Fix FEPointEvaluation for non-zero starting component

diff --git a/doc/news/changes/minor/20211001Gassmoeller b/doc/news/changes/minor/20211001Gassmoeller
new file mode 100644 (file)
index 0000000..d7d21d0
--- /dev/null
+++ b/doc/news/changes/minor/20211001Gassmoeller
@@ -0,0 +1,3 @@
+Fixed: The FEPointEvaluation class always evaluated a solution starting at the component 0 of the selected vector-valued base element, even if a different component was selected by the caller. This has been fixed to correctly start evaluating at the selected component.
+<br>
+(Rene Gassmoeller, 2021/10/01)

diff --git a/include/deal.II/matrix_free/fe_point_evaluation.h b/include/deal.II/matrix_free/fe_point_evaluation.h
index 5fd7f6cf6b13d5c3486d0c133e43b19aa8161dec..32aadd9e0aaaa5e2683088905e812df0bdb8cc32 100644 (file)
--- a/include/deal.II/matrix_free/fe_point_evaluation.h
+++ b/include/deal.II/matrix_free/fe_point_evaluation.h
@@ -653,6 +653,11 @@ private:
    */
   unsigned int dofs_per_component;
 
+  /**
+   * The first selected component in the active base element.
+   */
+  unsigned int component_in_base_element;
+
   /**
    * For complicated FiniteElement objects this variable informs us about
    * which unknowns actually carry degrees of freedom in the selected
@@ -742,6 +747,7 @@ FEPointEvaluation<n_components, dim, spacedim, Number>::FEPointEvaluation(
 
   bool         same_base_element   = true;
   unsigned int base_element_number = 0;
+  component_in_base_element        = 0;
   unsigned int component           = 0;
   for (; base_element_number < fe.n_base_elements(); ++base_element_number)
     if (component + fe.element_multiplicity(base_element_number) >
@@ -750,10 +756,12 @@ FEPointEvaluation<n_components, dim, spacedim, Number>::FEPointEvaluation(
         if (first_selected_component + n_components >
             component + fe.element_multiplicity(base_element_number))
           same_base_element = false;
+        component_in_base_element = first_selected_component - component;
         break;
       }
     else
       component += fe.element_multiplicity(base_element_number);
+
   if (fill_mapping_data_for_generic_points &&
       internal::FEPointEvaluation::is_fast_path_supported(
         fe, base_element_number) &&
@@ -868,7 +876,9 @@ FEPointEvaluation<n_components, dim, spacedim, Number>::evaluate(
         for (unsigned int i = 0; i < dofs_per_component; ++i)
           internal::FEPointEvaluation::
             EvaluatorTypeTraits<dim, n_components, Number>::read_value(
-              solution_values[renumber[comp * dofs_per_component + i]],
+              solution_values[renumber[(component_in_base_element + comp) *
+                                         dofs_per_component +
+                                       i]],
               comp,
               solution_renumbered[i]);
 

diff --git a/tests/matrix_free/point_evaluation_14.cc b/tests/matrix_free/point_evaluation_14.cc
new file mode 100644 (file)
index 0000000..b7cfe43
--- /dev/null
+++ b/tests/matrix_free/point_evaluation_14.cc
@@ -0,0 +1,160 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 - 2021 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.
+//
+// ---------------------------------------------------------------------
+
+
+// check FEPointEvaluation for vector-valued FE_Q and MappingQ
+// with a starting component in the middle of a vector-valued
+// base element.
+
+#include <deal.II/base/function_lib.h>
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/fe/mapping_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/vector.h>
+
+#include <deal.II/matrix_free/fe_point_evaluation.h>
+
+#include <deal.II/numerics/vector_tools.h>
+
+#include <iostream>
+
+#include "../tests.h"
+
+
+
+template <int dim>
+class MyFunction : public Function<dim>
+{
+public:
+  MyFunction()
+    : Function<dim>(dim)
+  {}
+
+  double
+  value(const Point<dim> &p, const unsigned int component) const override
+  {
+    return component + p[component];
+  }
+};
+
+
+
+template <int dim>
+void
+test(const unsigned int degree)
+{
+  using namespace dealii;
+  Triangulation<dim> tria;
+
+  if (dim > 1)
+    GridGenerator::hyper_shell(tria, Point<dim>(), 0.5, 1, 6);
+  else
+    GridGenerator::subdivided_hyper_cube(tria, 2, 0, 1);
+
+  MappingQ<dim> mapping(degree);
+  deallog << "Mapping of degree " << degree << std::endl;
+
+  std::vector<Point<dim>> unit_points;
+  for (unsigned int i = 0; i < 13; ++i)
+    {
+      Point<dim> p;
+      for (unsigned int d = 0; d < dim; ++d)
+        p[d] = static_cast<double>(i) / 17. + 0.015625 * d;
+      unit_points.push_back(p);
+    }
+
+  FESystem<dim> fe(FE_Q<dim>(degree), dim);
+  FEValues<dim> fe_values(mapping,
+                          fe,
+                          Quadrature<dim>(unit_points),
+                          update_values | update_gradients);
+
+  DoFHandler<dim> dof_handler(tria);
+  dof_handler.distribute_dofs(fe);
+  Vector<double> vector(dof_handler.n_dofs());
+
+  FEPointEvaluation<1, dim> evaluator(mapping,
+                                      fe,
+                                      update_values | update_gradients,
+                                      1);
+
+  VectorTools::interpolate(mapping, dof_handler, MyFunction<dim>(), vector);
+
+  std::vector<double>         solution_values(fe.dofs_per_cell);
+  std::vector<double>         function_values(unit_points.size());
+  std::vector<Tensor<1, dim>> function_gradients(unit_points.size());
+
+  FEValuesExtractors::Scalar extractor(1);
+
+  for (const auto &cell : dof_handler.active_cell_iterators())
+    {
+      fe_values.reinit(cell);
+      fe_values[extractor].get_function_values(vector, function_values);
+      fe_values[extractor].get_function_gradients(vector, function_gradients);
+
+      cell->get_dof_values(vector,
+                           solution_values.begin(),
+                           solution_values.end());
+
+      evaluator.reinit(cell, unit_points);
+      evaluator.evaluate(solution_values,
+                         EvaluationFlags::values | EvaluationFlags::gradients);
+
+      deallog << "Cell with center " << cell->center(true) << std::endl;
+      for (unsigned int i = 0; i < function_values.size(); ++i)
+        deallog << mapping.transform_unit_to_real_cell(cell, unit_points[i])
+                << ": " << evaluator.get_value(i) << " error value "
+                << (function_values[i] - evaluator.get_value(i))
+                << " error grad "
+                << (evaluator.get_gradient(i) - function_gradients[i]).norm()
+                << std::endl;
+
+      deallog << std::endl;
+
+      for (unsigned int i = 0; i < unit_points.size(); ++i)
+        {
+          evaluator.submit_value(evaluator.get_value(i), i);
+          evaluator.submit_gradient(evaluator.get_gradient(i), i);
+        }
+
+      evaluator.integrate(solution_values,
+                          EvaluationFlags::values | EvaluationFlags::gradients);
+
+      for (const auto i : solution_values)
+        deallog << i << " ";
+      deallog << std::endl;
+    }
+}
+
+
+
+int
+main()
+{
+  initlog();
+  deallog << std::setprecision(10);
+
+  test<2>(2);
+  test<2>(6);
+  test<3>(5);
+}

diff --git a/tests/matrix_free/point_evaluation_14.output b/tests/matrix_free/point_evaluation_14.output
new file mode 100644 (file)
index 0000000..b9203f5
--- /dev/null
+++ b/tests/matrix_free/point_evaluation_14.output
@@ -0,0 +1,292 @@
+
+DEAL::Mapping of degree 2
+DEAL::Cell with center 0.6495190528 0.3750000000
+DEAL::0.9921875000 0.000000000: 1.000000000 error value 0.000000000 error grad 0.000000000
+DEAL::0.9591965610 0.06332871922: 1.063328719 error value -2.220446049e-16 error grad 5.311767473e-16
+DEAL::0.9234265460 0.1210574346: 1.121057435 error value 0.000000000 error grad 6.206335383e-16
+DEAL::0.8851608469 0.1733497625: 1.173349762 error value -2.220446049e-16 error grad 1.696726283e-15
+DEAL::0.8446828558 0.2203693193: 1.220369319 error value 4.440892099e-16 error grad 8.005932085e-16
+DEAL::0.8022759646 0.2622797217: 1.262279722 error value 2.220446049e-16 error grad 3.885780586e-16
+DEAL::0.7582235654 0.2992445859: 1.299244586 error value -2.220446049e-16 error grad 2.220446049e-16
+DEAL::0.7128090500 0.3314275284: 1.331427528 error value 2.220446049e-16 error grad 1.276756478e-15
+DEAL::0.6663158106 0.3589921657: 1.358992166 error value 0.000000000 error grad 4.577566799e-16
+DEAL::0.6190272391 0.3821021142: 1.382102114 error value 0.000000000 error grad 3.376611507e-16
+DEAL::0.5712267275 0.4009209903: 1.400920990 error value 0.000000000 error grad 5.551115123e-16
+DEAL::0.5231976677 0.4156124105: 1.415612411 error value 2.220446049e-16 error grad 3.376611507e-16
+DEAL::0.4752234518 0.4263399913: 1.426339991 error value 0.000000000 error grad 1.093442870e-15
+DEAL::
+DEAL::-3.748628693 0.000000000 -3.173305599 0.000000000 1.519866565 0.000000000 0.3917604893 0.000000000 -15.07404237 0.000000000 9.522955246 0.000000000 20.12140751 0.000000000 -10.85961324 0.000000000 17.75462483 0.000000000 
+DEAL::Cell with center 4.592425497e-17 0.7500000000
+DEAL::0.4960937500 0.8592595803: 1.859259580 error value 0.000000000 error grad 1.494683490e-15
+DEAL::0.4247540009 0.8623529487: 1.862352949 error value -4.440892099e-16 error grad 8.881784197e-16
+DEAL::0.3568744593 0.8602395646: 1.860239565 error value -4.440892099e-16 error grad 1.558272272e-15
+DEAL::0.2924551254 0.8532466611: 1.853246661 error value -2.220446049e-16 error grad 1.578899528e-15
+DEAL::0.2314959991 0.8417014709: 1.841701471 error value 0.000000000 error grad 2.685271255e-15
+DEAL::0.1739970804 0.8259312270: 1.825931227 error value 0.000000000 error grad 8.496108186e-16
+DEAL::0.1199583694 0.8062631623: 1.806263162 error value 0.000000000 error grad 4.475452091e-16
+DEAL::0.06937986592 0.7830245096: 1.783024510 error value 0.000000000 error grad 2.444421742e-15
+DEAL::0.02226157007 0.7565425018: 1.756542502 error value 0.000000000 error grad 1.221324176e-15
+DEAL::-0.02139651817 0.7271443718: 1.727144372 error value 2.220446049e-16 error grad 1.119744856e-15
+DEAL::-0.06159439879 0.6951573525: 1.695157352 error value -2.220446049e-16 error grad 6.697380712e-16
+DEAL::-0.09833207180 0.6609086767: 1.660908677 error value 0.000000000 error grad 1.861072920e-15
+DEAL::-0.1316095372 0.6247255774: 1.624725577 error value 4.440892099e-16 error grad 3.911074787e-15
+DEAL::
+DEAL::19.05183452 0.000000000 -3.521816114 0.000000000 3.867266826 0.000000000 -1.808699521 0.000000000 -21.42003086 0.000000000 3.064029263 0.000000000 28.44238381 0.000000000 -14.80007062 0.000000000 10.28160031 0.000000000 
+DEAL::Cell with center -0.6495190528 0.3750000000
+DEAL::-0.4960937500 0.8592595803: 1.859259580 error value 0.000000000 error grad 1.489520492e-15
+DEAL::-0.5344425601 0.7990242294: 1.799024229 error value 0.000000000 error grad 1.294731410e-15
+DEAL::-0.5665520866 0.7391821301: 1.739182130 error value -4.440892099e-16 error grad 1.489520492e-15
+DEAL::-0.5927057215 0.6798968986: 1.679896899 error value 0.000000000 error grad 9.436895709e-16
+DEAL::-0.6131868567 0.6213321516: 1.621332152 error value -2.220446049e-16 error grad 2.715511107e-15
+DEAL::-0.6282788842 0.5636515054: 1.563651505 error value 2.220446049e-16 error grad 8.473409487e-16
+DEAL::-0.6382651960 0.5070185764: 1.507018576 error value -2.220446049e-16 error grad 2.775557562e-16
+DEAL::-0.6434291841 0.4515969812: 1.451596981 error value 0.000000000 error grad 9.305364598e-16
+DEAL::-0.6440542406 0.3975503361: 1.397550336 error value 0.000000000 error grad 5.389157964e-16
+DEAL::-0.6404237573 0.3450422576: 1.345042258 error value -2.220446049e-16 error grad 2.482534153e-16
+DEAL::-0.6328211262 0.2942363621: 1.294236362 error value -2.220446049e-16 error grad 4.965068306e-16
+DEAL::-0.6215297395 0.2452962662: 1.245296266 error value 2.220446049e-16 error grad 1.563208212e-15
+DEAL::-0.6068329890 0.1983855861: 1.198385586 error value -2.220446049e-16 error grad 8.881784197e-16
+DEAL::
+DEAL::25.40382863 0.000000000 -0.6719210962 0.000000000 1.968925409 0.000000000 -1.981597541 0.000000000 -4.837315045 0.000000000 -6.444343269 0.000000000 9.458322834 0.000000000 -3.780823029 0.000000000 0.5863959717 0.000000000 
+DEAL::Cell with center -0.6495190528 -0.3750000000
+DEAL::-0.9921875000 1.215079246e-16: 1.000000000 error value 0.000000000 error grad 6.507046391e-16
+DEAL::-0.9591965610 -0.06332871922: 0.9366712808 error value -1.110223025e-16 error grad 4.718447855e-16
+DEAL::-0.9234265460 -0.1210574346: 0.8789425654 error value 0.000000000 error grad 7.114312260e-16
+DEAL::-0.8851608469 -0.1733497625: 0.8266502375 error value -1.110223025e-16 error grad 2.618455767e-16
+DEAL::-0.8446828558 -0.2203693193: 0.7796306807 error value 0.000000000 error grad 1.005349708e-15
+DEAL::-0.8022759646 -0.2622797217: 0.7377202783 error value 0.000000000 error grad 8.400361490e-16
+DEAL::-0.7582235654 -0.2992445859: 0.7007554141 error value 1.110223025e-16 error grad 5.978733960e-16
+DEAL::-0.7128090500 -0.3314275284: 0.6685724716 error value -1.110223025e-16 error grad 4.577566799e-16
+DEAL::-0.6663158106 -0.3589921657: 0.6410078343 error value -1.110223025e-16 error grad 4.002966042e-16
+DEAL::-0.6190272391 -0.3821021142: 0.6178978858 error value -2.220446049e-16 error grad 2.989366980e-16
+DEAL::-0.5712267275 -0.4009209903: 0.5990790097 error value -1.110223025e-16 error grad 5.551115123e-16
+DEAL::-0.5231976677 -0.4156124105: 0.5843875895 error value 0.000000000 error grad 3.140184917e-16
+DEAL::-0.4752234518 -0.4263399913: 0.5736600087 error value 1.110223025e-16 error grad 1.691041330e-15
+DEAL::
+DEAL::8.955359530 0.000000000 2.526484436 0.000000000 -2.276816270 0.000000000 0.04596444941 0.000000000 18.09138927 0.000000000 -9.493789817 0.000000000 -17.84671444 0.000000000 11.17888194 0.000000000 -1.635783837 0.000000000 
+DEAL::Cell with center -1.377727649e-16 -0.7500000000
+DEAL::-0.4960937500 -0.8592595803: 0.1407404197 error value 0.000000000 error grad 1.002111781e-15
+DEAL::-0.4247540009 -0.8623529487: 0.1376470513 error value -2.775557562e-17 error grad 6.497413669e-16
+DEAL::-0.3568744593 -0.8602395646: 0.1397604354 error value 0.000000000 error grad 5.236911533e-16
+DEAL::-0.2924551254 -0.8532466611: 0.1467533389 error value 0.000000000 error grad 6.473657049e-16
+DEAL::-0.2314959991 -0.8417014709: 0.1582985291 error value 5.551115123e-17 error grad 4.002966042e-16
+DEAL::-0.1739970804 -0.8259312270: 0.1740687730 error value 0.000000000 error grad 2.775557562e-17
+DEAL::-0.1199583694 -0.8062631623: 0.1937368377 error value -2.775557562e-17 error grad 2.618455767e-16
+DEAL::-0.06937986592 -0.7830245096: 0.2169754904 error value 5.551115123e-17 error grad 3.510833469e-16
+DEAL::-0.02226157007 -0.7565425018: 0.2434574982 error value 0.000000000 error grad 4.518280360e-16
+DEAL::0.02139651817 -0.7271443718: 0.2728556282 error value 0.000000000 error grad 2.177751705e-16
+DEAL::0.06159439879 -0.6951573525: 0.3048426475 error value 5.551115123e-17 error grad 0.000000000
+DEAL::0.09833207180 -0.6609086767: 0.3390913233 error value -5.551115123e-17 error grad 2.618455767e-16
+DEAL::0.1316095372 -0.6247255774: 0.3752744226 error value -5.551115123e-17 error grad 7.108895958e-16
+DEAL::
+DEAL::-13.84510368 0.000000000 2.874994950 0.000000000 -4.624216531 0.000000000 2.246424460 0.000000000 24.43737776 0.000000000 -3.034863834 0.000000000 -26.16769073 0.000000000 15.11933931 0.000000000 5.837240688 0.000000000 
+DEAL::Cell with center 0.6495190528 -0.3750000000
+DEAL::0.4960937500 -0.8592595803: 0.1407404197 error value 0.000000000 error grad 5.613217784e-16
+DEAL::0.5344425601 -0.7990242294: 0.2009757706 error value 0.000000000 error grad 2.547623189e-16
+DEAL::0.5665520866 -0.7391821301: 0.2608178699 error value -5.551115123e-17 error grad 2.288783399e-16
+DEAL::0.5927057215 -0.6798968986: 0.3201031014 error value 0.000000000 error grad 1.042959842e-15
+DEAL::0.6131868567 -0.6213321516: 0.3786678484 error value 1.110223025e-16 error grad 2.775557562e-16
+DEAL::0.6282788842 -0.5636515054: 0.4363484946 error value -1.110223025e-16 error grad 5.551115123e-17
+DEAL::0.6382651960 -0.5070185764: 0.4929814236 error value 5.551115123e-17 error grad 6.684427777e-16
+DEAL::0.6434291841 -0.4515969812: 0.5484030188 error value 0.000000000 error grad 1.110223025e-16
+DEAL::0.6440542406 -0.3975503361: 0.6024496639 error value 0.000000000 error grad 3.232409453e-16
+DEAL::0.6404237573 -0.3450422576: 0.6549577424 error value -2.220446049e-16 error grad 2.288783399e-16
+DEAL::0.6328211262 -0.2942363621: 0.7057636379 error value 1.110223025e-16 error grad 2.220446049e-16
+DEAL::0.6215297395 -0.2452962662: 0.7547037338 error value 0.000000000 error grad 0.000000000
+DEAL::0.6068329890 -0.1983855861: 0.8016144139 error value 0.000000000 error grad 1.110223025e-16
+DEAL::
+DEAL::-20.19709779 0.000000000 0.02509993277 0.000000000 -2.725875113 0.000000000 2.419322480 0.000000000 7.854661940 0.000000000 6.473508698 0.000000000 -7.183629755 0.000000000 4.100091724 0.000000000 15.53244502 0.000000000 
+DEAL::Mapping of degree 6
+DEAL::Cell with center 0.6495190528 0.3750000000
+DEAL::0.9921875000 0.000000000: 1.000000000 error value -1.110223025e-16 error grad 8.105388471e-15
+DEAL::0.9609496573 0.05926936446: 1.059269364 error value 2.220446049e-16 error grad 6.001641841e-16
+DEAL::0.9262895583 0.1146994816: 1.114699482 error value 0.000000000 error grad 6.744447820e-15
+DEAL::0.8885607198 0.1661007475: 1.166100748 error value 4.440892099e-16 error grad 1.679212325e-15
+DEAL::0.8481266485 0.2133123969: 1.213312397 error value 4.440892099e-16 error grad 4.543465650e-15
+DEAL::0.8053586039 0.2562030323: 1.256203032 error value 4.440892099e-16 error grad 4.639085208e-15
+DEAL::0.7606333492 0.2946709691: 1.294670969 error value 0.000000000 error grad 2.979170280e-15
+DEAL::0.7143309018 0.3286444014: 1.328644401 error value 2.220446049e-16 error grad 2.886579864e-15
+DEAL::0.6668322927 0.3580813945: 1.358081395 error value 0.000000000 error grad 1.702165976e-15
+DEAL::0.6185173440 0.3829697098: 1.382969710 error value 4.440892099e-16 error grad 2.047150107e-15
+DEAL::0.5697624746 0.4033264664: 1.403326466 error value -2.220446049e-16 error grad 1.777223989e-15
+DEAL::0.5209385434 0.4191976473: 1.419197647 error value 2.220446049e-16 error grad 3.768221901e-15
+DEAL::0.4724087397 0.4306574530: 1.430657453 error value 0.000000000 error grad 4.965068306e-16
+DEAL::
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+DEAL::Cell with center 4.592425497e-17 0.7500000000
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+DEAL::0.4291460533 0.8618414972: 1.861841497 error value 0.000000000 error grad 1.865323882e-15
+DEAL::0.3638121143 0.8595400296: 1.859540030 error value 8.881784197e-16 error grad 2.993004836e-15
+DEAL::0.3004328929 0.8525665299: 1.852566530 error value 0.000000000 error grad 8.593074914e-15
+DEAL::0.2393293696 0.8411554217: 1.841155422 error value -4.440892099e-16 error grad 3.748647122e-15
+DEAL::0.1808009674 0.8255625263: 1.825562526 error value 0.000000000 error grad 4.234249289e-15
+DEAL::0.1251241296 0.8060632879: 1.806063288 error value 0.000000000 error grad 3.783014701e-15
+DEAL::0.07255105048 0.7829509083: 1.782950908 error value -2.220446049e-16 error grad 2.625837351e-15
+DEAL::0.02330856204 0.7565344028: 1.756534403 error value -6.661338148e-16 error grad 1.337790132e-15
+DEAL::-0.02240282557 0.7271365875: 1.727136588 error value -4.440892099e-16 error grad 7.837034492e-16
+DEAL::-0.06440972863 0.6950920104: 1.695092010 error value -2.220446049e-16 error grad 3.730415447e-15
+DEAL::-0.1025665400 0.6607448360: 1.660744836 error value -2.220446049e-16 error grad 4.748074737e-15
+DEAL::-0.1367559248 0.6244466961: 1.624446696 error value 0.000000000 error grad 4.636427468e-15
+DEAL::
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+DEAL::Cell with center -0.6495190528 0.3750000000
+DEAL::-0.4960937500 0.8592595803: 1.859259580 error value -2.220446049e-16 error grad 9.913685895e-15
+DEAL::-0.5318036039 0.8025721327: 1.802572133 error value 4.440892099e-16 error grad 5.670177136e-15
+DEAL::-0.5624774440 0.7448405480: 1.744840548 error value 4.440892099e-16 error grad 4.714034443e-15
+DEAL::-0.5881278268 0.6864657824: 1.686465782 error value 4.440892099e-16 error grad 3.477992085e-15
+DEAL::-0.6087972789 0.6278430248: 1.627843025 error value -2.220446049e-16 error grad 6.479604370e-15
+DEAL::-0.6245576365 0.5693594940: 1.569359494 error value -2.220446049e-16 error grad 6.255731312e-15
+DEAL::-0.6355092196 0.5113923188: 1.511392319 error value -4.440892099e-16 error grad 4.796157493e-15
+DEAL::-0.6417798513 0.4543065070: 1.454306507 error value 4.440892099e-16 error grad 5.497846389e-15
+DEAL::-0.6435237306 0.3984530082: 1.398453008 error value 4.440892099e-16 error grad 1.177896401e-15
+DEAL::-0.6409201696 0.3441668777: 1.344166878 error value -2.220446049e-16 error grad 3.182373739e-15
+DEAL::-0.6341722033 0.2917655439: 1.291765544 error value 2.220446049e-16 error grad 1.804112415e-15
+DEAL::-0.6235050834 0.2415471888: 1.241547189 error value 0.000000000 error grad 2.231520662e-15
+DEAL::-0.6091646645 0.1937892431: 1.193789243 error value 2.220446049e-16 error grad 3.510833469e-15
+DEAL::
+DEAL::39.94505195 0.000000000 0.1731207989 0.000000000 0.4960327424 0.000000000 0.01569220080 0.000000000 -29.49826873 7.918751497 -3.253193306 1.690642008 -1.304558938 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.4074726205 -0.3083035991 -0.3354597471 0.7014592327 -0.05163605977 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -1.575815140 0.5033649568 -0.9453665937 0.8162427435 -0.4543332386 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -0.4411889085 0.4160002467 0.1394562192 -0.1465172110 -0.04040071710 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 12.29123392 10.83902979 -3.302450703 1.408800265 -1.083654500 -14.69039198 7.263407499 3.800406662 -0.7570326160 0.8256918358 3.190607424 -4.242966100 4.609771696 -4.291854971 1.034940434 -0.8687373980 0.005723775154 6.823264335 -15.93402263 -2.129930933 1.157327965 -1.090042868 -0.5617540848 0.4228860212 0.1372633808 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::Cell with center -0.6495190528 -0.3750000000
+DEAL::-0.9921875000 1.215079246e-16: 1.000000000 error value 0.000000000 error grad 9.925787355e-15
+DEAL::-0.9609496573 -0.05926936446: 0.9407306355 error value -1.110223025e-16 error grad 4.747765439e-15
+DEAL::-0.9262895583 -0.1146994816: 0.8853005184 error value 2.220446049e-16 error grad 3.627130491e-15
+DEAL::-0.8885607198 -0.1661007475: 0.8338992525 error value 1.110223025e-16 error grad 1.227620552e-15
+DEAL::-0.8481266485 -0.2133123969: 0.7866876031 error value 0.000000000 error grad 1.272544713e-15
+DEAL::-0.8053586039 -0.2562030323: 0.7437969677 error value 2.220446049e-16 error grad 5.440730029e-16
+DEAL::-0.7606333492 -0.2946709691: 0.7053290309 error value 1.110223025e-16 error grad 6.522560270e-16
+DEAL::-0.7143309018 -0.3286444014: 0.6713555986 error value 1.110223025e-16 error grad 3.518094482e-15
+DEAL::-0.6668322927 -0.3580813945: 0.6419186055 error value -1.110223025e-16 error grad 2.039657146e-15
+DEAL::-0.6185173440 -0.3829697098: 0.6170302902 error value -1.110223025e-16 error grad 1.309227883e-15
+DEAL::-0.5697624746 -0.4033264664: 0.5966735336 error value 2.220446049e-16 error grad 6.866350198e-16
+DEAL::-0.5209385434 -0.4191976473: 0.5808023527 error value -1.110223025e-16 error grad 1.151438307e-15
+DEAL::-0.4724087397 -0.4306574530: 0.5693425470 error value -1.110223025e-16 error grad 2.047150107e-15
+DEAL::
+DEAL::15.09262941 0.000000000 0.8182903873 0.000000000 -0.2430908254 0.000000000 -0.09636396028 0.000000000 18.23992174 -6.964721477 4.291287110 -2.145962378 0.6518532039 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -0.6575056497 1.490380892 -2.609490041 1.488255605 0.2693756865 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -21.49499132 11.03148876 -7.186149989 4.574945747 -2.210593441 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.6790144998 -1.318787036 2.639068850 -2.561580152 0.3190764361 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -10.32884832 -16.77640128 10.48049203 -6.213791641 1.904822152 26.86443806 -6.995228628 -26.82340692 13.14889966 -4.323717577 -12.96352507 33.95920069 -7.253040401 -30.40868484 7.990256238 6.118896756 -12.46945793 35.05686244 -1.986166739 -4.606947328 -1.841843780 3.692447803 -7.953374696 8.111606379 -0.9069721942 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::Cell with center -1.377727649e-16 -0.7500000000
+DEAL::-0.4960937500 -0.8592595803: 0.1407404197 error value 0.000000000 error grad 2.185652450e-15
+DEAL::-0.4291460533 -0.8618414972: 0.1381585028 error value 2.775557562e-17 error grad 4.911643985e-15
+DEAL::-0.3638121143 -0.8595400296: 0.1404599704 error value 5.551115123e-17 error grad 4.651776718e-15
+DEAL::-0.3004328929 -0.8525665299: 0.1474334701 error value -2.775557562e-17 error grad 3.115243157e-15
+DEAL::-0.2393293696 -0.8411554217: 0.1588445783 error value -2.775557562e-17 error grad 1.844418172e-15
+DEAL::-0.1808009674 -0.8255625263: 0.1744374737 error value 0.000000000 error grad 9.178506991e-16
+DEAL::-0.1251241296 -0.8060632879: 0.1939367121 error value 2.775557562e-17 error grad 1.391105463e-15
+DEAL::-0.07255105048 -0.7829509083: 0.2170490917 error value -2.775557562e-17 error grad 1.152363108e-15
+DEAL::-0.02330856204 -0.7565344028: 0.2434655972 error value -2.775557562e-17 error grad 1.464160052e-15
+DEAL::0.02240282557 -0.7271365875: 0.2728634125 error value -5.551115123e-17 error grad 5.863365349e-16
+DEAL::0.06440972863 -0.6950920104: 0.3049079896 error value 5.551115123e-17 error grad 8.473409487e-16
+DEAL::0.1025665400 -0.6607448360: 0.3392551640 error value -5.551115123e-17 error grad 6.959765931e-16
+DEAL::0.1367559248 -0.6244466961: 0.3755533039 error value 0.000000000 error grad 1.353604628e-15
+DEAL::
+DEAL::-24.10092617 0.000000000 0.6307199289 0.000000000 -0.7661489612 0.000000000 -0.1001806193 0.000000000 48.11342820 -15.09475776 7.715699123 -4.000914653 2.031246209 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -1.024467387 1.763040351 -2.270923092 0.9239244390 0.2850245737 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -20.07412100 10.52737745 -6.188065866 3.662105817 -1.715111717 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 1.177352808 -1.796748772 2.541672387 -2.304221421 0.3238556403 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -20.57505150 -27.57725022 13.61354188 -7.349456492 2.872690611 42.09388726 -10.93549472 -30.51985211 13.56410713 -5.039306236 -16.55264832 38.82332520 -8.140210259 -25.73583383 6.924694352 7.376349461 -13.02355138 29.06975056 15.93216149 -2.905906477 -3.160705202 4.966947510 -7.539970127 7.341855159 -0.9358275609 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::Cell with center 0.6495190528 -0.3750000000
+DEAL::0.4960937500 -0.8592595803: 0.1407404197 error value 0.000000000 error grad 8.908848018e-16
+DEAL::0.5318036039 -0.8025721327: 0.1974278673 error value -8.326672685e-17 error grad 3.141351920e-15
+DEAL::0.5624774440 -0.7448405480: 0.2551594520 error value -5.551115123e-17 error grad 1.398680172e-15
+DEAL::0.5881278268 -0.6864657824: 0.3135342176 error value -5.551115123e-17 error grad 1.298315076e-15
+DEAL::0.6087972789 -0.6278430248: 0.3721569752 error value 0.000000000 error grad 2.733686434e-15
+DEAL::0.6245576365 -0.5693594940: 0.4306405060 error value 1.110223025e-16 error grad 1.723823793e-15
+DEAL::0.6355092196 -0.5113923188: 0.4886076812 error value 0.000000000 error grad 1.979470755e-15
+DEAL::0.6417798513 -0.4543065070: 0.5456934930 error value -1.110223025e-16 error grad 1.427794399e-15
+DEAL::0.6435237306 -0.3984530082: 0.6015469918 error value 1.110223025e-16 error grad 2.298900685e-15
+DEAL::0.6409201696 -0.3441668777: 0.6558331223 error value 1.110223025e-16 error grad 2.140061076e-15
+DEAL::0.6341722033 -0.2917655439: 0.7082344561 error value -2.220446049e-16 error grad 3.775166432e-16
+DEAL::0.6235050834 -0.2415471888: 0.7584528112 error value 0.000000000 error grad 1.457101634e-15
+DEAL::0.6091646645 -0.1937892431: 0.8062107569 error value 0.000000000 error grad 5.551115123e-17
+DEAL::
+DEAL::-38.44205920 0.000000000 -0.2020201180 0.000000000 -0.5500835292 0.000000000 0.008058882779 0.000000000 30.24874418 -8.341321073 3.595630721 -2.019262542 1.454227073 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -0.3264508534 0.2370153188 0.3416741498 -0.4272031000 -0.02033828536 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 1.265925491 -0.5048576679 1.050801653 -1.009437116 0.5366302110 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.5554877075 -0.5399232240 -0.05533670611 0.3682002514 -0.03084230874 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 -8.201172456 -10.76266808 2.963648998 -0.8625294373 0.8520824178 15.76850642 -0.6171246758 -3.592483723 0.07338232633 -0.6054854829 -3.987639064 5.485282920 2.835431981 5.053847036 -1.096183339 1.646168011 -1.102463125 -5.150959433 19.90263383 1.272150768 -1.480394878 1.458956547 0.2650550542 -1.116616419 0.07955264751 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 
+DEAL::Mapping of degree 5
+DEAL::Cell with center 0.000000000 0.000000000 -0.7500000000
+DEAL::-0.5759520655 -0.5527659841 -0.5759520655: 0.4472340159 error value 0.000000000 error grad 4.310924484e-15
+DEAL::-0.5254898676 -0.5029040719 -0.6187865537: 0.4970959281 error value -1.110223025e-16 error grad 1.047250853e-15
+DEAL::-0.4685426073 -0.4464599093 -0.6616551149: 0.5535400907 error value -2.220446049e-16 error grad 1.070558519e-15
+DEAL::-0.4051542510 -0.3835292107 -0.7012978956: 0.6164707893 error value -4.440892099e-16 error grad 5.879529117e-15
+DEAL::-0.3359932318 -0.3148223149 -0.7343028440: 0.6851776851 error value -3.330669074e-16 error grad 1.310960958e-15
+DEAL::-0.2623766962 -0.2416891159 -0.7575161861: 0.7583108841 error value -2.220446049e-16 error grad 1.974679249e-15
+DEAL::-0.1861925434 -0.1660412603 -0.7684224851: 0.8339587397 error value -5.551115123e-16 error grad 1.005603851e-15
+DEAL::-0.1097387169 -0.09019150189 -0.7654365722: 0.9098084981 error value 3.330669074e-16 error grad 7.904326100e-16
+DEAL::-0.03550798632 -0.01663873419 -0.7480737719: 0.9833612658 error value 2.220446049e-16 error grad 4.046993501e-15
+DEAL::0.03404970570 0.05216906594 -0.7169856075: 1.052169066 error value 0.000000000 error grad 3.087836811e-15
+DEAL::0.09675558003 0.1140621810 -0.6738655685: 1.114062181 error value 2.220446049e-16 error grad 2.329307346e-15
+DEAL::0.1508930055 0.1673387801 -0.6212435337: 1.167338780 error value 2.220446049e-16 error grad 5.838192723e-15
+DEAL::0.1953394317 0.2108952300 -0.5621980946: 1.210895230 error value 2.220446049e-16 error grad 2.758609612e-15
+DEAL::
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+DEAL::0.5640861853 0.1963417794 0.2277818661: 1.196341779 error value 2.220446049e-16 error grad 4.922703884e-15
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