From: Peter Munch <peterrmuench@gmail.com>
Date: Mon, 3 Apr 2023 12:02:03 +0000 (+0200)
Subject: Add interface for non-nested two level transfer
X-Git-Tag: v9.5.0-rc1~245^2~1
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=55f7b43615a2885f7e22861559016f80b90419f1;p=dealii.git

Add interface for non-nested two level transfer

Co-authored-by: peterrum <peterrmuench@gmail.com>
---

diff --git a/include/deal.II/multigrid/mg_transfer_global_coarsening.h b/include/deal.II/multigrid/mg_transfer_global_coarsening.h
index ce9d9e69bc..55c64c1f22 100644
--- a/include/deal.II/multigrid/mg_transfer_global_coarsening.h
+++ b/include/deal.II/multigrid/mg_transfer_global_coarsening.h
@@ -17,6 +17,7 @@
 #define dealii_mg_transfer_global_coarsening_h
 
 #include <deal.II/base/mg_level_object.h>
+#include <deal.II/base/mpi_remote_point_evaluation.h>
 #include <deal.II/base/vectorization.h>
 
 #include <deal.II/dofs/dof_handler.h>
@@ -30,6 +31,8 @@
 #include <deal.II/multigrid/mg_base.h>
 #include <deal.II/multigrid/mg_transfer_matrix_free.h>
 
+
+
 DEAL_II_NAMESPACE_OPEN
 
 // Forward declarations
@@ -646,6 +649,145 @@ private:
 
 
 
+/**
+ * Class for transfer between two non-nested multigrid levels.
+ *
+ */
+template <int dim, typename VectorType>
+class MGTwoLevelTransferNonNested : public MGTwoLevelTransferBase<VectorType>
+{
+public:
+  /**
+   * Perform prolongation.
+   */
+  void
+  prolongate_and_add(VectorType &dst, const VectorType &src) const override;
+
+  /**
+   * Perform restriction.
+   */
+  void
+  restrict_and_add(VectorType &dst, const VectorType &src) const override;
+
+  /**
+   * Perform interpolation of a solution vector from the fine level to the
+   * coarse level. This function is different from restriction, where a
+   * weighted residual is transferred to a coarser level (transposition of
+   * prolongation matrix).
+   */
+  void
+  interpolate(VectorType &dst, const VectorType &src) const override;
+
+  /**
+   * Return the memory consumption of the allocated memory in this class.
+   */
+  std::size_t
+  memory_consumption() const override;
+};
+
+
+
+/**
+ * Class for transfer between two non-nested multigrid levels.
+ *
+ * Specialization for LinearAlgebra::distributed::Vector.
+ *
+ */
+template <int dim, typename Number>
+class MGTwoLevelTransferNonNested<dim,
+                                  LinearAlgebra::distributed::Vector<Number>>
+  : public MGTwoLevelTransferBase<LinearAlgebra::distributed::Vector<Number>>
+{
+private:
+  using VectorizedArrayType = VectorizedArray<Number, 1>;
+
+public:
+  /**
+   * Set up transfer operator between the given DoFHandler objects (
+   * @p dof_handler_fine and @p dof_handler_coarse).
+   */
+  void
+  reinit(const DoFHandler<dim> &          dof_handler_fine,
+         const DoFHandler<dim> &          dof_handler_coarse,
+         const Mapping<dim> &             mapping_fine,
+         const Mapping<dim> &             mapping_coarse,
+         const AffineConstraints<Number> &constraint_fine =
+           AffineConstraints<Number>(),
+         const AffineConstraints<Number> &constraint_coarse =
+           AffineConstraints<Number>());
+
+  /**
+   * Perform interpolation of a solution vector from the fine level to the
+   * coarse level. This function is different from restriction, where a
+   * weighted residual is transferred to a coarser level (transposition of
+   * prolongation matrix).
+   */
+  void
+  interpolate(
+    LinearAlgebra::distributed::Vector<Number> &      dst,
+    const LinearAlgebra::distributed::Vector<Number> &src) const override;
+
+  /**
+   * Enable inplace vector operations if external and internal vectors
+   * are compatible.
+   */
+  void
+  enable_inplace_operations_if_possible(
+    const std::shared_ptr<const Utilities::MPI::Partitioner>
+      &partitioner_coarse,
+    const std::shared_ptr<const Utilities::MPI::Partitioner> &partitioner_fine)
+    override;
+
+  /**
+   * Return the memory consumption of the allocated memory in this class.
+   */
+  std::size_t
+  memory_consumption() const override;
+
+protected:
+  /**
+   * Perform prolongation.
+   */
+  void
+  prolongate_and_add_internal(
+    LinearAlgebra::distributed::Vector<Number> &      dst,
+    const LinearAlgebra::distributed::Vector<Number> &src) const override;
+
+  /**
+   * Perform restriction.
+   */
+  void
+  restrict_and_add_internal(
+    LinearAlgebra::distributed::Vector<Number> &      dst,
+    const LinearAlgebra::distributed::Vector<Number> &src) const override;
+
+private:
+  /**
+   * Object to evaluate shape functions on one mesh on visited support points of
+   * the other mesh.
+   */
+  Utilities::MPI::RemotePointEvaluation<dim> rpe;
+
+  /**
+   * MappingInfo object needed as Mapping argument by FEPointEvaluation.
+   */
+  std::shared_ptr<NonMatching::MappingInfo<dim, dim>> mapping_info;
+
+  /**
+   * Helper class for reading from and writing to global vectors and for
+   * applying constraints.
+   */
+  internal::MatrixFreeFunctions::ConstraintInfo<dim, VectorizedArrayType>
+    constraint_info;
+
+  /**
+   * Finite element of the coarse DoFHandler passed to reinit().
+   */
+  std::unique_ptr<FiniteElement<dim>> fe_coarse;
+};
+
+
+
 /**
  * Implementation of the MGTransferBase. In contrast to
  * other multigrid transfer operators, the user can provide separate
diff --git a/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h b/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h
index d89f92a36b..d15aa7a0a1 100644
--- a/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h
+++ b/include/deal.II/multigrid/mg_transfer_global_coarsening.templates.h
@@ -21,7 +21,6 @@
 
 #include <deal.II/base/mpi_compute_index_owner_internal.h>
 #include <deal.II/base/mpi_consensus_algorithms.h>
-#include <deal.II/base/mpi_remote_point_evaluation.h>
 
 #include <deal.II/distributed/fully_distributed_tria.h>
 #include <deal.II/distributed/repartitioning_policy_tools.h>
@@ -32,6 +31,7 @@
 #include <deal.II/dofs/dof_tools.h>
 
 #include <deal.II/fe/fe_tools.h>
+#include <deal.II/fe/fe_values.h>
 
 #include <deal.II/grid/cell_id_translator.h>
 #include <deal.II/grid/filtered_iterator.h>
@@ -3181,8 +3181,6 @@ MGTwoLevelTransferBase<LinearAlgebra::distributed::Vector<Number>>::
     }
 }
 
-
-
 template <int dim, typename Number>
 void
 MGTwoLevelTransfer<dim, LinearAlgebra::distributed::Vector<Number>>::
@@ -3472,6 +3470,373 @@ MGTransferBlockGlobalCoarsening<dim, VectorType>::get_matrix_free_transfer(
   return transfer_operator;
 }
 
+namespace internal
+{
+  namespace
+  {
+    template <int dim>
+    std::shared_ptr<NonMatching::MappingInfo<dim>>
+    fill_mapping_info(const Utilities::MPI::RemotePointEvaluation<dim> &rpe)
+    {
+      const auto &cell_data = rpe.get_cell_data();
+
+      std::vector<typename Triangulation<dim>::active_cell_iterator>
+                                           cell_iterators;
+      std::vector<std::vector<Point<dim>>> unit_points_vector;
+
+      for (unsigned int i = 0; i < cell_data.cells.size(); ++i)
+        {
+          typename Triangulation<dim>::active_cell_iterator cell = {
+            &rpe.get_triangulation(),
+            cell_data.cells[i].first,
+            cell_data.cells[i].second};
+
+          const ArrayView<const Point<dim>> unit_points(
+            cell_data.reference_point_values.data() +
+              cell_data.reference_point_ptrs[i],
+            cell_data.reference_point_ptrs[i + 1] -
+              cell_data.reference_point_ptrs[i]);
+
+          std::vector<Point<dim>> unit_points_vector_cell;
+
+          unit_points_vector_cell.insert(unit_points_vector_cell.begin(),
+                                         unit_points.begin(),
+                                         unit_points.end());
+
+          cell_iterators.emplace_back(cell);
+          unit_points_vector.emplace_back(unit_points_vector_cell);
+        }
+
+      auto mapping_info =
+        std::make_shared<NonMatching::MappingInfo<dim>>(rpe.get_mapping(),
+                                                        update_values);
+      mapping_info->reinit_cells(cell_iterators, unit_points_vector);
+
+      return mapping_info;
+    }
+  } // namespace
+} // namespace internal
+
+
+template <int dim, typename Number>
+void
+MGTwoLevelTransferNonNested<dim, LinearAlgebra::distributed::Vector<Number>>::
+  reinit(const DoFHandler<dim> &          dof_handler_fine,
+         const DoFHandler<dim> &          dof_handler_coarse,
+         const Mapping<dim> &             mapping_fine,
+         const Mapping<dim> &             mapping_coarse,
+         const AffineConstraints<Number> &constraint_fine,
+         const AffineConstraints<Number> &constraint_coarse)
+{
+  AssertThrow(dof_handler_coarse.get_fe().has_support_points(),
+              ExcNotImplemented());
+  Assert(dof_handler_coarse.get_fe().n_components() > 0 &&
+           dof_handler_fine.get_fe().n_components() > 0,
+         ExcNotImplemented());
+  Assert(dof_handler_fine.n_dofs() > dof_handler_coarse.n_dofs(),
+         ExcMessage(
+           "The coarser DoFHandler has more DoFs than the finer DoFHandler."));
+
+  this->fine_element_is_continuous = true;
+
+  // create partitioners and internal vectors
+  {
+    IndexSet locally_relevant_dofs;
+    DoFTools::extract_locally_relevant_dofs(dof_handler_coarse,
+                                            locally_relevant_dofs);
+    this->partitioner_coarse.reset(
+      new Utilities::MPI::Partitioner(dof_handler_coarse.locally_owned_dofs(),
+                                      locally_relevant_dofs,
+                                      dof_handler_coarse.get_communicator()));
+
+    this->vec_coarse.reinit(this->partitioner_coarse);
+  }
+  {
+    this->partitioner_fine.reset(
+      new Utilities::MPI::Partitioner(dof_handler_fine.locally_owned_dofs(),
+                                      dof_handler_fine.get_communicator()));
+
+    this->vec_fine.reinit(this->partitioner_fine);
+  }
+
+
+  // Loop over fine cells and collect points, removing possible duplicates
+  auto &      fe_space = dof_handler_fine.get_fe();
+  const auto &unit_pts = fe_space.get_unit_support_points();
+  std::vector<std::pair<types::global_dof_index, Point<dim>>> points_all;
+  std::vector<Point<dim>>                                     points;
+  std::vector<types::global_dof_index>                        dof_indices(
+    dof_handler_fine.get_fe().n_dofs_per_cell());
+
+  const auto &local_indices_fine = dof_handler_fine.locally_owned_dofs();
+
+  Quadrature<dim> quadrature(unit_pts);
+  FEValues<dim>   fe_values(mapping_fine,
+                          fe_space,
+                          quadrature,
+                          update_quadrature_points);
+
+  for (const auto &cell : dof_handler_fine.active_cell_iterators() |
+                            IteratorFilters::LocallyOwnedCell())
+    {
+      fe_values.reinit(cell);
+      cell->get_dof_indices(dof_indices);
+
+      for (unsigned int i = 0; i < dof_indices.size(); ++i)
+        if (local_indices_fine.is_element(dof_indices[i]) &&
+            (constraint_fine.is_constrained(dof_indices[i]) == false))
+          points_all.emplace_back(local_indices_fine.index_within_set(
+                                    dof_indices[i]),
+                                  fe_values.quadrature_point(i));
+    }
+
+  std::sort(points_all.begin(),
+            points_all.end(),
+            [](const auto &a, const auto &b) { return a.first < b.first; });
+  points_all.erase(std::unique(points_all.begin(),
+                               points_all.end(),
+                               [](const auto &a, const auto &b) {
+                                 return a.first == b.first;
+                               }),
+                   points_all.end());
+
+  for (const auto &i : points_all)
+    {
+      this->level_dof_indices_fine.push_back(i.first);
+      points.push_back(i.second);
+    }
+
+  // Duplicates support points have been removed, hand them over to rpe.
+  rpe.reinit(points, dof_handler_coarse.get_triangulation(), mapping_coarse);
+
+  // set up MappingInfo for easier data access
+  mapping_info = internal::fill_mapping_info(rpe);
+
+  // set up constraints
+  const auto &cell_data = rpe.get_cell_data();
+
+  constraint_info.reinit(dof_handler_coarse,
+                         cell_data.cells.size(),
+                         false /*TODO*/);
+
+  for (unsigned int i = 0; i < cell_data.cells.size(); ++i)
+    {
+      typename DoFHandler<dim>::active_cell_iterator cell = {
+        &rpe.get_triangulation(),
+        cell_data.cells[i].first,
+        cell_data.cells[i].second,
+        &dof_handler_coarse};
+
+      constraint_info.read_dof_indices(i,
+                                       numbers::invalid_unsigned_int,
+                                       cell,
+                                       constraint_coarse,
+                                       this->partitioner_coarse);
+    }
+
+  constraint_info.finalize();
+
+  const auto &fe_base = dof_handler_coarse.get_fe().base_element(0);
+
+  if (const auto fe = dynamic_cast<const FE_Q<dim> *>(&fe_base))
+    fe_coarse = std::make_unique<FE_DGQ<dim>>(fe->get_degree());
+  else if (const auto fe = dynamic_cast<const FE_DGQ<dim> *>(&fe_base))
+    fe_coarse = fe->clone();
+  else
+    AssertThrow(false, ExcMessage(dof_handler_coarse.get_fe().get_name()));
+}
+
+
+
+template <int dim, typename Number>
+void
+MGTwoLevelTransferNonNested<dim, LinearAlgebra::distributed::Vector<Number>>::
+  prolongate_and_add_internal(
+    LinearAlgebra::distributed::Vector<Number> &      dst,
+    const LinearAlgebra::distributed::Vector<Number> &src) const
+{
+  std::vector<Number> evaluation_point_results;
+  std::vector<Number> buffer;
+
+  const auto evaluation_function = [&](auto &values, const auto &cell_data) {
+    std::vector<Number> solution_values;
+
+    FEPointEvaluation<1, dim, dim, Number> evaluator(*mapping_info, *fe_coarse);
+
+    for (unsigned int cell = 0; cell < cell_data.cells.size(); ++cell)
+      {
+        solution_values.resize(fe_coarse->n_dofs_per_cell());
+
+        // gather and resolve constraints
+        internal::VectorReader<Number, VectorizedArrayType> reader;
+        constraint_info.read_write_operation(
+          reader,
+          src,
+          reinterpret_cast<VectorizedArrayType *>(solution_values.data()),
+          cell,
+          1,
+          solution_values.size(),
+          true);
+
+        // evaluate and scatter
+        evaluator.reinit(cell);
+
+        evaluator.evaluate(solution_values, dealii::EvaluationFlags::values);
+
+        for (const auto q : evaluator.quadrature_point_indices())
+          values[q + cell_data.reference_point_ptrs[cell]] =
+            evaluator.get_value(q);
+      }
+  };
+
+  rpe.template evaluate_and_process<Number>(evaluation_point_results,
+                                            buffer,
+                                            evaluation_function);
+
+  // Weight operator in case some points are owned by multiple cells.
+  if (rpe.is_map_unique() == false)
+    {
+      const auto evaluation_point_results_temp = evaluation_point_results;
+      evaluation_point_results.assign(rpe.get_point_ptrs().size() - 1, 0);
+
+      const auto &ptr = rpe.get_point_ptrs();
+
+      for (unsigned int i = 0; i < ptr.size() - 1; ++i)
+        {
+          const auto n_entries = ptr[i + 1] - ptr[i];
+          if (n_entries == 0)
+            continue;
+
+          Number result = 0.0;
+
+          for (unsigned int j = 0; j < n_entries; ++j)
+            result += evaluation_point_results_temp[ptr[i] + j];
+          result /= n_entries;
+
+          evaluation_point_results[i] = result;
+        }
+    }
+
+  for (unsigned int j = 0; j < evaluation_point_results.size(); ++j)
+    dst.local_element(this->level_dof_indices_fine[j]) +=
+      evaluation_point_results[j];
+}
+
+
+
+template <int dim, typename Number>
+void
+MGTwoLevelTransferNonNested<dim, LinearAlgebra::distributed::Vector<Number>>::
+  restrict_and_add_internal(
+    LinearAlgebra::distributed::Vector<Number> &      dst,
+    const LinearAlgebra::distributed::Vector<Number> &src) const
+{
+  std::vector<Number> evaluation_point_results;
+  std::vector<Number> buffer;
+
+  evaluation_point_results.resize(rpe.get_point_ptrs().size() - 1);
+
+  for (unsigned int j = 0; j < evaluation_point_results.size(); ++j)
+    evaluation_point_results[j] =
+      src.local_element(this->level_dof_indices_fine[j]);
+
+  // Weight operator in case some points are owned by multiple cells.
+  if (rpe.is_map_unique() == false)
+    {
+      const auto &ptr = rpe.get_point_ptrs();
+
+      for (unsigned int i = 0; i < ptr.size() - 1; ++i)
+        {
+          const auto n_entries = ptr[i + 1] - ptr[i];
+          if (n_entries == 0)
+            continue;
+
+          evaluation_point_results[i] /= n_entries;
+        }
+    }
+
+  const auto evaluation_function = [&](const auto &values,
+                                       const auto &cell_data) {
+    std::vector<Number>                    solution_values;
+    FEPointEvaluation<1, dim, dim, Number> evaluator(*mapping_info, *fe_coarse);
+
+    for (unsigned int cell = 0; cell < cell_data.cells.size(); ++cell)
+      {
+        solution_values.resize(fe_coarse->n_dofs_per_cell());
+
+        // gather and integrate
+        evaluator.reinit(cell);
+
+        for (const auto q : evaluator.quadrature_point_indices())
+          evaluator.submit_value(
+            values[q + cell_data.reference_point_ptrs[cell]], q);
+
+        evaluator.integrate(solution_values, EvaluationFlags::values);
+
+        // resolve constraints and scatter
+        internal::VectorDistributorLocalToGlobal<Number, VectorizedArrayType>
+          writer;
+        constraint_info.read_write_operation(
+          writer,
+          dst,
+          reinterpret_cast<VectorizedArrayType *>(solution_values.data()),
+          cell,
+          1,
+          solution_values.size(),
+          true);
+      }
+  };
+
+  rpe.template process_and_evaluate<Number>(evaluation_point_results,
+                                            buffer,
+                                            evaluation_function);
+}
+
+
+
+template <int dim, typename Number>
+void
+MGTwoLevelTransferNonNested<dim, LinearAlgebra::distributed::Vector<Number>>::
+  interpolate(LinearAlgebra::distributed::Vector<Number> &      dst,
+              const LinearAlgebra::distributed::Vector<Number> &src) const
+{
+  AssertThrow(false, ExcNotImplemented());
+  (void)dst;
+  (void)src;
+}
+
+
+
+template <int dim, typename Number>
+void
+MGTwoLevelTransferNonNested<dim, LinearAlgebra::distributed::Vector<Number>>::
+  enable_inplace_operations_if_possible(
+    const std::shared_ptr<const Utilities::MPI::Partitioner>
+      &external_partitioner_coarse,
+    const std::shared_ptr<const Utilities::MPI::Partitioner>
+      &external_partitioner_fine)
+{
+  this->internal_enable_inplace_operations_if_possible(
+    external_partitioner_coarse, external_partitioner_fine, constraint_info);
+}
+
+
+
+template <int dim, typename Number>
+std::size_t
+MGTwoLevelTransferNonNested<dim, LinearAlgebra::distributed::Vector<Number>>::
+  memory_consumption() const
+{
+  std::size_t size = 0;
+
+  size += this->partitioner_coarse->memory_consumption();
+  size += this->vec_coarse.memory_consumption();
+  size += MemoryConsumption::memory_consumption(this->level_dof_indices_fine);
+  // TODO: add consumption for rpe, mapping_info and constraint_info.
+
+  return size;
+}
+
 
 DEAL_II_NAMESPACE_CLOSE
 
diff --git a/source/multigrid/mg_transfer_global_coarsening.inst.in b/source/multigrid/mg_transfer_global_coarsening.inst.in
index 409970190a..79b08a4c41 100644
--- a/source/multigrid/mg_transfer_global_coarsening.inst.in
+++ b/source/multigrid/mg_transfer_global_coarsening.inst.in
@@ -19,6 +19,9 @@ for (deal_II_dimension : DIMENSIONS; S1 : REAL_SCALARS)
   {
     template class MGTwoLevelTransfer<deal_II_dimension,
                                       LinearAlgebra::distributed::Vector<S1>>;
+    template class MGTwoLevelTransferNonNested<
+      deal_II_dimension,
+      LinearAlgebra::distributed::Vector<S1>>;
     template class MGTransferBlockMatrixFreeBase<
       deal_II_dimension,
       S1,
diff --git a/tests/multigrid-global-coarsening/mg_transfer_util.h b/tests/multigrid-global-coarsening/mg_transfer_util.h
index f9280925f2..931981f9ae 100644
--- a/tests/multigrid-global-coarsening/mg_transfer_util.h
+++ b/tests/multigrid-global-coarsening/mg_transfer_util.h
@@ -16,6 +16,11 @@
 #ifndef dealii_multigrid_transfer_tests_h
 #define dealii_multigrid_transfer_tests_h
 
+#include <deal.II/base/function_lib.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <deal.II/numerics/vector_tools.h>
+
 #include "../tests.h"
 
 using namespace dealii;
@@ -167,4 +172,138 @@ test_transfer_operator(
   }
 }
 
+
+
+template <int dim, typename Number, typename MeshType>
+void
+test_non_nested_transfer(
+  const MGTwoLevelTransferNonNested<dim,
+                                    LinearAlgebra::distributed::Vector<Number>>
+    &                          transfer,
+  const MeshType &             dof_handler_fine,
+  const MeshType &             dof_handler_coarse,
+  const Function<dim, Number> &function =
+    Functions::ZeroFunction<dim, Number>(),
+  const unsigned int mg_level_fine   = numbers::invalid_unsigned_int,
+  const unsigned int mg_level_coarse = numbers::invalid_unsigned_int)
+{
+  AffineConstraints<Number> constraint_fine;
+  DoFTools::make_hanging_node_constraints(dof_handler_fine, constraint_fine);
+  constraint_fine.close();
+
+  // perform prolongation
+  LinearAlgebra::distributed::Vector<Number> src, dst;
+
+  initialize_dof_vector(dst, dof_handler_fine, mg_level_fine);
+  initialize_dof_vector(src, dof_handler_coarse, mg_level_coarse);
+
+  // test prolongation
+  {
+    src = 0.0;
+    VectorTools::interpolate(dof_handler_coarse, function, src); // src = 1.0
+    dst = 0.0;
+    transfer.prolongate_and_add(dst, src);
+
+    // transfer operator sets only non-constrained dofs -> update the rest
+    // via constraint matrix
+    constraint_fine.distribute(dst);
+
+    // Visualize the result
+    {
+      DataOut<2> data_out;
+      data_out.attach_dof_handler(dof_handler_coarse);
+      data_out.add_data_vector(
+        src,
+        "coarse_solution",
+        DataOut_DoFData<dim, dim>::DataVectorType::type_dof_data);
+      data_out.build_patches();
+      std::ofstream output_coarse("coarse_sol.vtk");
+      data_out.write_vtk(output_coarse);
+      data_out.clear();
+      std::ofstream output_fine("prolonged_sol.vtk");
+      data_out.attach_dof_handler(dof_handler_fine);
+      data_out.add_data_vector(
+        dst,
+        "prolonged_solution",
+        DataOut_DoFData<dim, dim>::DataVectorType::type_dof_data);
+
+      data_out.build_patches();
+      data_out.write_vtk(output_fine);
+    }
+
+    // print norms
+    if (true)
+      {
+        deallog << dst.l2_norm() << std::endl;
+      }
+
+    // print vectors
+    if (true)
+      {
+        print(src);
+        print(dst);
+      }
+
+    // print full prolongation matrix
+    if (Utilities::MPI::n_mpi_processes(MPI_COMM_WORLD) == 1 && false)
+      {
+        FullMatrix<Number> prolongation_matrix(dst.size(), src.size());
+        for (unsigned int i = 0; i < src.size(); ++i)
+          {
+            src    = 0.0;
+            src[i] = 1.0;
+            dst    = 0.0;
+
+            transfer.prolongate_and_add(dst, src);
+
+            for (unsigned int j = 0; j < dst.size(); ++j)
+              prolongation_matrix[j][i] = dst[j];
+          }
+
+        prolongation_matrix.print_formatted(
+          deallog.get_file_stream(), 2, false, 5, "", 1, 1e-5);
+      }
+  }
+
+  // test restriction
+  {
+    VectorTools::interpolate(dof_handler_fine, function, dst); // dst = 1.0
+    src = 0.0;
+    transfer.restrict_and_add(src, dst);
+
+    // print norms
+    if (true)
+      {
+        deallog << src.l2_norm() << std::endl;
+      }
+
+    // print vectors
+    if (true)
+      {
+        print(dst);
+        print(src);
+      }
+
+    // print full restriction matrix
+    if (Utilities::MPI::n_mpi_processes(MPI_COMM_WORLD) == 1 && false)
+      {
+        FullMatrix<Number> restriction_matrix(src.size(), dst.size());
+        for (unsigned int i = 0; i < dst.size(); ++i)
+          {
+            dst    = 0.0;
+            dst[i] = 1.0;
+            src    = 0.0;
+
+            transfer.restrict_and_add(src, dst);
+
+            for (unsigned int j = 0; j < src.size(); ++j)
+              restriction_matrix[j][i] = src[j];
+          }
+
+        restriction_matrix.print_formatted(
+          deallog.get_file_stream(), 2, false, 5, "", 1, 1e-5);
+      }
+  }
+}
+
 #endif
diff --git a/tests/multigrid-global-coarsening/non_nested_multigrid_01.cc b/tests/multigrid-global-coarsening/non_nested_multigrid_01.cc
new file mode 100644
index 0000000000..2b2b504a65
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_multigrid_01.cc
@@ -0,0 +1,155 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 - 2022 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+/**
+ * Test global-coarsening multigrid for a uniformly refined mesh both for
+ * simplex and hypercube mesh.
+ */
+
+#include <deal.II/grid/grid_tools.h>
+
+#include "multigrid_util.h"
+
+template <int dim, typename Number = double>
+void
+test(const unsigned int n_refinements,
+     const unsigned int fe_degree_fine,
+     const bool         do_simplex_mesh)
+{
+  using VectorType = LinearAlgebra::distributed::Vector<Number>;
+
+  const unsigned int min_level = 0;
+  const unsigned int max_level = n_refinements;
+
+  MGLevelObject<Triangulation<dim>>        triangulations(min_level, max_level);
+  MGLevelObject<DoFHandler<dim>>           dof_handlers(min_level, max_level);
+  MGLevelObject<AffineConstraints<Number>> constraints(min_level, max_level);
+  MGLevelObject<std::unique_ptr<Mapping<dim>>> mappings(min_level, max_level);
+  MGLevelObject<std::shared_ptr<MGTwoLevelTransferNonNested<dim, VectorType>>>
+                                       transfers(min_level, max_level);
+  MGLevelObject<Operator<dim, Number>> operators(min_level, max_level);
+
+
+  // set up levels
+  for (auto l = min_level; l <= max_level; ++l)
+    {
+      auto &tria        = triangulations[l];
+      auto &dof_handler = dof_handlers[l];
+      auto &constraint  = constraints[l];
+      auto &op          = operators[l];
+
+      std::unique_ptr<FiniteElement<dim>> fe;
+      std::unique_ptr<Quadrature<dim>>    quad;
+      std::unique_ptr<Mapping<dim>>       mapping;
+
+      if (do_simplex_mesh)
+        {
+          fe      = std::make_unique<FE_SimplexP<dim>>(fe_degree_fine);
+          quad    = std::make_unique<QGaussSimplex<dim>>(fe_degree_fine + 1);
+          mapping = std::make_unique<MappingFE<dim>>(FE_SimplexP<dim>(1));
+        }
+      else
+        {
+          fe      = std::make_unique<FE_Q<dim>>(fe_degree_fine);
+          quad    = std::make_unique<QGauss<dim>>(fe_degree_fine + 1);
+          mapping = std::make_unique<MappingQ<dim>>(1);
+        }
+
+      mappings[l] = mapping->clone();
+
+      // set up triangulation
+      if (do_simplex_mesh)
+        GridGenerator::subdivided_hyper_cube_with_simplices(tria, 2);
+      else
+        GridGenerator::subdivided_hyper_cube(tria, 2);
+      tria.refine_global(l);
+
+      // set up dofhandler
+      dof_handler.reinit(tria);
+      dof_handler.distribute_dofs(*fe);
+
+      // set up constraints
+      IndexSet locally_relevant_dofs;
+      DoFTools::extract_locally_relevant_dofs(dof_handler,
+                                              locally_relevant_dofs);
+      constraint.reinit(locally_relevant_dofs);
+      VectorTools::interpolate_boundary_values(
+        *mapping, dof_handler, 0, Functions::ZeroFunction<dim>(), constraint);
+      constraint.close();
+
+      // set up operator
+      op.reinit(*mapping, dof_handler, *quad, constraint);
+    }
+
+  // set up transfer operator
+  for (unsigned int l = min_level; l < max_level; ++l)
+    {
+      transfers[l + 1] =
+        std::make_shared<MGTwoLevelTransferNonNested<dim, VectorType>>();
+      transfers[l + 1]->reinit(dof_handlers[l + 1],
+                               dof_handlers[l],
+                               *mappings[l + 1],
+                               *mappings[l],
+                               constraints[l + 1],
+                               constraints[l]);
+    }
+
+  MGTransferGlobalCoarsening<dim, VectorType> transfer(
+    transfers,
+    [&](const auto l, auto &vec) { operators[l].initialize_dof_vector(vec); });
+
+
+  GMGParameters mg_data; // TODO
+
+  VectorType dst, src;
+  operators[max_level].initialize_dof_vector(dst);
+  operators[max_level].initialize_dof_vector(src);
+
+  operators[max_level].rhs(src);
+
+  ReductionControl solver_control(
+    mg_data.maxiter, mg_data.abstol, mg_data.reltol, false, false);
+
+  mg_solve(solver_control,
+           dst,
+           src,
+           mg_data,
+           dof_handlers[max_level],
+           operators[max_level],
+           operators,
+           transfer);
+
+  deallog << dim << ' ' << fe_degree_fine << ' ' << n_refinements << ' '
+          << (do_simplex_mesh ? "tri " : "quad") << ' '
+          << solver_control.last_step() << std::endl;
+}
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    all;
+
+  deallog.precision(8);
+
+  for (unsigned int n_refinements = 2; n_refinements <= 4; ++n_refinements)
+    for (unsigned int degree = 1; degree <= 4; ++degree)
+      test<2>(n_refinements, degree, false /*quadrilateral*/);
+
+  // for (unsigned int n_refinements = 2; n_refinements <= 4; ++n_refinements)
+  //   for (unsigned int degree = 1; degree <= 2; ++degree)
+  //     test<2>(n_refinements, degree, true /*triangle*/);
+}
diff --git a/tests/multigrid-global-coarsening/non_nested_multigrid_01.output b/tests/multigrid-global-coarsening/non_nested_multigrid_01.output
new file mode 100644
index 0000000000..6e180875b3
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_multigrid_01.output
@@ -0,0 +1,13 @@
+
+DEAL:0::2 1 2 quad 2
+DEAL:0::2 2 2 quad 3
+DEAL:0::2 3 2 quad 3
+DEAL:0::2 4 2 quad 3
+DEAL:0::2 1 3 quad 3
+DEAL:0::2 2 3 quad 3
+DEAL:0::2 3 3 quad 3
+DEAL:0::2 4 3 quad 3
+DEAL:0::2 1 4 quad 3
+DEAL:0::2 2 4 quad 3
+DEAL:0::2 3 4 quad 3
+DEAL:0::2 4 4 quad 3
diff --git a/tests/multigrid-global-coarsening/non_nested_multigrid_02.cc b/tests/multigrid-global-coarsening/non_nested_multigrid_02.cc
new file mode 100644
index 0000000000..ea553b4b0b
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_multigrid_02.cc
@@ -0,0 +1,142 @@
+// // ---------------------------------------------------------------------
+// //
+// // Copyright (C) 2020 - 2022 by the deal.II authors
+// //
+// // This file is part of the deal.II library.
+// //
+// // The deal.II library is free software; you can use it, redistribute
+// // it, and/or modify it under the terms of the GNU Lesser General
+// // Public License as published by the Free Software Foundation; either
+// // version 2.1 of the License, or (at your option) any later version.
+// // The full text of the license can be found in the file LICENSE.md at
+// // the top level directory of deal.II.
+// //
+// // ---------------------------------------------------------------------
+
+
+/**
+ * Test global-coarsening multigrid for a uniformly refined mesh both for
+ * simplex and hypercube mesh.
+ */
+
+#include <deal.II/grid/grid_tools.h>
+
+#include "multigrid_util.h"
+
+template <int dim, typename Number = double>
+void
+test(const unsigned int n_refinements,
+     const unsigned int fe_degree_fine,
+     const double       factor)
+{
+  using VectorType = LinearAlgebra::distributed::Vector<Number>;
+
+  const unsigned int min_level = 0;
+  const unsigned int max_level = n_refinements;
+
+  MGLevelObject<Triangulation<dim>>        triangulations(min_level, max_level);
+  MGLevelObject<DoFHandler<dim>>           dof_handlers(min_level, max_level);
+  MGLevelObject<AffineConstraints<Number>> constraints(min_level, max_level);
+  MGLevelObject<MappingQ1<dim>>            mappings(min_level, max_level);
+  MGLevelObject<std::shared_ptr<MGTwoLevelTransferNonNested<dim, VectorType>>>
+                                       transfers(min_level, max_level);
+  MGLevelObject<Operator<dim, Number>> operators(min_level, max_level);
+
+
+  // set up levels
+  for (auto l = min_level; l <= max_level; ++l)
+    {
+      auto &tria        = triangulations[l];
+      auto &dof_handler = dof_handlers[l];
+      auto &constraint  = constraints[l];
+      auto &mapping     = mappings[l];
+      auto &op          = operators[l];
+
+      std::unique_ptr<FiniteElement<dim>> fe =
+        std::make_unique<FE_Q<dim>>(fe_degree_fine);
+      std::unique_ptr<Quadrature<dim>> quad =
+        std::make_unique<QGauss<dim>>(fe_degree_fine + 1);
+      std::unique_ptr<Mapping<dim>> _mapping =
+        std::make_unique<MappingFE<dim>>(FE_Q<dim>(1));
+
+
+      // set up triangulation
+      GridGenerator::subdivided_hyper_cube(tria, 2);
+      tria.refine_global(l);
+      GridTools::distort_random(factor,
+                                tria,
+                                true,
+                                boost::random::mt19937::default_seed);
+
+      // set up dofhandler
+      dof_handler.reinit(tria);
+      dof_handler.distribute_dofs(*fe);
+
+      // set up constraints
+      IndexSet locally_relevant_dofs;
+      DoFTools::extract_locally_relevant_dofs(dof_handler,
+                                              locally_relevant_dofs);
+      constraint.reinit(locally_relevant_dofs);
+      VectorTools::interpolate_boundary_values(
+        *_mapping, dof_handler, 0, Functions::ZeroFunction<dim>(), constraint);
+      constraint.close();
+
+      // set up operator
+      op.reinit(*_mapping, dof_handler, *quad, constraint);
+    }
+
+  // set up transfer operator
+  for (unsigned int l = min_level; l < max_level; ++l)
+    {
+      transfers[l + 1] =
+        std::make_shared<MGTwoLevelTransferNonNested<dim, VectorType>>();
+      transfers[l + 1]->reinit(dof_handlers[l + 1],
+                               dof_handlers[l],
+                               mappings[l + 1],
+                               mappings[l],
+                               constraints[l + 1],
+                               constraints[l]);
+    }
+
+  MGTransferGlobalCoarsening<dim, VectorType> transfer(
+    transfers,
+    [&](const auto l, auto &vec) { operators[l].initialize_dof_vector(vec); });
+
+
+  GMGParameters mg_data; // TODO
+
+  VectorType dst, src;
+  operators[max_level].initialize_dof_vector(dst);
+  operators[max_level].initialize_dof_vector(src);
+
+  operators[max_level].rhs(src);
+
+  ReductionControl solver_control(
+    mg_data.maxiter, mg_data.abstol, mg_data.reltol, false, false);
+
+  mg_solve(solver_control,
+           dst,
+           src,
+           mg_data,
+           dof_handlers[max_level],
+           operators[max_level],
+           operators,
+           transfer);
+
+  deallog << dim << ' ' << fe_degree_fine << ' ' << n_refinements << ' '
+          << "quad" << ' ' << solver_control.last_step() << std::endl;
+}
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    all;
+
+  deallog.precision(8);
+
+  const double factor = .36;
+  for (unsigned int n_refinements = 2; n_refinements <= 4; ++n_refinements)
+    for (unsigned int degree = 1; degree <= 4; ++degree)
+      test<2>(n_refinements, degree, factor);
+}
diff --git a/tests/multigrid-global-coarsening/non_nested_multigrid_02.output b/tests/multigrid-global-coarsening/non_nested_multigrid_02.output
new file mode 100644
index 0000000000..f3cc641f1d
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_multigrid_02.output
@@ -0,0 +1,13 @@
+
+DEAL:0::2 1 2 quad 3
+DEAL:0::2 2 2 quad 3
+DEAL:0::2 3 2 quad 3
+DEAL:0::2 4 2 quad 4
+DEAL:0::2 1 3 quad 3
+DEAL:0::2 2 3 quad 3
+DEAL:0::2 3 3 quad 3
+DEAL:0::2 4 3 quad 4
+DEAL:0::2 1 4 quad 3
+DEAL:0::2 2 4 quad 3
+DEAL:0::2 3 4 quad 3
+DEAL:0::2 4 4 quad 4
diff --git a/tests/multigrid-global-coarsening/non_nested_multigrid_03.cc b/tests/multigrid-global-coarsening/non_nested_multigrid_03.cc
new file mode 100644
index 0000000000..5f932b3dce
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_multigrid_03.cc
@@ -0,0 +1,133 @@
+// // ---------------------------------------------------------------------
+// //
+// // Copyright (C) 2020 - 2022 by the deal.II authors
+// //
+// // This file is part of the deal.II library.
+// //
+// // The deal.II library is free software; you can use it, redistribute
+// // it, and/or modify it under the terms of the GNU Lesser General
+// // Public License as published by the Free Software Foundation; either
+// // version 2.1 of the License, or (at your option) any later version.
+// // The full text of the license can be found in the file LICENSE.md at
+// // the top level directory of deal.II.
+// //
+// // ---------------------------------------------------------------------
+
+
+/**
+ * Test global-coarsening multigrid with non-nested levels for a hyper_ball with
+ * a SphericalManifold attached to it.
+ */
+
+#include <deal.II/grid/grid_tools.h>
+
+#include "multigrid_util.h"
+
+template <int dim, typename Number = double>
+void
+test(const unsigned int n_refinements, const unsigned int fe_degree_fine)
+{
+  using VectorType = LinearAlgebra::distributed::Vector<Number>;
+
+  const unsigned int min_level = 0;
+  const unsigned int max_level = n_refinements;
+
+  MGLevelObject<Triangulation<dim>>        triangulations(min_level, max_level);
+  MGLevelObject<DoFHandler<dim>>           dof_handlers(min_level, max_level);
+  MGLevelObject<AffineConstraints<Number>> constraints(min_level, max_level);
+  MGLevelObject<MappingQ1<dim>>            mappings(min_level, max_level);
+  MGLevelObject<std::shared_ptr<MGTwoLevelTransferNonNested<dim, VectorType>>>
+                                       transfers(min_level, max_level);
+  MGLevelObject<Operator<dim, Number>> operators(min_level, max_level);
+
+
+  // set up levels
+  for (auto l = min_level; l <= max_level; ++l)
+    {
+      auto &tria        = triangulations[l];
+      auto &dof_handler = dof_handlers[l];
+      auto &constraint  = constraints[l];
+      auto &mapping     = mappings[l];
+      auto &op          = operators[l];
+
+      std::unique_ptr<FiniteElement<dim>> fe =
+        std::make_unique<FE_Q<dim>>(fe_degree_fine);
+      std::unique_ptr<Quadrature<dim>> quad =
+        std::make_unique<QGauss<dim>>(fe_degree_fine + 1);
+
+      // set up triangulation
+      GridGenerator::hyper_ball(tria, {}, 1.0);
+      tria.refine_global(l);
+
+      // set up dofhandler
+      dof_handler.reinit(tria);
+      dof_handler.distribute_dofs(*fe);
+
+      // set up constraints
+      IndexSet locally_relevant_dofs;
+      DoFTools::extract_locally_relevant_dofs(dof_handler,
+                                              locally_relevant_dofs);
+      constraint.reinit(locally_relevant_dofs);
+      VectorTools::interpolate_boundary_values(
+        mapping, dof_handler, 0, Functions::ZeroFunction<dim>(), constraint);
+      constraint.close();
+
+      // set up operator
+      op.reinit(mapping, dof_handler, *quad, constraint);
+    }
+
+  // set up transfer operator
+  for (unsigned int l = min_level; l < max_level; ++l)
+    {
+      transfers[l + 1] =
+        std::make_shared<MGTwoLevelTransferNonNested<dim, VectorType>>();
+      transfers[l + 1]->reinit(dof_handlers[l + 1],
+                               dof_handlers[l],
+                               mappings[l + 1],
+                               mappings[l],
+                               constraints[l + 1],
+                               constraints[l]);
+    }
+
+  MGTransferGlobalCoarsening<dim, VectorType> transfer(
+    transfers,
+    [&](const auto l, auto &vec) { operators[l].initialize_dof_vector(vec); });
+
+
+  GMGParameters mg_data; // TODO
+
+  VectorType dst, src;
+  operators[max_level].initialize_dof_vector(dst);
+  operators[max_level].initialize_dof_vector(src);
+
+  operators[max_level].rhs(src);
+
+  ReductionControl solver_control(
+    mg_data.maxiter, mg_data.abstol, mg_data.reltol, false, false);
+
+  mg_solve(solver_control,
+           dst,
+           src,
+           mg_data,
+           dof_handlers[max_level],
+           operators[max_level],
+           operators,
+           transfer);
+
+  deallog << dim << ' ' << fe_degree_fine << ' ' << n_refinements << ' '
+          << "quad" << ' ' << solver_control.last_step() << std::endl;
+}
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    all;
+
+  deallog.precision(8);
+
+
+  for (unsigned int n_refinements = 2; n_refinements <= 4; ++n_refinements)
+    for (unsigned int degree = 1; degree <= 4; ++degree)
+      test<2>(n_refinements, degree);
+}
diff --git a/tests/multigrid-global-coarsening/non_nested_multigrid_03.output b/tests/multigrid-global-coarsening/non_nested_multigrid_03.output
new file mode 100644
index 0000000000..81dfdb94c8
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_multigrid_03.output
@@ -0,0 +1,13 @@
+
+DEAL:0::2 1 2 quad 3
+DEAL:0::2 2 2 quad 3
+DEAL:0::2 3 2 quad 4
+DEAL:0::2 4 2 quad 4
+DEAL:0::2 1 3 quad 3
+DEAL:0::2 2 3 quad 3
+DEAL:0::2 3 3 quad 4
+DEAL:0::2 4 3 quad 4
+DEAL:0::2 1 4 quad 3
+DEAL:0::2 2 4 quad 3
+DEAL:0::2 3 4 quad 4
+DEAL:0::2 4 4 quad 4
diff --git a/tests/multigrid-global-coarsening/non_nested_transfer_01.cc b/tests/multigrid-global-coarsening/non_nested_transfer_01.cc
new file mode 100644
index 0000000000..c0397213a6
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_transfer_01.cc
@@ -0,0 +1,148 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 - 2022 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+/**
+ * Test prolongation with non-nested levels.
+ *
+ * Example:
+ *
+ * +---+---+-----+      +-----+-----+
+ * | k | k |     |      |     |     |
+ * |---+---|  k  |      |  k  |  k  |
+ * | k | k |     |  0   |     |     |
+ * +---+---+-----+  ->  +-----+-----+
+ * | k | k |     |      |     |     |
+ * |---+---|  k  |      |  k  |  k  |
+ * | k | k |     |      |     |     |
+ * +---+---+-----+      +-----+-----+
+ *
+ *                 ... with fe_degree in the cells
+ */
+
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/function.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/mpi.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/distributed/tria.h>
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_tools.h>
+#include <deal.II/fe/mapping_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+
+#include <deal.II/matrix_free/fe_evaluation.h>
+#include <deal.II/matrix_free/matrix_free.h>
+
+#include <deal.II/multigrid/mg_constrained_dofs.h>
+#include <deal.II/multigrid/mg_transfer_global_coarsening.h>
+
+#include "mg_transfer_util.h"
+
+using namespace dealii;
+
+template <int dim, typename Number>
+void
+do_test(const FiniteElement<dim> &   fe_fine,
+        const FiniteElement<dim> &   fe_coarse,
+        const Function<dim, Number> &function)
+{
+  // create coarse grid
+  parallel::distributed::Triangulation<dim> tria_coarse(MPI_COMM_WORLD);
+  GridGenerator::hyper_cube(tria_coarse);
+  tria_coarse.refine_global();
+
+  // create fine grid
+  parallel::distributed::Triangulation<dim> tria_fine(MPI_COMM_WORLD);
+  GridGenerator::hyper_cube(tria_fine);
+  tria_fine.refine_global();
+  tria_fine.refine_global();
+
+  // setup dof-handlers
+  DoFHandler<dim> dof_handler_fine(tria_fine);
+  dof_handler_fine.distribute_dofs(fe_fine);
+
+  DoFHandler<dim> dof_handler_coarse(tria_coarse);
+  dof_handler_coarse.distribute_dofs(fe_coarse);
+
+  // setup constraint matrix
+  AffineConstraints<Number> constraint_coarse;
+  constraint_coarse.close();
+
+  AffineConstraints<Number> constraint_fine;
+  constraint_fine.close();
+
+  // setup transfer operator
+  MGTwoLevelTransferNonNested<dim, LinearAlgebra::distributed::Vector<Number>>
+                 transfer;
+  MappingQ1<dim> mapping_fine, mapping_coarse;
+  transfer.reinit(dof_handler_fine,
+                  dof_handler_coarse,
+                  mapping_fine,
+                  mapping_coarse,
+                  constraint_fine,
+                  constraint_coarse);
+
+  test_non_nested_transfer(transfer,
+                           dof_handler_fine,
+                           dof_handler_coarse,
+                           function);
+}
+
+template <int dim, typename Number>
+void
+test(int fe_degree, const Function<dim, Number> &function)
+{
+  const auto str_fine   = std::to_string(fe_degree);
+  const auto str_coarse = std::to_string(fe_degree);
+
+  if (fe_degree > 0)
+    {
+      deallog.push("CG<2>(" + str_fine + ")<->CG<2>(" + str_coarse + ")");
+      do_test<dim, double>(FE_Q<dim>(fe_degree),
+                           FE_Q<dim>(fe_degree),
+                           function);
+      deallog.pop();
+    }
+
+  if (false)
+    {
+      deallog.push("DG<2>(" + str_fine + ")<->DG<2>(" + str_coarse + ")");
+      do_test<dim, double>(FE_DGQ<dim>(fe_degree),
+                           FE_DGQ<dim>(fe_degree),
+                           function);
+      deallog.pop();
+    }
+}
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    all;
+
+  deallog.precision(8);
+
+  Functions::ConstantFunction<2, double> constant(1.);
+  for (unsigned int i = 0; i < 5; ++i)
+    test<2, double>(i, constant);
+}
diff --git a/tests/multigrid-global-coarsening/non_nested_transfer_01.with_p4est=true.mpirun=1.output b/tests/multigrid-global-coarsening/non_nested_transfer_01.with_p4est=true.mpirun=1.output
new file mode 100644
index 0000000000..d2e2e4860c
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_transfer_01.with_p4est=true.mpirun=1.output
@@ -0,0 +1,25 @@
+
+DEAL:0:CG<2>(1)<->CG<2>(1)::5.0000000
+DEAL:0:CG<2>(1)<->CG<2>(1)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(1)<->CG<2>(1)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(1)<->CG<2>(1)::8.5000000
+DEAL:0:CG<2>(1)<->CG<2>(1)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(1)<->CG<2>(1)::2.2500000 3.0000000 3.0000000 4.0000000 2.2500000 3.0000000 2.2500000 3.0000000 2.2500000 
+DEAL:0:CG<2>(2)<->CG<2>(2)::9.0000000
+DEAL:0:CG<2>(2)<->CG<2>(2)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(2)<->CG<2>(2)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(2)<->CG<2>(2)::17.875000
+DEAL:0:CG<2>(2)<->CG<2>(2)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(2)<->CG<2>(2)::1.5625000 1.8750000 1.8750000 2.2500000 3.1250000 3.7500000 3.1250000 3.7500000 6.2500000 1.5625000 1.8750000 3.1250000 3.1250000 3.7500000 6.2500000 1.5625000 1.8750000 3.1250000 3.7500000 3.1250000 6.2500000 1.5625000 3.1250000 3.1250000 6.2500000 
+DEAL:0:CG<2>(3)<->CG<2>(3)::13.000000
+DEAL:0:CG<2>(3)<->CG<2>(3)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(3)<->CG<2>(3)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(3)<->CG<2>(3)::26.656250
+DEAL:0:CG<2>(3)<->CG<2>(3)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(3)<->CG<2>(3)::1.2656250 1.4062500 1.4062500 1.5625000 2.6718750 2.6718750 2.9687500 2.9687500 2.6718750 2.6718750 2.9687500 2.9687500 5.6406250 5.6406250 5.6406250 5.6406250 1.2656250 1.4062500 2.6718750 2.6718750 2.6718750 2.6718750 2.9687500 2.9687500 5.6406250 5.6406250 5.6406250 5.6406250 1.2656250 1.4062500 2.6718750 2.6718750 2.9687500 2.9687500 2.6718750 2.6718750 5.6406250 5.6406250 5.6406250 5.6406250 1.2656250 2.6718750 2.6718750 2.6718750 2.6718750 5.6406250 5.6406250 5.6406250 5.6406250 
+DEAL:0:CG<2>(4)<->CG<2>(4)::17.000000
+DEAL:0:CG<2>(4)<->CG<2>(4)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(4)<->CG<2>(4)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(4)<->CG<2>(4)::36.037598
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+DEAL:0:CG<2>(4)<->CG<2>(4)::1.4582719 1.7089545 1.7089545 2.0027304 2.1321498 3.6874601 2.1321498 2.4986747 4.3213489 2.4986747 2.1321498 3.6874601 2.1321498 2.4986747 4.3213489 2.4986747 3.1174316 5.3914621 3.1174316 5.3914621 9.3242985 5.3914621 3.1174316 5.3914621 3.1174316 1.4582719 1.7089545 2.1321498 3.6874601 2.1321498 2.1321498 3.6874601 2.1321498 2.4986747 4.3213489 2.4986747 3.1174316 5.3914621 3.1174316 5.3914621 9.3242985 5.3914621 3.1174316 5.3914621 3.1174316 1.4582719 1.7089545 2.1321498 3.6874601 2.1321498 2.4986747 4.3213489 2.4986747 2.1321498 3.6874601 2.1321498 3.1174316 5.3914621 3.1174316 5.3914621 9.3242985 5.3914621 3.1174316 5.3914621 3.1174316 1.4582719 2.1321498 3.6874601 2.1321498 2.1321498 3.6874601 2.1321498 3.1174316 5.3914621 3.1174316 5.3914621 9.3242985 5.3914621 3.1174316 5.3914621 3.1174316 
diff --git a/tests/multigrid-global-coarsening/non_nested_transfer_01.with_p4est=true.mpirun=2.output b/tests/multigrid-global-coarsening/non_nested_transfer_01.with_p4est=true.mpirun=2.output
new file mode 100644
index 0000000000..53beceb42c
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_transfer_01.with_p4est=true.mpirun=2.output
@@ -0,0 +1,51 @@
+
+DEAL:0:CG<2>(1)<->CG<2>(1)::5.0000000
+DEAL:0:CG<2>(1)<->CG<2>(1)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(1)<->CG<2>(1)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(1)<->CG<2>(1)::8.5000000
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+DEAL:0:CG<2>(1)<->CG<2>(1)::2.2500000 3.0000000 3.0000000 4.0000000 2.2500000 3.0000000 2.2500000 3.0000000 2.2500000 
+DEAL:0:CG<2>(2)<->CG<2>(2)::9.0000000
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+DEAL:0:CG<2>(2)<->CG<2>(2)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(2)<->CG<2>(2)::17.875000
+DEAL:0:CG<2>(2)<->CG<2>(2)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:0:CG<2>(2)<->CG<2>(2)::1.5625000 1.8750000 1.8750000 2.2500000 3.1250000 3.7500000 3.1250000 3.7500000 6.2500000 1.5625000 1.8750000 3.1250000 3.1250000 3.7500000 6.2500000 1.5625000 1.8750000 3.1250000 3.7500000 3.1250000 6.2500000 1.5625000 3.1250000 3.1250000 6.2500000 
+DEAL:0:CG<2>(3)<->CG<2>(3)::13.000000
+DEAL:0:CG<2>(3)<->CG<2>(3)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
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+DEAL:0:CG<2>(3)<->CG<2>(3)::26.656250
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+DEAL:0:CG<2>(4)<->CG<2>(4)::1.4582719 1.7089545 1.7089545 2.0027304 2.1321498 3.6874601 2.1321498 2.4986747 4.3213489 2.4986747 2.1321498 3.6874601 2.1321498 2.4986747 4.3213489 2.4986747 3.1174316 5.3914621 3.1174316 5.3914621 9.3242985 5.3914621 3.1174316 5.3914621 3.1174316 1.4582719 1.7089545 2.1321498 3.6874601 2.1321498 2.1321498 3.6874601 2.1321498 2.4986747 4.3213489 2.4986747 3.1174316 5.3914621 3.1174316 5.3914621 9.3242985 5.3914621 3.1174316 5.3914621 3.1174316 1.4582719 1.7089545 2.1321498 3.6874601 2.1321498 2.4986747 4.3213489 2.4986747 2.1321498 3.6874601 2.1321498 3.1174316 5.3914621 3.1174316 5.3914621 9.3242985 5.3914621 3.1174316 5.3914621 3.1174316 1.4582719 2.1321498 3.6874601 2.1321498 2.1321498 3.6874601 2.1321498 3.1174316 5.3914621 3.1174316 5.3914621 9.3242985 5.3914621 3.1174316 5.3914621 3.1174316 
+
+DEAL:1:CG<2>(1)<->CG<2>(1)::5.0000000
+DEAL:1:CG<2>(1)<->CG<2>(1)::
+DEAL:1:CG<2>(1)<->CG<2>(1)::1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 
+DEAL:1:CG<2>(1)<->CG<2>(1)::8.5000000
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+DEAL:1:CG<2>(1)<->CG<2>(1)::
+DEAL:1:CG<2>(2)<->CG<2>(2)::9.0000000
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+DEAL:1:CG<2>(2)<->CG<2>(2)::
+DEAL:1:CG<2>(3)<->CG<2>(3)::13.000000
+DEAL:1:CG<2>(3)<->CG<2>(3)::
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+DEAL:1:CG<2>(3)<->CG<2>(3)::26.656250
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+DEAL:1:CG<2>(3)<->CG<2>(3)::
+DEAL:1:CG<2>(4)<->CG<2>(4)::17.000000
+DEAL:1:CG<2>(4)<->CG<2>(4)::
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+DEAL:1:CG<2>(4)<->CG<2>(4)::36.037598
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+DEAL:1:CG<2>(4)<->CG<2>(4)::
+
diff --git a/tests/multigrid-global-coarsening/non_nested_transfer_02.cc b/tests/multigrid-global-coarsening/non_nested_transfer_02.cc
new file mode 100644
index 0000000000..3710e810de
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_transfer_02.cc
@@ -0,0 +1,141 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 - 2022 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+/**
+ * Test prolongation and restriction with "non-nested" triangulations.
+ *
+ */
+
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/mpi.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/distributed/tria.h>
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_tools.h>
+#include <deal.II/fe/mapping_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/grid_tools.h>
+
+#include <deal.II/matrix_free/fe_evaluation.h>
+#include <deal.II/matrix_free/matrix_free.h>
+
+#include <deal.II/multigrid/mg_constrained_dofs.h>
+#include <deal.II/multigrid/mg_transfer_global_coarsening.h>
+
+#include "mg_transfer_util.h"
+
+using namespace dealii;
+
+template <int dim, typename Number>
+void
+do_test(const FiniteElement<dim> &   fe_fine,
+        const FiniteElement<dim> &   fe_coarse,
+        const Function<dim, Number> &function)
+{
+  // create coarse grid
+  parallel::distributed::Triangulation<dim> tria_coarse(MPI_COMM_WORLD);
+  GridGenerator::hyper_cube(tria_coarse, -1. + .2, 1. + .2);
+  const double angle = .5 * numbers::PI_4;
+  GridTools::rotate(angle, tria_coarse);
+  tria_coarse.refine_global(2);
+
+  // create fine grid
+  parallel::distributed::Triangulation<dim> tria_fine(MPI_COMM_WORLD);
+  GridGenerator::hyper_cube(tria_fine, -2., +2.);
+  tria_fine.refine_global(5);
+
+  // setup dof-handlers
+  DoFHandler<dim> dof_handler_fine(tria_fine);
+  dof_handler_fine.distribute_dofs(fe_fine);
+
+  DoFHandler<dim> dof_handler_coarse(tria_coarse);
+  dof_handler_coarse.distribute_dofs(fe_coarse);
+
+  // setup constraint matrix
+  AffineConstraints<Number> constraint_coarse;
+  constraint_coarse.close();
+
+  AffineConstraints<Number> constraint_fine;
+  constraint_fine.close();
+
+  // setup transfer operator
+  MGTwoLevelTransferNonNested<dim, LinearAlgebra::distributed::Vector<Number>>
+                 transfer;
+  MappingQ1<dim> mapping_fine, mapping_coarse;
+  transfer.reinit(dof_handler_fine,
+                  dof_handler_coarse,
+                  mapping_fine,
+                  mapping_coarse,
+                  constraint_fine,
+                  constraint_coarse);
+
+  test_non_nested_transfer(transfer,
+                           dof_handler_fine,
+                           dof_handler_coarse,
+                           function);
+}
+
+template <int dim, typename Number>
+void
+test(int fe_degree, const Function<dim, Number> &function)
+{
+  const auto str_fine   = std::to_string(fe_degree);
+  const auto str_coarse = std::to_string(fe_degree);
+
+  if (false && fe_degree > 0)
+    {
+      deallog.push("CG<2>(" + str_fine + ")<->CG<2>(" + str_coarse + ")");
+      do_test<dim, double>(FE_Q<dim>(fe_degree),
+                           FE_Q<dim>(fe_degree),
+                           function);
+      deallog.pop();
+    }
+
+
+  {
+    deallog.push("DG<2>(" + str_fine + ")<->DG<2>(" + str_coarse + ")");
+    do_test<dim, double>(FE_DGQ<dim>(fe_degree),
+                         FE_DGQ<dim>(fe_degree),
+                         function);
+    deallog.pop();
+  }
+}
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    all;
+
+  deallog.precision(8);
+  Functions::Monomial<2> linear_function(Tensor<1, 2>({1, 0}));   // f(x,y)= x
+  Functions::Monomial<2> bilinear_function(Tensor<1, 2>({1, 1})); // f(x,y)= xy
+  std::vector<Functions::Monomial<2, double>> functions;
+  functions.push_back(linear_function);
+  functions.push_back(bilinear_function);
+
+  for (const auto &f : functions)
+    for (unsigned int i = 0; i < 5; ++i)
+      test<2, double>(i, f);
+}
diff --git a/tests/multigrid-global-coarsening/non_nested_transfer_02.with_p4est=true.mpirun=1.output b/tests/multigrid-global-coarsening/non_nested_transfer_02.with_p4est=true.mpirun=1.output
new file mode 100644
index 0000000000..413d7239b3
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_transfer_02.with_p4est=true.mpirun=1.output
@@ -0,0 +1,61 @@
+
+DEAL:0:DG<2>(0)<->DG<2>(0)::9.1102818
+DEAL:0:DG<2>(0)<->DG<2>(0)::-0.29765786 0.16428191 -0.48899957 -0.027059805 0.62622168 1.0881614 0.43487996 0.89681973 -0.68034129 -0.21840152 -0.87168300 -0.40974324 0.24353825 0.70547801 0.052196529 0.51413630 
+DEAL:0:DG<2>(0)<->DG<2>(0)::0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 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diff --git a/tests/multigrid-global-coarsening/non_nested_transfer_02.with_p4est=true.mpirun=2.output b/tests/multigrid-global-coarsening/non_nested_transfer_02.with_p4est=true.mpirun=2.output
new file mode 100644
index 0000000000..8ef4dc3454
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_transfer_02.with_p4est=true.mpirun=2.output
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2.2215068 2.2684203 2.2931683 2.2265625 2.2521937 2.3007812 2.3493688 2.3750000 2.3032797 2.3297940 2.3800557 2.4303174 2.4568317 2.3437500 2.3707302 2.4218750 2.4730198 2.5000000 1.8750000 1.9019802 1.9531250 2.0042698 2.0312500 1.9073762 1.9348223 1.9868502 2.0388782 2.0663242 1.9687500 1.9970792 2.0507812 2.1044833 2.1328125 2.0301238 2.0593361 2.1147123 2.1700884 2.1993008 2.0625000 2.0921782 2.1484375 2.2046968 2.2343750 2.0312500 2.0582302 2.1093750 2.1605198 2.1875000 2.0663242 2.0937703 2.1457982 2.1978262 2.2252723 2.1328125 2.1611417 2.2148438 2.2685458 2.2968750 2.1993008 2.2285131 2.2838893 2.3392654 2.3684777 2.2343750 2.2640532 2.3203125 2.3765718 2.4062500 2.0625000 2.0921782 2.1484375 2.2046968 2.2343750 2.0948762 2.1250203 2.1821627 2.2393052 2.2694492 2.1562500 2.1872772 2.2460938 2.3049103 2.3359375 2.2176238 2.2495341 2.3100248 2.3705154 2.4024258 2.2500000 2.2823762 2.3437500 2.4051238 2.4375000 2.2343750 2.2640532 2.3203125 2.3765718 2.4062500 2.2694492 2.2995933 2.3567357 2.4138782 2.4440223 2.3359375 2.3669647 2.4257812 2.4845978 2.5156250 2.4024258 2.4343361 2.4948268 2.5553174 2.5872277 2.4375000 2.4698762 2.5312500 2.5926238 2.6250000 2.1875000 2.2144802 2.2656250 2.3167698 2.3437500 2.2252723 2.2527183 2.3047463 2.3567742 2.3842203 2.2968750 2.3252042 2.3789062 2.4326083 2.4609375 2.3684777 2.3976901 2.4530662 2.5084424 2.5376547 2.4062500 2.4359282 2.4921875 2.5484468 2.5781250 2.3437500 2.3707302 2.4218750 2.4730198 2.5000000 2.3842203 2.4116663 2.4636943 2.5157222 2.5431683 2.4609375 2.4892667 2.5429688 2.5966708 2.6250000 2.5376547 2.5668671 2.6222432 2.6776194 2.7068317 2.5781250 2.6078032 2.6640625 2.7203218 2.7500000 2.4062500 2.4359282 2.4921875 2.5484468 2.5781250 2.4440223 2.4741663 2.5313088 2.5884512 2.6185953 2.5156250 2.5466522 2.6054688 2.6642853 2.6953125 2.5872277 2.6191381 2.6796287 2.7401194 2.7720297 2.6250000 2.6573762 2.7187500 2.7801238 2.8125000 2.5781250 2.6078032 2.6640625 2.7203218 2.7500000 2.6185953 2.6487393 2.7058818 2.7630242 2.7931683 2.6953125 2.7263397 2.7851562 2.8439728 2.8750000 2.7720297 2.8039401 2.8644307 2.9249214 2.9568317 2.8125000 2.8448762 2.9062500 2.9676238 3.0000000 1.5000000 1.5323762 1.5937500 1.6551238 1.6875000 1.5215841 1.5544262 1.6166832 1.6789401 1.7117822 1.5625000 1.5962252 1.6601562 1.7240873 1.7578125 1.6034159 1.6380242 1.7036293 1.7692345 1.8038428 1.6250000 1.6600742 1.7265625 1.7930508 1.8281250 1.6875000 1.7198762 1.7812500 1.8426238 1.8750000 1.7117822 1.7446243 1.8068812 1.8691381 1.9019802 1.7578125 1.7915377 1.8554688 1.9193998 1.9531250 1.8038428 1.8384512 1.9040563 1.9696615 2.0042698 1.8281250 1.8631992 1.9296875 1.9961758 2.0312500 1.6250000 1.6600742 1.7265625 1.7930508 1.8281250 1.6465841 1.6821243 1.7494957 1.8168671 1.8524072 1.6875000 1.7239232 1.7929688 1.8620143 1.8984375 1.7284159 1.7657222 1.8364418 1.9071615 1.9444678 1.7500000 1.7877723 1.8593750 1.9309777 1.9687500 1.8281250 1.8631992 1.9296875 1.9961758 2.0312500 1.8524072 1.8879473 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2.3669647 2.4343361 2.4698762 2.3203125 2.3567357 2.4257812 2.4948268 2.5312500 2.3765718 2.4138782 2.4845978 2.5553174 2.5926238 2.4062500 2.4440223 2.5156250 2.5872277 2.6250000 1.7500000 1.7877723 1.8593750 1.9309777 1.9687500 1.7715841 1.8098223 1.8823082 1.9547940 1.9930322 1.8125000 1.8516213 1.9257812 1.9999412 2.0390625 1.8534159 1.8934203 1.9692543 2.0450884 2.0850928 1.8750000 1.9154703 1.9921875 2.0689047 2.1093750 1.9687500 2.0065223 2.0781250 2.1497277 2.1875000 1.9930322 2.0312703 2.1037562 2.1762421 2.2144802 2.0390625 2.0781838 2.1523438 2.2265037 2.2656250 2.0850928 2.1250972 2.2009313 2.2767654 2.3167698 2.1093750 2.1498453 2.2265625 2.3032797 2.3437500 1.8750000 1.9154703 1.9921875 2.0689047 2.1093750 1.8965841 1.9375203 2.0151207 2.0927210 2.1336572 1.9375000 1.9793193 2.0585938 2.1378682 2.1796875 1.9784159 2.0211183 2.1020668 2.1830154 2.2257178 2.0000000 2.0431683 2.1250000 2.2068317 2.2500000 2.1093750 2.1498453 2.2265625 2.3032797 2.3437500 2.1336572 2.1745933 2.2521937 2.3297940 2.3707302 2.1796875 2.2215068 2.3007812 2.3800557 2.4218750 2.2257178 2.2684203 2.3493688 2.4303174 2.4730198 2.2500000 2.2931683 2.3750000 2.4568317 2.5000000 2.1875000 2.2252723 2.2968750 2.3684777 2.4062500 2.2144802 2.2527183 2.3252042 2.3976901 2.4359282 2.2656250 2.3047463 2.3789062 2.4530662 2.4921875 2.3167698 2.3567742 2.4326083 2.5084424 2.5484468 2.3437500 2.3842203 2.4609375 2.5376547 2.5781250 2.4062500 2.4440223 2.5156250 2.5872277 2.6250000 2.4359282 2.4741663 2.5466522 2.6191381 2.6573762 2.4921875 2.5313088 2.6054688 2.6796287 2.7187500 2.5484468 2.5884512 2.6642853 2.7401194 2.7801238 2.5781250 2.6185953 2.6953125 2.7720297 2.8125000 2.3437500 2.3842203 2.4609375 2.5376547 2.5781250 2.3707302 2.4116663 2.4892667 2.5668671 2.6078032 2.4218750 2.4636943 2.5429688 2.6222432 2.6640625 2.4730198 2.5157222 2.5966708 2.6776194 2.7203218 2.5000000 2.5431683 2.6250000 2.7068317 2.7500000 2.5781250 2.6185953 2.6953125 2.7720297 2.8125000 2.6078032 2.6487393 2.7263397 2.8039401 2.8448762 2.6640625 2.7058818 2.7851562 2.8644307 2.9062500 2.7203218 2.7630242 2.8439728 2.9249214 2.9676238 2.7500000 2.7931683 2.8750000 2.9568317 3.0000000 2.2500000 2.2823762 2.3437500 2.4051238 2.4375000 2.2823762 2.3152183 2.3774752 2.4397321 2.4725742 2.3437500 2.3774752 2.4414062 2.5053373 2.5390625 2.4051238 2.4397321 2.5053373 2.5709424 2.6055508 2.4375000 2.4725742 2.5390625 2.6055508 2.6406250 2.4375000 2.4698762 2.5312500 2.5926238 2.6250000 2.4725742 2.5054163 2.5676732 2.6299302 2.6627723 2.5390625 2.5727877 2.6367188 2.7006498 2.7343750 2.6055508 2.6401591 2.7057643 2.7713694 2.8059777 2.6406250 2.6756992 2.7421875 2.8086758 2.8437500 2.4375000 2.4725742 2.5390625 2.6055508 2.6406250 2.4698762 2.5054163 2.5727877 2.6401591 2.6756992 2.5312500 2.5676732 2.6367188 2.7057643 2.7421875 2.5926238 2.6299302 2.7006498 2.7713694 2.8086758 2.6250000 2.6627723 2.7343750 2.8059777 2.8437500 2.6406250 2.6756992 2.7421875 2.8086758 2.8437500 2.6756992 2.7112393 2.7786107 2.8459821 2.8815223 2.7421875 2.7786107 2.8476562 2.9167018 2.9531250 2.8086758 2.8459821 2.9167018 2.9874214 3.0247277 2.8437500 2.8815223 2.9531250 3.0247277 3.0625000 2.6250000 2.6573762 2.7187500 2.7801238 2.8125000 2.6627723 2.6956143 2.7578713 2.8201282 2.8529703 2.7343750 2.7681002 2.8320312 2.8959623 2.9296875 2.8059777 2.8405861 2.9061912 2.9717964 3.0064047 2.8437500 2.8788242 2.9453125 3.0118008 3.0468750 2.8125000 2.8448762 2.9062500 2.9676238 3.0000000 2.8529703 2.8858124 2.9480693 3.0103262 3.0431683 2.9296875 2.9634127 3.0273438 3.0912748 3.1250000 3.0064047 3.0410131 3.1066182 3.1722233 3.2068317 3.0468750 3.0819492 3.1484375 3.2149258 3.2500000 2.8437500 2.8788242 2.9453125 3.0118008 3.0468750 2.8815223 2.9170624 2.9844338 3.0518052 3.0873453 2.9531250 2.9895482 3.0585938 3.1276393 3.1640625 3.0247277 3.0620341 3.1327537 3.2034733 3.2407797 3.0625000 3.1002723 3.1718750 3.2434777 3.2812500 3.0468750 3.0819492 3.1484375 3.2149258 3.2500000 3.0873453 3.1228854 3.1902568 3.2576282 3.2931683 3.1640625 3.2004857 3.2695312 3.3385768 3.3750000 3.2407797 3.2780861 3.3488057 3.4195253 3.4568317 3.2812500 3.3190223 3.3906250 3.4622277 3.5000000 2.6250000 2.6627723 2.7343750 2.8059777 2.8437500 2.6573762 2.6956143 2.7681002 2.8405861 2.8788242 2.7187500 2.7578713 2.8320312 2.9061912 2.9453125 2.7801238 2.8201282 2.8959623 2.9717964 3.0118008 2.8125000 2.8529703 2.9296875 3.0064047 3.0468750 2.8437500 2.8815223 2.9531250 3.0247277 3.0625000 2.8788242 2.9170624 2.9895482 3.0620341 3.1002723 2.9453125 2.9844338 3.0585938 3.1327537 3.1718750 3.0118008 3.0518052 3.1276393 3.2034733 3.2434777 3.0468750 3.0873453 3.1640625 3.2407797 3.2812500 2.8125000 2.8529703 2.9296875 3.0064047 3.0468750 2.8448762 2.8858124 2.9634127 3.0410131 3.0819492 2.9062500 2.9480693 3.0273438 3.1066182 3.1484375 2.9676238 3.0103262 3.0912748 3.1722233 3.2149258 3.0000000 3.0431683 3.1250000 3.2068317 3.2500000 3.0468750 3.0873453 3.1640625 3.2407797 3.2812500 3.0819492 3.1228854 3.2004857 3.2780861 3.3190223 3.1484375 3.1902568 3.2695312 3.3488057 3.3906250 3.2149258 3.2576282 3.3385768 3.4195253 3.4622277 3.2500000 3.2931683 3.3750000 3.4568317 3.5000000 3.0625000 3.1002723 3.1718750 3.2434777 3.2812500 3.1002723 3.1385104 3.2109963 3.2834821 3.3217203 3.1718750 3.2109963 3.2851562 3.3593162 3.3984375 3.2434777 3.2834821 3.3593162 3.4351503 3.4751547 3.2812500 3.3217203 3.3984375 3.4751547 3.5156250 3.2812500 3.3190223 3.3906250 3.4622277 3.5000000 3.3217203 3.3599584 3.4324443 3.5049302 3.5431683 3.3984375 3.4375588 3.5117188 3.5858787 3.6250000 3.4751547 3.5151591 3.5909932 3.6668273 3.7068317 3.5156250 3.5560953 3.6328125 3.7095297 3.7500000 3.2812500 3.3217203 3.3984375 3.4751547 3.5156250 3.3190223 3.3599584 3.4375588 3.5151591 3.5560953 3.3906250 3.4324443 3.5117188 3.5909932 3.6328125 3.4622277 3.5049302 3.5858787 3.6668273 3.7095297 3.5000000 3.5431683 3.6250000 3.7068317 3.7500000 3.5156250 3.5560953 3.6328125 3.7095297 3.7500000 3.5560953 3.5970314 3.6746318 3.7522321 3.7931683 3.6328125 3.6746318 3.7539062 3.8331807 3.8750000 3.7095297 3.7522321 3.8331807 3.9141293 3.9568317 3.7500000 3.7931683 3.8750000 3.9568317 4.0000000 
+DEAL:1:DG<2>(4)<->DG<2>(4)::0.025903112 0.12453371 0.15887278 -0.082695679 -0.094445517 0.12115593 0.25081619 -1.3394734 -1.4729893 -0.087885062 -0.78725585 -4.8742652 -6.7852177 -5.8917630 -1.2469044 -0.41031221 -7.3121987 -10.859544 -6.4562690 -0.96387204 0.23794831 -1.9763004 -2.5215570 -1.2438298 -0.34571395 0.010607602 -0.17858146 -0.13829203 0.070169088 0.020385760 -0.63222757 -1.7001662 -1.3880328 -0.12396924 0.091269169 -0.43874627 -4.7216599 -4.5335364 -1.0304504 0.038843638 -2.1248078 -6.2513654 -5.7231926 -2.6262102 -0.076228573 -0.59768865 -0.80840366 -1.3945653 -0.80312919 0.068436157 -1.3292702 -2.1038560 -1.7518709 -2.9900416 0.18267757 -2.7095474 -13.100648 -16.106048 -11.364725 -2.1042179 -3.2481118 -23.406168 -29.902342 -19.597195 -3.1475843 -5.3117759 -24.466848 -28.807129 -21.959120 -3.1239126 0.27566993 -4.5849522 -8.4448709 -2.1519177 -1.1276779 0.017860211 -1.9443367 -1.5870898 -0.30181447 -0.27036613 -1.2859792 -9.9155242 -9.4407922 -4.3196160 -0.78694232 -4.9178311 -16.657998 -17.805726 -9.5156873 -0.71683172 -1.6094557 -18.799694 -18.451235 -9.6749258 -2.7785577 -0.47428818 -4.2847292 -2.7293956 -2.7844545 -0.10317691 0.021619619 0.21711113 1.1454790 0.97951989 0.0097699052 0.098215204 1.9580139 4.8922798 6.8587029 1.9602202 0.049425632 1.6925936 7.5038398 9.7080794 1.5922756 -0.19683917 0.74359136 4.9560534 8.0698138 2.4702266 -0.074251743 0.12277360 0.39132894 1.4510739 1.0050051 0.42801422 2.4006644 1.6554008 4.2162705 1.1429946 1.8095083 9.2546919 19.855233 17.453600 2.5475647 2.8970191 15.756819 27.327855 28.489875 5.0914770 1.2672322 12.697763 23.149201 23.388363 7.5370662 0.57208042 0.78583783 5.8714750 3.6180289 -0.61325350 0.12267868 -0.25719162 1.3047182 1.5503637 -0.13744886 -0.55799381 -0.79424986 4.2186751 7.2099123 0.71579279 -1.1931169 -4.0025389 2.5581292 9.2123375 2.5991997 -1.0529727 -5.0027322 -0.24478296 4.7167863 0.98261856 -0.48638833 -0.85901543 -0.51076987 0.45795765 0.57830811 0.24334514 2.8743672 4.1421951 3.4139283 0.58007320 2.6787218 14.365772 22.583730 27.613405 6.3808280 2.0276016 15.713851 33.470174 31.688794 8.7047132 2.2139810 12.642610 23.231176 27.473088 3.4203871 0.28503267 2.4844114 4.2508470 6.4399739 1.3478113 
+
diff --git a/tests/multigrid-global-coarsening/non_nested_transfer_03.cc b/tests/multigrid-global-coarsening/non_nested_transfer_03.cc
new file mode 100644
index 0000000000..8859c9da07
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_transfer_03.cc
@@ -0,0 +1,153 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2020 - 2022 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE.md at
+// the top level directory of deal.II.
+//
+// ---------------------------------------------------------------------
+
+
+/**
+ * Test prolongation and restriction with "non-nested" triangulations where one
+ * is obtained from the other by a "random" distortion.
+ *
+ */
+
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/logstream.h>
+#include <deal.II/base/mpi.h>
+#include <deal.II/base/quadrature_lib.h>
+
+#include <deal.II/distributed/tria.h>
+
+#include <deal.II/dofs/dof_handler.h>
+
+#include <deal.II/fe/fe_dgq.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/fe/fe_tools.h>
+#include <deal.II/fe/mapping_q.h>
+
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/grid_out.h>
+#include <deal.II/grid/grid_tools.h>
+
+#include <deal.II/matrix_free/fe_evaluation.h>
+#include <deal.II/matrix_free/matrix_free.h>
+
+#include <deal.II/multigrid/mg_constrained_dofs.h>
+#include <deal.II/multigrid/mg_transfer_global_coarsening.h>
+
+#include "mg_transfer_util.h"
+
+using namespace dealii;
+
+template <int dim, typename Number>
+void
+do_test(const FiniteElement<dim> &   fe_fine,
+        const FiniteElement<dim> &   fe_coarse,
+        const Function<dim, Number> &function)
+{
+  // create coarse grid
+  parallel::distributed::Triangulation<dim> tria_coarse(MPI_COMM_WORLD);
+  GridGenerator::hyper_cube(tria_coarse, -1., 1.);
+  tria_coarse.refine_global(3);
+  const double factor = 0.25;
+  GridTools::distort_random(factor,
+                            tria_coarse,
+                            true,
+                            boost::random::mt19937::default_seed);
+
+  // create fine grid
+  parallel::distributed::Triangulation<dim> tria_fine(MPI_COMM_WORLD);
+  GridGenerator::hyper_cube(tria_fine, -1., 1.);
+  tria_fine.refine_global(4);
+  GridTools::distort_random(factor,
+                            tria_fine,
+                            true,
+                            boost::random::mt19937::default_seed);
+
+
+  {
+    // Just print the grids.
+    std::ofstream coarse_filename("initial_tria.vtk");
+    std::ofstream fine_filename("distorted_tria.vtk");
+    GridOut       go;
+    go.write_vtk(tria_coarse, coarse_filename);
+    go.write_vtk(tria_fine, fine_filename);
+  }
+
+  // setup dof-handlers
+  DoFHandler<dim> dof_handler_fine(tria_fine);
+  dof_handler_fine.distribute_dofs(fe_fine);
+
+  DoFHandler<dim> dof_handler_coarse(tria_coarse);
+  dof_handler_coarse.distribute_dofs(fe_coarse);
+
+  // setup constraint matrix
+  AffineConstraints<Number> constraint_coarse;
+  constraint_coarse.close();
+
+  AffineConstraints<Number> constraint_fine;
+  constraint_fine.close();
+
+  // setup transfer operator
+  MGTwoLevelTransferNonNested<dim, LinearAlgebra::distributed::Vector<Number>>
+                 transfer;
+  MappingQ1<dim> mapping_fine, mapping_coarse;
+  transfer.reinit(dof_handler_fine,
+                  dof_handler_coarse,
+                  mapping_fine,
+                  mapping_coarse,
+                  constraint_fine,
+                  constraint_coarse);
+
+  test_non_nested_transfer(transfer,
+                           dof_handler_fine,
+                           dof_handler_coarse,
+                           function);
+}
+
+template <int dim, typename Number>
+void
+test(int fe_degree, const Function<dim, Number> &function)
+{
+  const auto str_fine   = std::to_string(fe_degree);
+  const auto str_coarse = std::to_string(fe_degree);
+
+  if (false && fe_degree > 0)
+    {
+      deallog.push("CG<2>(" + str_fine + ")<->CG<2>(" + str_coarse + ")");
+      do_test<dim, double>(FE_Q<dim>(fe_degree),
+                           FE_Q<dim>(fe_degree),
+                           function);
+      deallog.pop();
+    }
+
+
+  {
+    deallog.push("DG<2>(" + str_fine + ")<->DG<2>(" + str_coarse + ")");
+    do_test<dim, double>(FE_DGQ<dim>(fe_degree),
+                         FE_DGQ<dim>(fe_degree),
+                         function);
+    deallog.pop();
+  }
+}
+
+int
+main(int argc, char **argv)
+{
+  Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
+  MPILogInitAll                    all;
+
+  deallog.precision(8);
+  Functions::Monomial<2> linear_function(Tensor<1, 2>({1, 0})); // f(x,y)= x
+  for (unsigned int i = 0; i < 5; ++i)
+    test<2, double>(i, linear_function);
+}
diff --git a/tests/multigrid-global-coarsening/non_nested_transfer_03.with_p4est=true.mpirun=1.output b/tests/multigrid-global-coarsening/non_nested_transfer_03.with_p4est=true.mpirun=1.output
new file mode 100644
index 0000000000..42c4b4a4bd
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_transfer_03.with_p4est=true.mpirun=1.output
@@ -0,0 +1,31 @@
+
+DEAL:0:DG<2>(0)<->DG<2>(0)::9.1426608
+DEAL:0:DG<2>(0)<->DG<2>(0)::-0.86478889 -0.60273954 -0.87451662 -0.59951560 -0.35407707 -0.13164496 -0.35017792 -0.13921796 -0.87413917 -0.60017225 -0.87745460 -0.60551357 -0.34820017 -0.12145316 -0.32822840 -0.11009100 0.10638934 0.38671835 0.11741831 0.41189230 0.64704900 0.88223854 0.64770233 0.86726736 0.14731533 0.42664274 0.14072519 0.42648435 0.65561163 0.87557029 0.65371645 0.87787886 -0.88131926 -0.63377744 -0.85937528 -0.63730723 -0.37254197 -0.14160095 -0.42083510 -0.14418921 -0.85889276 -0.63234467 -0.86779359 -0.62669751 -0.39270454 -0.12291875 -0.36828233 -0.12411966 0.11455283 0.39157928 0.12914527 0.38291275 0.60284591 0.84733662 0.60878194 0.85630052 0.11405748 0.38307851 0.095026206 0.36672947 0.64361538 0.87826047 0.63892120 0.88195918 
+DEAL:0:DG<2>(0)<->DG<2>(0)::-0.86478889 -0.86478889 -0.86478889 -0.86478889 -0.60273954 -0.60273954 -0.60273954 -0.60273954 -0.87451662 -0.87451662 -0.87451662 -0.87451662 -0.59951560 -0.59951560 -0.59951560 -0.59951560 -0.35407707 -0.35407707 -0.35407707 -0.35407707 -0.13164496 -0.13164496 -0.13164496 -0.13164496 -0.35017792 -0.35017792 -0.35017792 -0.35017792 -0.13921796 0.11741831 -0.13921796 -0.13921796 -0.87413917 -0.87413917 -0.87413917 -0.87413917 -0.60017225 -0.60017225 -0.60017225 -0.60017225 -0.87745460 -0.87745460 -0.87745460 -0.87745460 -0.60551357 -0.60551357 -0.60551357 -0.60551357 -0.34820017 -0.34820017 -0.34820017 -0.34820017 -0.12145316 -0.12145316 -0.12145316 -0.12145316 -0.32822840 -0.32822840 -0.32822840 -0.32822840 -0.11009100 -0.11009100 -0.11009100 -0.14160095 0.10638934 0.10638934 0.10638934 0.10638934 0.38671835 0.38671835 0.38671835 0.38671835 0.11741831 0.11741831 0.11741831 0.11741831 0.41189230 0.41189230 0.41189230 0.41189230 0.64704900 0.64704900 0.64704900 0.64704900 0.88223854 0.88223854 0.88223854 0.88223854 0.64770233 0.64770233 0.64770233 0.64770233 0.86726736 0.86726736 0.86726736 0.86726736 0.14731533 0.14731533 0.14731533 0.14731533 0.42664274 0.42664274 0.42664274 0.42664274 0.14072519 0.14072519 0.14072519 0.14072519 0.42648435 0.42648435 0.42648435 0.42648435 0.65561163 0.65561163 0.42664274 0.65561163 0.87557029 0.87557029 0.87557029 0.87557029 0.42648435 0.65371645 0.65371645 0.65371645 0.87787886 0.87787886 0.87787886 0.87787886 -0.88131926 -0.88131926 -0.88131926 -0.88131926 -0.63377744 -0.63377744 -0.63377744 -0.63377744 -0.85937528 -0.85937528 -0.85937528 -0.85937528 -0.63730723 -0.63730723 -0.63730723 -0.63730723 -0.37254197 -0.37254197 -0.37254197 -0.37254197 -0.14160095 0.11455283 -0.14160095 -0.14160095 -0.42083510 -0.42083510 -0.42083510 -0.42083510 -0.14418921 -0.14418921 -0.14418921 -0.14418921 -0.85889276 -0.85889276 -0.85889276 -0.85889276 -0.63234467 -0.63234467 -0.63234467 -0.63234467 -0.86779359 -0.86779359 -0.86779359 -0.86779359 -0.62669751 -0.62669751 -0.62669751 -0.62669751 -0.39270454 -0.39270454 -0.39270454 -0.39270454 -0.12291875 -0.12291875 -0.12291875 -0.12291875 -0.36828233 -0.36828233 -0.36828233 -0.36828233 -0.12411966 -0.12411966 -0.12411966 -0.12411966 0.11455283 0.11455283 0.11455283 0.11455283 0.39157928 0.39157928 0.39157928 0.38291275 0.12914527 0.12914527 0.12914527 0.12914527 0.38291275 0.38291275 0.38291275 0.38291275 0.60284591 0.60284591 0.60284591 0.60284591 0.84733662 0.84733662 0.84733662 0.84733662 0.60878194 0.60878194 0.60878194 0.60878194 0.85630052 0.85630052 0.85630052 0.85630052 0.11405748 0.11405748 0.11405748 0.11405748 0.38307851 0.38307851 0.38307851 0.38307851 0.095026206 0.095026206 0.095026206 0.095026206 0.36672947 0.36672947 0.36672947 0.36672947 0.64361538 0.64361538 0.64361538 0.64361538 0.87826047 0.87826047 0.87826047 0.87826047 0.63892120 0.63892120 0.63892120 0.63892120 0.88195918 0.88195918 0.88195918 0.88195918 
+DEAL:0:DG<2>(0)<->DG<2>(0)::18.304952
+DEAL:0:DG<2>(0)<->DG<2>(0)::-0.93239445 -0.80136977 -0.93725831 -0.79975780 -0.67703853 -0.56582248 -0.67508896 -0.56960898 -0.93706959 -0.80008613 -0.93872730 -0.80275679 -0.67410008 -0.56072658 -0.66411420 -0.55504550 -0.44680533 -0.30664082 -0.44129085 -0.29405385 -0.17647550 -0.066366319 -0.16263726 -0.053131923 -0.42557091 -0.28740525 -0.42789265 -0.29855279 -0.16458944 -0.052595633 -0.18030856 -0.068653613 -0.94803605 -0.82375375 -0.94645157 -0.82209461 -0.67814193 -0.56145417 -0.67672903 -0.56290858 -0.94369952 -0.81611769 -0.93478433 -0.80854362 -0.68460776 -0.57140957 -0.70137595 -0.57598500 -0.43527962 -0.30259791 -0.45159607 -0.30713479 -0.17976651 -0.067877966 -0.18299098 -0.072862035 -0.44475919 -0.31093116 -0.42607114 -0.30963314 -0.19083973 -0.070234723 -0.18951138 -0.055166983 0.062680231 0.20285971 0.070957260 0.19760103 0.31400212 0.42649220 0.31214400 0.42450668 0.070674550 0.18518725 0.061647765 0.19427038 0.30186817 0.42663490 0.30402772 0.43119418 0.55514885 0.69080815 0.55392759 0.69767346 0.82541930 0.94457603 0.82106806 0.93859292 0.56473572 0.70916398 0.56256875 0.70658266 0.80812045 0.92389632 0.81229766 0.92246066 0.057024736 0.20073137 0.063058721 0.19652751 0.32402832 0.44230631 0.31093247 0.42620047 0.058200122 0.18991146 0.056463025 0.18848577 0.30218300 0.42634355 0.31030145 0.44106750 0.56221066 0.70046947 0.55744103 0.68892736 0.80805407 0.92227034 0.81041588 0.93742512 0.55406286 0.68019088 0.57485503 0.70018263 0.81646774 0.93925477 0.81828450 0.92775405 -0.94133437 -0.80672039 -0.95100463 -0.81668602 -0.67832826 -0.55243711 -0.67833436 -0.55774654 -0.94683900 -0.81104534 -0.94321421 -0.80549648 -0.68833487 -0.58018463 -0.68574410 -0.58341142 -0.41976970 -0.30501363 -0.42666389 -0.30939223 -0.17935640 -0.040482548 -0.18601718 -0.050928789 -0.44777379 -0.33032679 -0.45630325 -0.33452972 -0.21239263 -0.078400735 -0.20981006 -0.082882376 -0.93255765 -0.79625319 -0.93077312 -0.80214535 -0.68587218 -0.57091013 -0.68899606 -0.56624869 -0.93312490 -0.81275545 -0.93284203 -0.81062104 -0.70010374 -0.58416417 -0.69614469 -0.57615412 -0.44652582 -0.33713497 -0.43712476 -0.31389774 -0.20097474 -0.075706850 -0.19336924 -0.078139743 -0.43890874 -0.30047231 -0.43845050 -0.31332858 -0.20124123 -0.084135366 -0.20099150 -0.074034677 0.077129820 0.19394235 0.081672986 0.20062602 0.31361292 0.43492528 0.32233817 0.43519174 0.071201013 0.19054420 0.051731029 0.18351917 0.31588826 0.43813776 0.32250306 0.45081899 0.56947309 0.69229008 0.54973057 0.67450451 0.80943494 0.93435800 0.80219695 0.93834994 0.55504019 0.69411342 0.57598741 0.70414394 0.81940265 0.94335395 0.82070868 0.94369645 0.041114765 0.18979987 0.054851094 0.19994970 0.33302041 0.46231881 0.31782421 0.43745878 0.058580797 0.18976886 0.056224154 0.18176548 0.30799998 0.42430842 0.31253209 0.43502889 0.57908624 0.68155323 0.55701216 0.66411637 0.80117751 0.93480176 0.80329453 0.94162548 0.54296454 0.66386615 0.55119960 0.67632445 0.81195991 0.95171047 0.81177030 0.94431702 
+DEAL:0:DG<2>(0)<->DG<2>(0)::-3.4707803 -2.4875590 -3.4786398 -2.4539864 -1.4887909 -0.45861100 -1.4394216 -0.41355162 -3.5403360 -2.4792337 -3.5031452 -2.5333783 -1.4966084 -0.50349749 -1.4913946 -0.45058584 0.53409824 1.4771450 0.45918432 1.4637250 2.4975581 3.5296563 2.5430511 3.4667751 0.51734234 2.0609086 0.49306038 2.0339584 1.9516075 3.4781654 1.9552285 3.5017611 -3.5157454 -2.4668463 -3.5065950 -2.5376750 -1.4608395 -0.47146935 -1.5689336 -0.58348580 -3.4617293 -2.5120271 -3.4893434 -2.5565667 -1.5346833 -0.54819058 -1.4911601 -0.56040277 0.51288863 1.0708764 0.49699542 1.9625398 2.4859982 3.4843398 2.5292850 3.5271617 0.48571542 1.5506222 0.48633929 1.4798694 2.4817680 3.4808993 2.4343547 3.5197577 
+DEAL:0:DG<2>(1)<->DG<2>(1)::18.554172
+DEAL:0:DG<2>(1)<->DG<2>(1)::-1.0000000 -0.75000000 -1.0000000 -0.70915557 -0.75000000 -0.50000000 -0.70915557 -0.45180260 -1.0000000 -0.70915557 -1.0000000 -0.78891093 -0.70915557 -0.45180260 -0.78891093 -0.44819331 -0.50000000 -0.25000000 -0.45180260 -0.21450567 -0.25000000 0.0000000 -0.21450567 -0.062074193 -0.45180260 -0.21450567 -0.44819331 -0.28621011 -0.21450567 -0.062074193 -0.28621011 0.0059181176 -1.0000000 -0.78891093 -1.0000000 -0.70764576 -0.78891093 -0.44819331 -0.70764576 -0.45593902 -1.0000000 -0.70764576 -1.0000000 -0.80217264 -0.70764576 -0.45593902 -0.80217264 -0.45629687 -0.44819331 -0.28621011 -0.45593902 -0.20245824 -0.28621011 0.0059181176 -0.20245824 -0.0030624158 -0.45593902 -0.20245824 -0.45629687 -0.19821946 -0.20245824 -0.0030624158 -0.19821946 -0.036623887 0.0000000 0.25000000 -0.062074193 0.23763155 0.25000000 0.50000000 0.23763155 0.55924186 -0.062074193 0.23763155 0.0059181176 0.28819776 0.23763155 0.55924186 0.28819776 0.56249801 0.50000000 0.75000000 0.55924186 0.77895416 0.75000000 1.0000000 0.77895416 1.0000000 0.55924186 0.77895416 0.56249801 0.69011529 0.77895416 1.0000000 0.69011529 1.0000000 0.0059181176 0.28819776 -0.0030624158 0.29820785 0.28819776 0.56249801 0.29820785 0.55766732 -0.0030624158 0.29820785 -0.036623887 0.30437923 0.29820785 0.55766732 0.30437923 0.54568301 0.56249801 0.69011529 0.55766732 0.81216589 0.69011529 1.0000000 0.81216589 1.0000000 0.55766732 0.81216589 0.54568301 0.69934957 0.81216589 1.0000000 0.69934957 1.0000000 -1.0000000 -0.80217264 -1.0000000 -0.72310439 -0.80217264 -0.45629687 -0.72310439 -0.55353584 -1.0000000 -0.72310439 -1.0000000 -0.71439671 -0.72310439 -0.55353584 -0.71439671 -0.55819197 -0.45629687 -0.19821946 -0.55353584 -0.28211572 -0.19821946 -0.036623887 -0.28211572 -0.049444753 -0.55353584 -0.28211572 -0.55819197 -0.28949687 -0.28211572 -0.049444753 -0.28949687 0.044300501 -1.0000000 -0.71439671 -1.0000000 -0.72117435 -0.71439671 -0.55819197 -0.72117435 -0.53561568 -1.0000000 -0.72117435 -1.0000000 -0.75000000 -0.72117435 -0.53561568 -0.75000000 -0.50000000 -0.55819197 -0.28949687 -0.53561568 -0.18751365 -0.28949687 0.044300501 -0.18751365 -0.058964970 -0.53561568 -0.18751365 -0.50000000 -0.25000000 -0.18751365 -0.058964970 -0.25000000 0.0000000 -0.036623887 0.30437923 -0.049444753 0.23990075 0.30437923 0.54568301 0.23990075 0.47635414 -0.049444753 0.23990075 0.044300501 0.28182458 0.23990075 0.47635414 0.28182458 0.53357155 0.54568301 0.69934957 0.47635414 0.68999691 0.69934957 1.0000000 0.68999691 1.0000000 0.47635414 0.68999691 0.53357155 0.73520517 0.68999691 1.0000000 0.73520517 1.0000000 0.044300501 0.28182458 -0.058964970 0.18906980 0.28182458 0.53357155 0.18906980 0.52784810 -0.058964970 0.18906980 0.0000000 0.25000000 0.18906980 0.52784810 0.25000000 0.50000000 0.53357155 0.73520517 0.52784810 0.77783671 0.73520517 1.0000000 0.77783671 1.0000000 0.52784810 0.77783671 0.50000000 0.75000000 0.77783671 1.0000000 0.75000000 1.0000000 
+DEAL:0:DG<2>(1)<->DG<2>(1)::-1.0000000 -0.87500000 -1.0000000 -0.85457778 -0.87500000 -0.75000000 -0.85457778 -0.72590130 -1.0000000 -0.85457778 -1.0000000 -0.89445546 -0.85457778 -0.72590130 -0.89445546 -0.72409666 -0.75000000 -0.62500000 -0.72590130 -0.60725283 -0.62500000 -0.50000000 -0.60725283 -0.53103710 -0.72590130 -0.60725283 -0.72409666 -0.64310506 -0.60725283 -0.53103710 -0.64310506 -0.49704094 -1.0000000 -0.89445546 -1.0000000 -0.85382288 -0.89445546 -0.72409666 -0.85382288 -0.72796951 -1.0000000 -0.85382288 -1.0000000 -0.90108632 -0.85382288 -0.72796951 -0.90108632 -0.72814843 -0.72409666 -0.64310506 -0.72796951 -0.60122912 -0.64310506 -0.49704094 -0.60122912 -0.50153121 -0.72796951 -0.60122912 -0.72814843 -0.59910973 -0.60122912 -0.50153121 -0.59910973 -0.51831194 -0.50000000 -0.37500000 -0.53103710 -0.38118422 -0.37500000 -0.25000000 -0.38118422 -0.22037907 -0.53103710 -0.38118422 -0.49704094 -0.35590112 -0.38118422 -0.22037907 -0.35590112 -0.21875099 -0.25000000 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diff --git a/tests/multigrid-global-coarsening/non_nested_transfer_03.with_p4est=true.mpirun=2.output b/tests/multigrid-global-coarsening/non_nested_transfer_03.with_p4est=true.mpirun=2.output
new file mode 100644
index 0000000000..74cb4feea6
--- /dev/null
+++ b/tests/multigrid-global-coarsening/non_nested_transfer_03.with_p4est=true.mpirun=2.output
@@ -0,0 +1,63 @@
+
+DEAL:0:DG<2>(0)<->DG<2>(0)::9.1326052
+DEAL:0:DG<2>(0)<->DG<2>(0)::-0.86478889 -0.60273954 -0.87451662 -0.59951560 -0.35407707 -0.13164496 -0.35017792 -0.13921796 -0.87413917 -0.60017225 -0.87745460 -0.60551357 -0.34820017 -0.12145316 -0.32822840 -0.11009100 0.10638934 0.38671835 0.11741831 0.41189230 0.64704900 0.88223854 0.64770233 0.86726736 0.14731533 0.42664274 0.14072519 0.42648435 0.65561163 0.87557029 0.65371645 0.87787886 
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+DEAL:1:DG<2>(0)<->DG<2>(0)::9.1326052
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+DEAL:1:DG<2>(0)<->DG<2>(0)::18.272464
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+DEAL:1:DG<2>(0)<->DG<2>(0)::-2.6654325 -3.2883093 -3.4786398 -2.4539864 -1.4850259 -0.45716300 -1.4394216 -0.41355162 -3.5403360 -2.9436730 -3.5152977 -2.4678178 -1.0926549 -0.48988821 -1.5065754 -0.55087821 0.46589158 1.5036761 0.47609973 1.4806281 2.5524613 3.4622335 2.5133393 3.5189872 0.53950070 1.4717689 0.54830163 2.0474084 2.4937983 3.4944579 1.9110403 3.4917966 
+DEAL:1:DG<2>(1)<->DG<2>(1)::18.520449
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