From: Timo Heister <timo.heister@gmail.com>
Date: Mon, 2 Sep 2019 14:05:08 +0000 (-0400)
Subject: initial version of mg_data_out
X-Git-Tag: v9.2.0-rc1~404^2~1
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=26f3c1dc4368d57abaf7a1964a85b933ae2d917f;p=dealii.git

initial version of mg_data_out
---

diff --git a/include/deal.II/numerics/data_out_dof_data.h b/include/deal.II/numerics/data_out_dof_data.h
index 6bd54c4e95..ff4d20f8c0 100644
--- a/include/deal.II/numerics/data_out_dof_data.h
+++ b/include/deal.II/numerics/data_out_dof_data.h
@@ -21,6 +21,7 @@
 #include <deal.II/base/config.h>
 
 #include <deal.II/base/data_out_base.h>
+#include <deal.II/base/mg_level_object.h>
 #include <deal.II/base/smartpointer.h>
 
 #include <deal.II/dofs/dof_handler.h>
@@ -854,6 +855,42 @@ public:
                   const DataPostprocessor<DoFHandlerType::space_dimension>
                     &data_postprocessor);
 
+  /**
+   * Add a multilevel data vector.
+   *
+   * This function adds the vector-valued multilevel vector @p data in the
+   * form of a vector on each level that belongs to the DoFHandler @p
+   * dof_handler to the graphical output. This function is typically used in
+   * conjunction with a call to set_cell_selection() that selects cells on a
+   * specific level and not the active cells (the default).
+   *
+   * A vector @p data can be obtained in several ways, for example by using
+   * Multigrid::solution or Multigrid::defect during or after a multigrid
+   * cycle or by interpolating a solution via
+   * MGTransferMatrixFree::interpolate_to_mg().
+   *
+   * The handling of @p names and @p data_component_interpretation is identical
+   * to the add_data_vector() function.
+   */
+  template <class VectorType>
+  void
+  add_mg_data_vector(
+    const DoFHandlerType &           dof_handler,
+    const MGLevelObject<VectorType> &data,
+    const std::vector<std::string> & names,
+    const std::vector<DataComponentInterpretation::DataComponentInterpretation>
+      &data_component_interpretation = std::vector<
+        DataComponentInterpretation::DataComponentInterpretation>());
+
+  /**
+   * Scalar version of the function above.
+   */
+  template <class VectorType>
+  void
+  add_mg_data_vector(const DoFHandlerType &           dof_handler,
+                     const MGLevelObject<VectorType> &data,
+                     const std::string &              name);
+
   /**
    * Release the pointers to the data vectors. This allows output of a new set
    * of vectors without supplying the DoF handler again. Therefore, the
@@ -999,6 +1036,11 @@ protected:
   template <class, int, int>
   friend class DataOut_DoFData;
 
+  /**
+   */
+  template <int, class>
+  friend class MGDataOut;
+
 private:
   /**
    * Common function called by the four public add_data_vector methods.
diff --git a/include/deal.II/numerics/data_out_dof_data.templates.h b/include/deal.II/numerics/data_out_dof_data.templates.h
index e120beba6a..1ce2ae5117 100644
--- a/include/deal.II/numerics/data_out_dof_data.templates.h
+++ b/include/deal.II/numerics/data_out_dof_data.templates.h
@@ -237,18 +237,23 @@ namespace internal
 
           if (duplicate == false)
             {
-              typename DoFHandlerType::active_cell_iterator dh_cell(
-                &cell->get_triangulation(),
-                cell->level(),
-                cell->index(),
-                dof_data[dataset]->dof_handler);
-              if (x_fe_values.empty())
+              if (cell->active())
                 {
-                  AssertIndexRange(face, GeometryInfo<dim>::faces_per_cell);
-                  x_fe_face_values[dataset]->reinit(dh_cell, face);
+                  typename DoFHandlerType::active_cell_iterator dh_cell(
+                    &cell->get_triangulation(),
+                    cell->level(),
+                    cell->index(),
+                    dof_data[dataset]->dof_handler);
+                  if (x_fe_values.empty())
+                    {
+                      AssertIndexRange(face, GeometryInfo<dim>::faces_per_cell);
+                      x_fe_face_values[dataset]->reinit(dh_cell, face);
+                    }
+                  else
+                    x_fe_values[dataset]->reinit(dh_cell);
                 }
               else
-                x_fe_values[dataset]->reinit(dh_cell);
+                x_fe_values[dataset]->reinit(cell);
             }
         }
       if (dof_data.empty())
@@ -388,6 +393,55 @@ namespace internal
     }
 
 
+    /**
+     * Helper class templated on vector type to allow different implementations
+     * to extract information from a vector.
+     */
+    template <typename VectorType>
+    struct VectorHelper
+    {
+      /**
+       * extract the @p indices from @p vector and put them into @p values.
+       */
+      static void
+      extract(const VectorType &                          vector,
+              const std::vector<types::global_dof_index> &indices,
+              const ComponentExtractor                    extract_component,
+              std::vector<double> &                       values);
+    };
+
+
+
+    template <typename VectorType>
+    void
+    VectorHelper<VectorType>::extract(
+      const VectorType &                          vector,
+      const std::vector<types::global_dof_index> &indices,
+      const ComponentExtractor                    extract_component,
+      std::vector<double> &                       values)
+    {
+      for (unsigned int i = 0; i < values.size(); ++i)
+        values[i] = get_component(vector[indices[i]], extract_component);
+    }
+
+
+
+#ifdef DEAL_II_WITH_TRILINOS
+    template <>
+    inline void
+    VectorHelper<LinearAlgebra::EpetraWrappers::Vector>::extract(
+      const LinearAlgebra::EpetraWrappers::Vector & /*vector*/,
+      const std::vector<types::global_dof_index> & /*indices*/,
+      const ComponentExtractor /*extract_component*/,
+      std::vector<double> & /*values*/)
+    {
+      // TODO: we don't have element access
+      Assert(false, ExcNotImplemented());
+    }
+#endif
+
+
+
     template <typename DoFHandlerType>
     DataEntryBase<DoFHandlerType>::DataEntryBase(
       const DoFHandlerType *          dofs,
@@ -979,6 +1033,263 @@ namespace internal
       vector            = nullptr;
       this->dof_handler = nullptr;
     }
+
+
+
+    /**
+     * Like DataEntry, but used to look up data from multigrid computations.
+     * Data will use level-DoF indices to look up in a
+     * MGLevelObject<VectorType> given on the specific level instead of
+     * interpolating data to coarser cells.
+     */
+    template <typename DoFHandlerType, typename VectorType>
+    class MGDataEntry : public DataEntryBase<DoFHandlerType>
+    {
+    public:
+      MGDataEntry(const DoFHandlerType *           dofs,
+                  const MGLevelObject<VectorType> *vectors,
+                  const std::vector<std::string> & names,
+                  const std::vector<
+                    DataComponentInterpretation::DataComponentInterpretation>
+                    &data_component_interpretation)
+        : DataEntryBase<DoFHandlerType>(dofs,
+                                        names,
+                                        data_component_interpretation)
+        , vectors(vectors)
+      {}
+
+      virtual double
+      get_cell_data_value(
+        const unsigned int       cell_number,
+        const ComponentExtractor extract_component) const override;
+
+      virtual void
+      get_function_values(
+        const FEValuesBase<DoFHandlerType::dimension,
+                           DoFHandlerType::space_dimension> &fe_patch_values,
+        const ComponentExtractor                             extract_component,
+        std::vector<double> &patch_values) const override;
+
+      /**
+       * Given a FEValuesBase object, extract the values on the present cell
+       * from the vector we actually store. This function does the same as the
+       * one above but for vector-valued finite elements.
+       */
+      virtual void
+      get_function_values(
+        const FEValuesBase<DoFHandlerType::dimension,
+                           DoFHandlerType::space_dimension> &fe_patch_values,
+        const ComponentExtractor                             extract_component,
+        std::vector<dealii::Vector<double>> &patch_values_system)
+        const override;
+
+      /**
+       * Given a FEValuesBase object, extract the gradients on the present
+       * cell from the vector we actually store.
+       */
+      virtual void
+      get_function_gradients(
+        const FEValuesBase<DoFHandlerType::dimension,
+                           DoFHandlerType::space_dimension>
+          & /*fe_patch_values*/,
+        const ComponentExtractor /*extract_component*/,
+        std::vector<Tensor<1, DoFHandlerType::space_dimension>>
+          & /*patch_gradients*/) const override
+      {
+        Assert(false, ExcNotImplemented());
+      }
+
+      /**
+       * Given a FEValuesBase object, extract the gradients on the present
+       * cell from the vector we actually store. This function does the same
+       * as the one above but for vector-valued finite elements.
+       */
+      virtual void
+      get_function_gradients(
+        const FEValuesBase<DoFHandlerType::dimension,
+                           DoFHandlerType::space_dimension>
+          & /*fe_patch_values*/,
+        const ComponentExtractor /*extract_component*/,
+        std::vector<std::vector<Tensor<1, DoFHandlerType::space_dimension>>>
+          & /*patch_gradients_system*/) const override
+      {
+        Assert(false, ExcNotImplemented());
+      }
+
+
+      /**
+       * Given a FEValuesBase object, extract the second derivatives on the
+       * present cell from the vector we actually store.
+       */
+      virtual void
+      get_function_hessians(
+        const FEValuesBase<DoFHandlerType::dimension,
+                           DoFHandlerType::space_dimension>
+          & /*fe_patch_values*/,
+        const ComponentExtractor /*extract_component*/,
+        std::vector<Tensor<2, DoFHandlerType::space_dimension>>
+          & /*patch_hessians*/) const override
+      {
+        Assert(false, ExcNotImplemented());
+      }
+
+      /**
+       * Given a FEValuesBase object, extract the second derivatives on the
+       * present cell from the vector we actually store. This function does
+       * the same as the one above but for vector-valued finite elements.
+       */
+      virtual void
+      get_function_hessians(
+        const FEValuesBase<DoFHandlerType::dimension,
+                           DoFHandlerType::space_dimension>
+          & /*fe_patch_values*/,
+        const ComponentExtractor /*extract_component*/,
+        std::vector<std::vector<Tensor<2, DoFHandlerType::space_dimension>>>
+          & /*patch_hessians_system*/) const override
+      {
+        Assert(false, ExcNotImplemented());
+      }
+
+      /**
+       * Return whether the data represented by (a derived class of) this object
+       * represents a complex-valued (as opposed to real-valued) information.
+       */
+      virtual bool
+      is_complex_valued() const override
+      {
+        Assert(
+          numbers::NumberTraits<typename VectorType::value_type>::is_complex ==
+            false,
+          ExcNotImplemented());
+        return numbers::NumberTraits<
+          typename VectorType::value_type>::is_complex;
+      }
+
+      /**
+       * Clear all references to the vectors.
+       */
+      virtual void
+      clear() override
+      {
+        vectors = nullptr;
+      }
+
+      /**
+       * Determine an estimate for the memory consumption (in bytes) of this
+       * object.
+       */
+      virtual std::size_t
+      memory_consumption() const override
+      {
+        return sizeof(vectors);
+      }
+
+    private:
+      const MGLevelObject<VectorType> *vectors;
+    };
+
+
+
+    template <typename DoFHandlerType, typename VectorType>
+    double
+    MGDataEntry<DoFHandlerType, VectorType>::get_cell_data_value(
+      const unsigned int       cell_number,
+      const ComponentExtractor extract_component) const
+    {
+      Assert(false, ExcNotImplemented());
+
+      (void)cell_number;
+      (void)extract_component;
+      return 0.0;
+    }
+
+
+
+    template <typename DoFHandlerType, typename VectorType>
+    void
+    MGDataEntry<DoFHandlerType, VectorType>::get_function_values(
+      const FEValuesBase<DoFHandlerType::dimension,
+                         DoFHandlerType::space_dimension> &fe_patch_values,
+      const ComponentExtractor                             extract_component,
+      std::vector<double> &                                patch_values) const
+    {
+      Assert(extract_component == ComponentExtractor::real_part,
+             ExcNotImplemented());
+
+      const typename DoFHandlerType::level_cell_iterator dof_cell(
+        &fe_patch_values.get_cell()->get_triangulation(),
+        fe_patch_values.get_cell()->level(),
+        fe_patch_values.get_cell()->index(),
+        this->dof_handler);
+
+      const VectorType *vector = &((*vectors)[dof_cell->level()]);
+
+      const unsigned int dofs_per_cell =
+        this->dof_handler->get_fe()[0].dofs_per_cell;
+
+      std::vector<types::global_dof_index> dof_indices(dofs_per_cell);
+      dof_cell->get_mg_dof_indices(dof_indices);
+      std::vector<double> values(dofs_per_cell);
+      VectorHelper<VectorType>::extract(*vector,
+                                        dof_indices,
+                                        extract_component,
+                                        values);
+      std::fill(patch_values.begin(), patch_values.end(), 0.0);
+
+      for (unsigned int i = 0; i < dofs_per_cell; ++i)
+        for (unsigned int q_point = 0; q_point < patch_values.size(); ++q_point)
+          patch_values[q_point] +=
+            values[i] * fe_patch_values.shape_value(i, q_point);
+    }
+
+
+
+    template <typename DoFHandlerType, typename VectorType>
+    void
+    MGDataEntry<DoFHandlerType, VectorType>::get_function_values(
+      const FEValuesBase<DoFHandlerType::dimension,
+                         DoFHandlerType::space_dimension> &fe_patch_values,
+      const ComponentExtractor                             extract_component,
+      std::vector<dealii::Vector<double>> &patch_values_system) const
+    {
+      Assert(extract_component == ComponentExtractor::real_part,
+             ExcNotImplemented());
+
+      typename DoFHandlerType::level_cell_iterator dof_cell(
+        &fe_patch_values.get_cell()->get_triangulation(),
+        fe_patch_values.get_cell()->level(),
+        fe_patch_values.get_cell()->index(),
+        this->dof_handler);
+
+      const VectorType *vector = &((*vectors)[dof_cell->level()]);
+
+      const unsigned int dofs_per_cell =
+        this->dof_handler->get_fe()[0].dofs_per_cell;
+
+      std::vector<types::global_dof_index> dof_indices(dofs_per_cell);
+      dof_cell->get_mg_dof_indices(dof_indices);
+      std::vector<double> values(dofs_per_cell);
+      VectorHelper<VectorType>::extract(*vector,
+                                        dof_indices,
+                                        extract_component,
+                                        values);
+
+      const unsigned int n_components = fe_patch_values.get_fe().n_components();
+      const unsigned int n_eval_points = fe_patch_values.n_quadrature_points;
+
+      AssertDimension(patch_values_system.size(), n_eval_points);
+      for (unsigned int q = 0; q < n_eval_points; q++)
+        {
+          AssertDimension(patch_values_system[q].size(), n_components);
+          patch_values_system[q] = 0.0;
+
+          for (unsigned int i = 0; i < dofs_per_cell; ++i)
+            for (unsigned int c = 0; c < n_components; ++c)
+              patch_values_system[q](c) +=
+                values[i] * fe_patch_values.shape_value_component(i, q, c);
+        }
+    }
+
   } // namespace DataOutImplementation
 } // namespace internal
 
@@ -1242,6 +1553,75 @@ DataOut_DoFData<DoFHandlerType, patch_dim, patch_space_dim>::
 
 
 
+template <typename DoFHandlerType, int patch_dim, int patch_space_dim>
+template <class VectorType>
+void
+DataOut_DoFData<DoFHandlerType, patch_dim, patch_space_dim>::add_mg_data_vector(
+  const DoFHandlerType &           dof_handler,
+  const MGLevelObject<VectorType> &data,
+  const std::string &              name)
+{
+  // forward the call to the vector version:
+  std::vector<std::string> names(1, name);
+  add_mg_data_vector(dof_handler, data, names);
+}
+
+
+
+template <typename DoFHandlerType, int patch_dim, int patch_space_dim>
+template <class VectorType>
+void
+DataOut_DoFData<DoFHandlerType, patch_dim, patch_space_dim>::add_mg_data_vector(
+  const DoFHandlerType &           dof_handler,
+  const MGLevelObject<VectorType> &data,
+  const std::vector<std::string> & names,
+  const std::vector<DataComponentInterpretation::DataComponentInterpretation>
+    &data_component_interpretation_)
+{
+  if (triangulation == nullptr)
+    triangulation =
+      SmartPointer<const Triangulation<DoFHandlerType::dimension,
+                                       DoFHandlerType::space_dimension>>(
+        &dof_handler.get_triangulation(), typeid(*this).name());
+
+  Assert(&dof_handler.get_triangulation() == triangulation,
+         ExcMessage("The triangulation attached to the DoFHandler does not "
+                    "match with the one set previously"));
+
+  const unsigned int       n_components  = dof_handler.get_fe(0).n_components();
+  std::vector<std::string> deduced_names = names;
+
+  if (names.size() == 1 && n_components > 1)
+    {
+      deduced_names.resize(n_components);
+      for (unsigned int i = 0; i < n_components; ++i)
+        {
+          deduced_names[i] = names[0] + '_' + std::to_string(i);
+        }
+    }
+
+  Assert(deduced_names.size() == n_components,
+         ExcMessage("Invalid number of names given."));
+
+  const std::vector<DataComponentInterpretation::DataComponentInterpretation>
+    &data_component_interpretation =
+      (data_component_interpretation_.size() != 0 ?
+         data_component_interpretation_ :
+         std::vector<DataComponentInterpretation::DataComponentInterpretation>(
+           n_components, DataComponentInterpretation::component_is_scalar));
+
+  Assert(data_component_interpretation.size() == n_components,
+         ExcMessage(
+           "Invalid number of entries in data_component_interpretation."));
+
+  auto new_entry = std_cxx14::make_unique<
+    internal::DataOutImplementation::MGDataEntry<DoFHandlerType, VectorType>>(
+    &dof_handler, &data, deduced_names, data_component_interpretation);
+  dof_data.emplace_back(std::move(new_entry));
+}
+
+
+
 template <typename DoFHandlerType, int patch_dim, int patch_space_dim>
 void
 DataOut_DoFData<DoFHandlerType, patch_dim, patch_space_dim>::
diff --git a/source/numerics/data_out_dof_data.inst.in b/source/numerics/data_out_dof_data.inst.in
index 92f16fdfb5..a48923f3cb 100644
--- a/source/numerics/data_out_dof_data.inst.in
+++ b/source/numerics/data_out_dof_data.inst.in
@@ -39,6 +39,24 @@ for (VEC : VECTOR_TYPES; DH : DOFHANDLER_TEMPLATES;
           DH<deal_II_dimension, deal_II_dimension>::space_dimension> &);
 
 
+    template void DataOut_DoFData<DH<deal_II_dimension, deal_II_dimension>,
+                                  deal_II_dimension,
+                                  deal_II_dimension>::
+      add_mg_data_vector<VEC>(const DH<deal_II_dimension, deal_II_dimension> &,
+                              const MGLevelObject<VEC> &,
+                              const std::string &);
+
+    template void DataOut_DoFData<DH<deal_II_dimension, deal_II_dimension>,
+                                  deal_II_dimension,
+                                  deal_II_dimension>::
+      add_mg_data_vector<VEC>(
+        const DH<deal_II_dimension, deal_II_dimension> &,
+        const MGLevelObject<VEC> &,
+        const std::vector<std::string> &,
+        const std::vector<
+          DataComponentInterpretation::DataComponentInterpretation> &);
+
+
 
     // stuff needed for face data
 
diff --git a/tests/multigrid/mg_data_out_02.cc b/tests/multigrid/mg_data_out_02.cc
index eb144683b2..a8b40271f7 100644
--- a/tests/multigrid/mg_data_out_02.cc
+++ b/tests/multigrid/mg_data_out_02.cc
@@ -90,7 +90,8 @@ do_test()
       deallog << "* owned on level " << level << std::endl;
       data_out.set_cell_selection(
         [level](const typename Triangulation<dim>::cell_iterator &cell) {
-          return (cell->level() == level && cell->is_locally_owned_on_level());
+          return (cell->level() == static_cast<int>(level) &&
+                  cell->is_locally_owned_on_level());
         });
       print(data_out, triangulation);
     }
diff --git a/tests/multigrid/mg_data_out_03.cc b/tests/multigrid/mg_data_out_03.cc
new file mode 100644
index 0000000000..60cb9737cc
--- /dev/null
+++ b/tests/multigrid/mg_data_out_03.cc
@@ -0,0 +1,121 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2006 - 2016 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+// Test DataOut::add_mg_data_vector for vector data in serial
+
+#include <deal.II/base/function_lib.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/timer.h>
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+
+#include <deal.II/multigrid/mg_tools.h>
+#include <deal.II/multigrid/mg_transfer.h>
+#include <deal.II/multigrid/mg_transfer_matrix_free.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include "../tests.h"
+
+using namespace dealii;
+
+template <int dim>
+void
+do_test()
+{
+  FE_Q<dim>          fe(1);
+  Triangulation<dim> triangulation(
+    Triangulation<dim>::limit_level_difference_at_vertices);
+  GridGenerator::hyper_cube(triangulation);
+  triangulation.refine_global(1);
+  triangulation.begin_active()->set_refine_flag();
+  triangulation.execute_coarsening_and_refinement();
+
+  DoFHandler<dim> dof_handler(triangulation);
+  dof_handler.distribute_dofs(fe);
+  dof_handler.distribute_mg_dofs(fe);
+
+  Vector<double> global_dof_vector(dof_handler.n_dofs());
+  VectorTools::interpolate(dof_handler,
+                           Functions::SquareFunction<dim>(),
+                           global_dof_vector);
+
+  {
+    DataOut<dim> data_out;
+    data_out.attach_dof_handler(dof_handler);
+    data_out.add_data_vector(dof_handler,
+                             global_dof_vector,
+                             std::vector<std::string>(1, "data"));
+    data_out.build_patches(0);
+    data_out.write_gnuplot(deallog.get_file_stream());
+    std::ofstream st("base.vtu");
+    data_out.write_vtu(st);
+  }
+
+  {
+    MGLevelObject<Vector<double>> dof_vector(0,
+                                             triangulation.n_global_levels() -
+                                               1);
+
+    MGTransferPrebuilt<Vector<double>> transfer;
+
+    transfer.build_matrices(dof_handler);
+
+    // This is not quite the correct thing to do, but "interpolate_to_mg"
+    // doesn't exist for serial vectors. Here it means that the level 0 is 0
+    // instead of having correct values.
+    transfer.copy_to_mg(dof_handler, dof_vector, global_dof_vector);
+
+    for (unsigned int level = 0; level < triangulation.n_global_levels();
+         ++level)
+      {
+        deallog << "* level " << level << std::endl;
+
+        DataOut<dim> data_out;
+        data_out.set_cell_selection(
+          [level](const typename Triangulation<dim>::cell_iterator &cell) {
+            return cell->level() == static_cast<int>(level);
+          });
+
+        data_out.attach_triangulation(triangulation);
+        data_out.add_mg_data_vector(dof_handler, dof_vector, "data");
+        data_out.build_patches(0);
+        data_out.write_gnuplot(deallog.get_file_stream());
+        std::ofstream st(std::string("level") + Utilities::to_string(level) +
+                         ".vtu");
+        data_out.write_vtu(st);
+      }
+  }
+}
+
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi(argc, argv, 1);
+  initlog();
+
+  do_test<2>();
+  /*
+  do_test<3>();*/
+  return 0;
+}
diff --git a/tests/multigrid/mg_data_out_03.output b/tests/multigrid/mg_data_out_03.output
new file mode 100644
index 0000000000..d6675f08e5
--- /dev/null
+++ b/tests/multigrid/mg_data_out_03.output
@@ -0,0 +1,144 @@
+
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.500000 0.00000 0.250000 
+1.00000 0.00000 1.00000 
+
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+
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+
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+
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+
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+
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+
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+
+
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+0.500000 0.250000 0.312500 
+
+0.250000 0.500000 0.312500 
+0.500000 0.500000 0.500000 
+
+
+DEAL::* level 0
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.00000 0.00000 0.00000 
+1.00000 0.00000 0.00000 
+
+0.00000 1.00000 0.00000 
+1.00000 1.00000 0.00000 
+
+
+DEAL::* level 1
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.00000 0.00000 0.00000 
+0.500000 0.00000 0.250000 
+
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+
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+
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+
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+0.500000 1.00000 1.25000 
+
+
+0.500000 0.500000 0.500000 
+1.00000 0.500000 1.25000 
+
+0.500000 1.00000 1.25000 
+1.00000 1.00000 2.00000 
+
+
+DEAL::* level 2
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.00000 0.00000 0.00000 
+0.250000 0.00000 0.0625000 
+
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+
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+
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+
+
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+
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+
+
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+0.500000 0.250000 0.312500 
+
+0.250000 0.500000 0.312500 
+0.500000 0.500000 0.500000 
+
+
diff --git a/tests/multigrid/mg_data_out_04.cc b/tests/multigrid/mg_data_out_04.cc
new file mode 100644
index 0000000000..ef795d0292
--- /dev/null
+++ b/tests/multigrid/mg_data_out_04.cc
@@ -0,0 +1,121 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2006 - 2016 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+// Test DataOut::add_mg_data_vector in parallel
+
+#include <deal.II/base/function_lib.h>
+
+#include <deal.II/distributed/tria.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+
+#include <deal.II/multigrid/mg_tools.h>
+#include <deal.II/multigrid/mg_transfer.h>
+#include <deal.II/multigrid/mg_transfer_matrix_free.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include "../tests.h"
+
+using namespace dealii;
+
+template <int dim>
+void
+do_test()
+{
+  parallel::distributed::Triangulation<dim> triangulation(
+    MPI_COMM_WORLD,
+    dealii::Triangulation<dim>::none,
+    parallel::distributed::Triangulation<dim>::construct_multigrid_hierarchy);
+
+  GridGenerator::hyper_cube(triangulation);
+  triangulation.refine_global(1);
+  triangulation.begin_active()->set_refine_flag();
+  triangulation.execute_coarsening_and_refinement();
+
+  FE_Q<dim>       fe(1);
+  DoFHandler<dim> dof_handler(triangulation);
+  dof_handler.distribute_dofs(fe);
+  dof_handler.distribute_mg_dofs(fe);
+
+  // Make FE vector
+  IndexSet locally_relevant_dofs;
+  DoFTools::extract_locally_relevant_dofs(dof_handler, locally_relevant_dofs);
+
+  using VectorType = LinearAlgebra::distributed::Vector<double>;
+  VectorType global_dof_vector;
+  global_dof_vector.reinit(dof_handler.locally_owned_dofs(),
+                           locally_relevant_dofs,
+                           MPI_COMM_WORLD);
+
+  VectorTools::interpolate(dof_handler,
+                           Functions::SquareFunction<dim>(),
+                           global_dof_vector);
+  global_dof_vector.update_ghost_values();
+
+  {
+    DataOut<dim> data_out;
+    data_out.attach_dof_handler(dof_handler);
+    data_out.add_data_vector(dof_handler,
+                             global_dof_vector,
+                             std::vector<std::string>(1, "data"));
+    data_out.build_patches(0);
+    data_out.write_gnuplot(deallog.get_file_stream());
+    data_out.write_vtu_in_parallel("base.vtu", MPI_COMM_WORLD);
+  }
+
+  {
+    MGLevelObject<VectorType>         dof_vector(0,
+                                         triangulation.n_global_levels() - 1);
+    MGTransferMatrixFree<dim, double> transfer;
+
+    transfer.build(dof_handler);
+    transfer.interpolate_to_mg(dof_handler, dof_vector, global_dof_vector);
+
+    for (unsigned int level = 0; level < triangulation.n_global_levels();
+         ++level)
+      {
+        deallog << "* level " << level << std::endl;
+        DataOut<dim> data_out;
+        data_out.set_cell_selection(
+          [level](const typename Triangulation<dim>::cell_iterator &cell) {
+            return (cell->level() == static_cast<int>(level) &&
+                    cell->is_locally_owned_on_level());
+          });
+        data_out.attach_triangulation(triangulation);
+        data_out.add_mg_data_vector(dof_handler, dof_vector, "data");
+        data_out.build_patches(0);
+        data_out.write_gnuplot(deallog.get_file_stream());
+        data_out.write_vtu_in_parallel(std::string("level") +
+                                         Utilities::to_string(level) + ".vtu",
+                                       MPI_COMM_WORLD);
+      }
+  }
+}
+
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi(argc, argv, 1);
+  MPILogInitAll                    log;
+
+  do_test<2>();
+  //  do_test<3>();
+  return 0;
+}
diff --git a/tests/multigrid/mg_data_out_04.with_p4est=true.mpirun=2.output b/tests/multigrid/mg_data_out_04.with_p4est=true.mpirun=2.output
new file mode 100644
index 0000000000..568ac41070
--- /dev/null
+++ b/tests/multigrid/mg_data_out_04.with_p4est=true.mpirun=2.output
@@ -0,0 +1,163 @@
+
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.00000 0.00000 0.00000 
+0.250000 0.00000 0.0625000 
+
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+
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+
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+
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+
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+
+
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+0.500000 0.250000 0.312500 
+
+0.250000 0.500000 0.312500 
+0.500000 0.500000 0.500000 
+
+
+DEAL:0::* level 0
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.00000 0.00000 0.00000 
+1.00000 0.00000 1.00000 
+
+0.00000 1.00000 1.00000 
+1.00000 1.00000 2.00000 
+
+
+DEAL:0::* level 1
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.00000 0.00000 0.00000 
+0.500000 0.00000 0.250000 
+
+0.00000 0.500000 0.250000 
+0.500000 0.500000 0.500000 
+
+
+DEAL:0::* level 2
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.00000 0.00000 0.00000 
+0.250000 0.00000 0.0625000 
+
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+
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+
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+
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+0.500000 0.250000 0.312500 
+
+0.250000 0.500000 0.312500 
+0.500000 0.500000 0.500000 
+
+
+
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.500000 0.00000 0.250000 
+1.00000 0.00000 1.00000 
+
+0.500000 0.500000 0.500000 
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+
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+
+
+0.500000 0.500000 0.500000 
+1.00000 0.500000 1.25000 
+
+0.500000 1.00000 1.25000 
+1.00000 1.00000 2.00000 
+
+
+DEAL:1::* level 0
+DEAL:1::* level 1
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data> 
+0.500000 0.00000 0.250000 
+1.00000 0.00000 1.00000 
+
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+
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+0.500000 0.500000 0.500000 
+
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+
+
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+
+0.500000 1.00000 1.25000 
+1.00000 1.00000 2.00000 
+
+
+DEAL:1::* level 2
+
diff --git a/tests/multigrid/mg_data_out_05.cc b/tests/multigrid/mg_data_out_05.cc
new file mode 100644
index 0000000000..d1e41fb6e6
--- /dev/null
+++ b/tests/multigrid/mg_data_out_05.cc
@@ -0,0 +1,151 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2006 - 2016 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 at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+// Test DataOut::add_mg_data_vector in parallel for a vector valued dof function
+
+#include <deal.II/base/function_lib.h>
+#include <deal.II/base/function_parser.h>
+
+#include <deal.II/distributed/tria.h>
+
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_system.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+
+#include <deal.II/multigrid/mg_tools.h>
+#include <deal.II/multigrid/mg_transfer.h>
+#include <deal.II/multigrid/mg_transfer_matrix_free.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+
+#include "../tests.h"
+
+using namespace dealii;
+
+template <int dim>
+void
+do_test()
+{
+  parallel::distributed::Triangulation<dim> triangulation(
+    MPI_COMM_WORLD,
+    dealii::Triangulation<dim>::none,
+    parallel::distributed::Triangulation<dim>::construct_multigrid_hierarchy);
+
+  GridGenerator::hyper_cube(triangulation);
+  triangulation.refine_global(1);
+  triangulation.begin_active()->set_refine_flag();
+  triangulation.execute_coarsening_and_refinement();
+
+  FESystem<dim> fe(FE_DGQ<dim>(1), dim + 1);
+
+  DoFHandler<dim> dof_handler(triangulation);
+  dof_handler.distribute_dofs(fe);
+  dof_handler.distribute_mg_dofs(fe);
+
+  // Make FE vector
+  IndexSet locally_relevant_dofs;
+  DoFTools::extract_locally_relevant_dofs(dof_handler, locally_relevant_dofs);
+
+  using VectorType = LinearAlgebra::distributed::Vector<double>;
+  VectorType global_dof_vector;
+  global_dof_vector.reinit(dof_handler.locally_owned_dofs(),
+                           locally_relevant_dofs,
+                           MPI_COMM_WORLD);
+
+  QGauss<dim> quadrature(3);
+
+  FunctionParser<dim> function(dim == 2 ? "y;-x;x*x+y*y" :
+                                          "y;-x;0;x*x+y*y+z*z");
+
+  AffineConstraints<double> constraints;
+  DoFTools::make_hanging_node_constraints(dof_handler, constraints);
+  constraints.close();
+  VectorTools::project(
+    dof_handler, constraints, quadrature, function, global_dof_vector);
+  /*  VectorTools::interpolate(dof_handler,
+                           Functions::SquareFunction<dim>(),
+                           global_dof_vector);
+  */
+
+  global_dof_vector.update_ghost_values();
+
+  std::vector<std::string> names(dim, "vec");
+  names.emplace_back("my_scalar");
+  std::vector<DataComponentInterpretation::DataComponentInterpretation>
+    interpretation(dim,
+                   DataComponentInterpretation::component_is_part_of_vector);
+  interpretation.emplace_back(DataComponentInterpretation::component_is_scalar);
+
+  {
+    DataOut<dim> data_out;
+    data_out.attach_dof_handler(dof_handler);
+    data_out.add_data_vector(dof_handler,
+                             global_dof_vector,
+                             names,
+                             interpretation);
+    data_out.build_patches(0);
+    data_out.write_gnuplot(deallog.get_file_stream());
+    data_out.write_vtu_in_parallel("base.vtu", MPI_COMM_WORLD);
+  }
+
+  {
+    MGLevelObject<VectorType>         dof_vector(0,
+                                         triangulation.n_global_levels() - 1);
+    MGTransferMatrixFree<dim, double> transfer;
+
+    transfer.build(dof_handler);
+    transfer.interpolate_to_mg(dof_handler, dof_vector, global_dof_vector);
+
+    for (unsigned int level = 0; level < triangulation.n_global_levels();
+         ++level)
+      {
+        deallog << "* level " << level << std::endl;
+        DataOut<dim> data_out;
+        data_out.set_cell_selection(
+          [level](const typename Triangulation<dim>::cell_iterator &cell) {
+            return (cell->level() == static_cast<int>(level) &&
+                    cell->is_locally_owned_on_level());
+          });
+        data_out.attach_triangulation(triangulation);
+        data_out.add_mg_data_vector(dof_handler, dof_vector, "data");
+        data_out.add_mg_data_vector(dof_handler,
+                                    dof_vector,
+                                    names,
+                                    interpretation);
+        data_out.build_patches(0);
+        data_out.write_gnuplot(deallog.get_file_stream());
+        data_out.write_vtu_in_parallel(std::string("level") +
+                                         Utilities::to_string(level) + ".vtu",
+                                       MPI_COMM_WORLD);
+      }
+  }
+}
+
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi(argc, argv, 1);
+  MPILogInitAll                    log;
+
+  do_test<2>();
+  //  do_test<3>();
+  return 0;
+}
diff --git a/tests/multigrid/mg_data_out_05.with_p4est=true.mpirun=2.output b/tests/multigrid/mg_data_out_05.with_p4est=true.mpirun=2.output
new file mode 100644
index 0000000000..b816a43ec9
--- /dev/null
+++ b/tests/multigrid/mg_data_out_05.with_p4est=true.mpirun=2.output
@@ -0,0 +1,163 @@
+
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <vec> <vec> <my_scalar> 
+0.00000 0.00000 -6.93889e-17 2.77556e-17 -0.0208333 
+0.250000 0.00000 -5.55112e-17 -0.250000 0.0416667 
+
+0.00000 0.250000 0.250000 2.77556e-17 0.0416667 
+0.250000 0.250000 0.250000 -0.250000 0.104167 
+
+
+0.250000 0.00000 -6.93889e-17 -0.250000 0.0416667 
+0.500000 0.00000 -5.55112e-17 -0.500000 0.229167 
+
+0.250000 0.250000 0.250000 -0.250000 0.104167 
+0.500000 0.250000 0.250000 -0.500000 0.291667 
+
+
+0.00000 0.250000 0.250000 2.77556e-17 0.0416667 
+0.250000 0.250000 0.250000 -0.250000 0.104167 
+
+0.00000 0.500000 0.500000 2.77556e-17 0.229167 
+0.250000 0.500000 0.500000 -0.250000 0.291667 
+
+
+0.250000 0.250000 0.250000 -0.250000 0.104167 
+0.500000 0.250000 0.250000 -0.500000 0.291667 
+
+0.250000 0.500000 0.500000 -0.250000 0.291667 
+0.500000 0.500000 0.500000 -0.500000 0.479167 
+
+
+DEAL:0::* level 0
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data_0> <data_1> <data_2> <vec> <vec> <my_scalar> 
+0.00000 0.00000 -2.35922e-16 1.24900e-16 -0.333333 -2.35922e-16 1.24900e-16 -0.333333 
+1.00000 0.00000 5.55112e-17 -1.00000 0.666667 5.55112e-17 -1.00000 0.666667 
+
+0.00000 1.00000 1.00000 1.66533e-16 0.666667 1.00000 1.66533e-16 0.666667 
+1.00000 1.00000 1.00000 -1.00000 1.66667 1.00000 -1.00000 1.66667 
+
+
+DEAL:0::* level 1
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data_0> <data_1> <data_2> <vec> <vec> <my_scalar> 
+0.00000 0.00000 -3.46945e-17 6.93889e-18 -0.0833333 -3.46945e-17 6.93889e-18 -0.0833333 
+0.500000 0.00000 0.00000 -0.500000 0.166667 0.00000 -0.500000 0.166667 
+
+0.00000 0.500000 0.500000 1.11022e-16 0.166667 0.500000 1.11022e-16 0.166667 
+0.500000 0.500000 0.500000 -0.500000 0.416667 0.500000 -0.500000 0.416667 
+
+
+DEAL:0::* level 2
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data_0> <data_1> <data_2> <vec> <vec> <my_scalar> 
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+
+
+
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <vec> <vec> <my_scalar> 
+0.500000 0.00000 -1.38778e-16 -0.500000 0.166667 
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+
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+
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+
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+
+
+DEAL:1::* level 0
+DEAL:1::* level 1
+# This file was generated by the deal.II library.
+
+
+#
+# For a description of the GNUPLOT format see the GNUPLOT manual.
+#
+# <x> <y> <data_0> <data_1> <data_2> <vec> <vec> <my_scalar> 
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+
+
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+
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+
+
+DEAL:1::* level 2
+