  shape 6,14: -0.0528793 0.325241 2.55515
+DEAL::  shape 7,14: 0.708721 -4.35908 9.63045
+DEAL::  shape 8,14: 0.228571 -1.40586 -12.1856
+DEAL::  JxW(15): 0.00189067
+DEAL::  p(15): 0.982642 0.982642
+DEAL::  shape 0,15: 0.00357488 -0.172740 -0.172740
+DEAL::  shape 1,15: -0.0479127 -0.651062 2.31516
+DEAL::  shape 2,15: -0.0479127 2.31516 -0.651062
+DEAL::  shape 3,15: 0.642155 8.72593 8.72593
+DEAL::  shape 4,15: -0.0154525 0.746669 0.823801
+DEAL::  shape 5,15: 0.207103 2.81422 -11.0411
+DEAL::  shape 6,15: -0.0154525 0.823801 0.746669
+DEAL::  shape 7,15: 0.207103 -11.0411 2.81422
+DEAL::  shape 8,15: 0.0667934 -3.56089 -3.56089
+DEAL::OK
+DEAL::
-- 
2.39.5