From e1ed42ad55951be975cdf5481ba86f0ee0289e61 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Wed, 21 Aug 2024 13:13:07 +0200
Subject: [PATCH 01/10] Remove refine option `distribute` and `ghost_mode` in
 favor of an explicit partitioner

---
 cpp/dolfinx/refinement/refine.h               |  67 ++--
 cpp/dolfinx/refinement/utils.h                |  45 ---
 cpp/test/mesh/refinement/interval.cpp         |   7 +-
 cpp/test/mesh/refinement/rectangle.cpp        |   6 +-
 cpp/test/transfer/transfer_matrix.cpp         | 315 ++++++++++++++++++
 python/dolfinx/mesh.py                        |  12 +-
 python/dolfinx/wrappers/refinement.cpp        |  78 ++++-
 python/test/unit/refinement/test_interval.py  |  12 +-
 .../test/unit/refinement/test_refinement.py   |  20 +-
 9 files changed, 434 insertions(+), 128 deletions(-)
 create mode 100644 cpp/test/transfer/transfer_matrix.cpp

diff --git a/cpp/dolfinx/refinement/refine.h b/cpp/dolfinx/refinement/refine.h
index 32f18d89827..50d2181207c 100644
--- a/cpp/dolfinx/refinement/refine.h
+++ b/cpp/dolfinx/refinement/refine.h
@@ -17,46 +17,40 @@
 #include <optional>
 #include <utility>
 
+#include "dolfinx/graph/AdjacencyList.h"
+#include "dolfinx/mesh/Mesh.h"
+#include "dolfinx/mesh/Topology.h"
+#include "dolfinx/mesh/cell_types.h"
+#include "dolfinx/mesh/utils.h"
+
+#include "interval.h"
+#include "plaza.h"
+
 namespace dolfinx::refinement
 {
-namespace impl
-{
-/// @brief create the refined mesh by optionally redistributing it
-template <std::floating_point T>
-mesh::Mesh<T>
-create_refined_mesh(const mesh::Mesh<T>& mesh,
-                    const graph::AdjacencyList<std::int64_t>& cell_adj,
-                    std::span<const T> new_vertex_coords,
-                    std::array<std::size_t, 2> xshape, bool redistribute,
-                    mesh::GhostMode ghost_mode)
+
+// TODO: move to cpp?
+inline graph::AdjacencyList<std::int32_t> maintain_coarse_partitioner(
+    MPI_Comm comm, int, const std::vector<mesh::CellType>& cell_types,
+    const std::vector<std::span<const std::int64_t>>& cell_topology)
 {
-  if (dolfinx::MPI::size(mesh.comm()) == 1)
-  {
-    // No parallel construction necessary, i.e. redistribute also has no
-    // effect
-    return mesh::create_mesh(mesh.comm(), cell_adj.array(),
-                             mesh.geometry().cmap(), new_vertex_coords, xshape,
-                             ghost_mode);
-  }
-  else
-  {
-    // Let partition handle the parallel construction of the mesh
-    return partition<T>(mesh, cell_adj, new_vertex_coords, xshape, redistribute,
-                        ghost_mode);
-  }
+  std::int32_t mpi_rank = MPI::rank(comm);
+  std::int32_t num_cell_vertices = mesh::num_cell_vertices(cell_types.front());
+  std::int32_t num_cells = cell_topology.front().size() / num_cell_vertices;
+  std::vector<std::int32_t> destinations(num_cells, mpi_rank);
+  std::vector<std::int32_t> dest_offsets(num_cells + 1);
+  std::iota(dest_offsets.begin(), dest_offsets.end(), 0);
+  return graph::AdjacencyList(std::move(destinations), std::move(dest_offsets));
 }
-} // namespace impl
 
 /// @brief Refine with markers, optionally redistributing, and
 /// optionally calculating the parent-child relationships.
 ///
 /// @param[in] mesh Input mesh to be refined
-/// @param[in] edges Optional indices of the edges that should be split
-/// by this refinement, if optional is not set, a uniform refinement is
-/// performed, same behavior as passing a list of all indices.
-/// @param[in] redistribute Flag to call the Mesh Partitioner to
-/// redistribute after refinement.
-/// @param[in] ghost_mode Ghost mode of the refined mesh.
+/// @param[in] edges Optional indices of the edges that should be split by this
+/// refinement, if optional is not set, a uniform refinement is performend, same
+/// behavior as passing a list of all indices.
+/// @param[in] partitioner partitioner to be used for the refined mesh
 /// @param[in] option Control the computation of parent facets, parent
 /// cells. If an option is unselected, an empty list is returned.
 /// @return New Mesh and optional parent cell index, parent facet
@@ -65,8 +59,8 @@ template <std::floating_point T>
 std::tuple<mesh::Mesh<T>, std::optional<std::vector<std::int32_t>>,
            std::optional<std::vector<std::int8_t>>>
 refine(const mesh::Mesh<T>& mesh,
-       std::optional<std::span<const std::int32_t>> edges, bool redistribute,
-       mesh::GhostMode ghost_mode = mesh::GhostMode::shared_facet,
+       std::optional<std::span<const std::int32_t>> edges,
+       mesh::CellPartitionFunction partitioner = maintain_coarse_partitioner,
        Option option = Option::none)
 {
   auto topology = mesh.topology();
@@ -80,9 +74,10 @@ refine(const mesh::Mesh<T>& mesh,
       = oned ? interval::compute_refinement_data(mesh, edges, option)
              : plaza::compute_refinement_data(mesh, edges, option);
 
-  mesh::Mesh<T> refined_mesh = impl::create_refined_mesh(
-      mesh, cell_adj, std::span<const T>(new_vertex_coords), xshape,
-      redistribute, ghost_mode);
+  mesh::Mesh<T> refined_mesh
+      = mesh::create_mesh(mesh.comm(), mesh.comm(), std::move(cell_adj).array(),
+                          mesh.geometry().cmap(), mesh.comm(),
+                          std::move(new_vertex_coords), xshape, partitioner);
 
   // Report the number of refined cellse
   const int D = topology->dim();
diff --git a/cpp/dolfinx/refinement/utils.h b/cpp/dolfinx/refinement/utils.h
index 275b40d7cc2..1c6af077551 100644
--- a/cpp/dolfinx/refinement/utils.h
+++ b/cpp/dolfinx/refinement/utils.h
@@ -264,51 +264,6 @@ create_new_vertices(MPI_Comm comm,
           xshape};
 }
 
-/// Use vertex and topology data to partition new mesh across
-/// processes
-/// @param[in] old_mesh
-/// @param[in] cell_topology Topology of cells, (vertex indices)
-/// @param[in] new_coords New coordinates, row-major storage
-/// @param[in] xshape The shape of `new_coords`
-/// @param[in] redistribute Call graph partitioner if true
-/// @param[in] ghost_mode None or shared_facet
-/// @return New mesh
-template <std::floating_point T>
-mesh::Mesh<T> partition(const mesh::Mesh<T>& old_mesh,
-                        const graph::AdjacencyList<std::int64_t>& cell_topology,
-                        std::span<const T> new_coords,
-                        std::array<std::size_t, 2> xshape, bool redistribute,
-                        mesh::GhostMode ghost_mode)
-{
-  if (redistribute)
-  {
-    return mesh::create_mesh(old_mesh.comm(), cell_topology.array(),
-                             old_mesh.geometry().cmap(), new_coords, xshape,
-                             ghost_mode);
-  }
-  else
-  {
-    auto partitioner
-        = [](MPI_Comm comm, int, const std::vector<mesh::CellType>& cell_types,
-             const std::vector<std::span<const std::int64_t>>& cell_topology)
-    {
-      std::int32_t mpi_rank = MPI::rank(comm);
-      std::int32_t num_cell_vertices
-          = mesh::num_cell_vertices(cell_types.front());
-      std::int32_t num_cells = cell_topology.front().size() / num_cell_vertices;
-      std::vector<std::int32_t> destinations(num_cells, mpi_rank);
-      std::vector<std::int32_t> dest_offsets(num_cells + 1);
-      std::iota(dest_offsets.begin(), dest_offsets.end(), 0);
-      return graph::AdjacencyList(std::move(destinations),
-                                  std::move(dest_offsets));
-    };
-
-    return mesh::create_mesh(old_mesh.comm(), old_mesh.comm(),
-                             cell_topology.array(), old_mesh.geometry().cmap(),
-                             old_mesh.comm(), new_coords, xshape, partitioner);
-  }
-}
-
 /// @brief Given an index map, add "n" extra indices at the end of local range
 ///
 /// @note The returned global indices (local and ghosts) are adjust for the
diff --git a/cpp/test/mesh/refinement/interval.cpp b/cpp/test/mesh/refinement/interval.cpp
index 763418ac4b3..74b3f434627 100644
--- a/cpp/test/mesh/refinement/interval.cpp
+++ b/cpp/test/mesh/refinement/interval.cpp
@@ -73,7 +73,7 @@ TEMPLATE_TEST_CASE("Interval uniform refinement",
 
   // TODO: parent_facet
   auto [refined_mesh, parent_edge, parent_facet] = refinement::refine(
-      mesh, std::nullopt, false, mesh::GhostMode::shared_facet,
+      mesh, std::nullopt, &refinement::maintain_coarse_partitioner,
       refinement::Option::parent_cell);
 
   std::vector<T> expected_x = {
@@ -114,7 +114,8 @@ TEMPLATE_TEST_CASE("Interval adaptive refinement",
   std::vector<std::int32_t> edges{1};
   // TODO: parent_facet
   auto [refined_mesh, parent_edge, parent_facet] = refinement::refine(
-      mesh, std::span(edges), false, mesh::GhostMode::shared_facet,
+      mesh, std::span(edges),
+      mesh::create_cell_partitioner(mesh::GhostMode::shared_facet),
       refinement::Option::parent_cell);
 
   std::vector<T> expected_x = {
@@ -192,7 +193,7 @@ TEMPLATE_TEST_CASE("Interval Refinement (parallel)",
 
   // TODO: parent_facet
   auto [refined_mesh, parent_edges, parent_facet] = refinement::refine(
-      mesh, std::nullopt, false, mesh::GhostMode::shared_facet,
+      mesh, std::nullopt, &refinement::maintain_coarse_partitioner,
       refinement::Option::parent_cell);
 
   T rank_d = static_cast<T>(rank);
diff --git a/cpp/test/mesh/refinement/rectangle.cpp b/cpp/test/mesh/refinement/rectangle.cpp
index 954879abb1d..ff2a67979df 100644
--- a/cpp/test/mesh/refinement/rectangle.cpp
+++ b/cpp/test/mesh/refinement/rectangle.cpp
@@ -99,9 +99,9 @@ plotter.show()
   // plaza requires the edges to be pre initialized!
   mesh.topology()->create_entities(1);
 
-  auto [mesh_fine, parent_cell, parent_facet]
-      = refinement::refine(mesh, std::nullopt, false, mesh::GhostMode::none,
-                           refinement::Option::parent_cell_and_facet);
+  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
+      mesh, std::nullopt, mesh::create_cell_partitioner(mesh::GhostMode::none),
+      refinement::Option::parent_cell_and_facet);
 
   // vertex layout:
   // 8---7---5
diff --git a/cpp/test/transfer/transfer_matrix.cpp b/cpp/test/transfer/transfer_matrix.cpp
new file mode 100644
index 00000000000..9747e776fcb
--- /dev/null
+++ b/cpp/test/transfer/transfer_matrix.cpp
@@ -0,0 +1,315 @@
+// Copyright (C) 2024 Paul Kühner
+//
+// This file is part of DOLFINX (https://www.fenicsproject.org)
+//
+// SPDX-License-Identifier:    LGPL-3.0-or-later
+
+#include <concepts>
+#include <cstdint>
+#include <memory>
+#include <optional>
+
+#include <mpi.h>
+
+#include <catch2/catch_template_test_macros.hpp>
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/matchers/catch_matchers.hpp>
+#include <catch2/matchers/catch_matchers_floating_point.hpp>
+#include <catch2/matchers/catch_matchers_range_equals.hpp>
+
+#include <dolfinx/fem/FunctionSpace.h>
+#include <dolfinx/fem/utils.h>
+#include <dolfinx/la/MatrixCSR.h>
+#include <dolfinx/la/SparsityPattern.h>
+#include <dolfinx/mesh/cell_types.h>
+#include <dolfinx/mesh/generation.h>
+#include <dolfinx/mesh/utils.h>
+#include <dolfinx/refinement/plaza.h>
+#include <dolfinx/refinement/refine.h>
+#include <dolfinx/transfer/transfer_matrix.h>
+
+#include "../mesh/util.h"
+
+using namespace dolfinx;
+using namespace Catch::Matchers;
+
+template <std::floating_point T>
+constexpr auto weight = [](std::int32_t d) -> T { return d == 0 ? 1. : .5; };
+
+TEMPLATE_TEST_CASE("Transfer Matrix 1D", "[transfer_matrix]",
+                   double) // TODO: float
+{
+  using T = TestType;
+
+  auto mesh_coarse
+      = std::make_shared<mesh::Mesh<T>>(dolfinx::mesh::create_interval<T>(
+          MPI_COMM_SELF, 2, {0.0, 1.0}, mesh::GhostMode::none));
+
+  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
+      *mesh_coarse, std::nullopt, &refinement::maintain_coarse_partitioner, mesh::GhostMode::none,
+      refinement::Option::parent_cell);
+
+  auto element = basix::create_element<T>(
+      basix::element::family::P, basix::cell::type::interval, 1,
+      basix::element::lagrange_variant::unset,
+      basix::element::dpc_variant::unset, false);
+
+  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
+      fem::create_functionspace<T>(mesh_coarse, element, {}));
+  auto V_fine
+      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
+          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
+
+  mesh_fine.topology()->create_connectivity(1, 0);
+  mesh_fine.topology()->create_connectivity(0, 1);
+
+  std::vector<std::int64_t> from_to_map{0, 2, 4}; // TODO: general computation!
+
+  la::MatrixCSR<T> transfer_matrix = transfer::create_transfer_matrix<T>(
+      *V_coarse, *V_fine, from_to_map, weight<T>);
+
+  std::vector<T> expected{1.0, .5, 0, 0, 0, 0, .5, 1, .5, 0, 0, 0, 0, .5, 1};
+  CHECK_THAT(transfer_matrix.to_dense(),
+             RangeEquals(expected, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+}
+
+TEMPLATE_TEST_CASE("Transfer Matrix 1D (parallel)", "[transfer_matrix]",
+                   double) // TODO: float
+{
+  using T = TestType;
+
+  int comm_size = dolfinx::MPI::size(MPI_COMM_WORLD);
+  int rank = dolfinx::MPI::rank(MPI_COMM_WORLD);
+
+  // TODO: see https://github.com/FEniCS/dolfinx/issues/3358
+  // auto part = mesh::create_cell_partitioner(mesh::GhostMode::shared_facet);
+  mesh::CellPartitionFunction part
+      = [&](MPI_Comm /* comm */, int /* nparts */,
+            const std::vector<mesh::CellType>& /* cell_types */,
+            const std::vector<std::span<const std::int64_t>>& /* cells */)
+  {
+    std::vector<std::vector<std::int32_t>> data;
+    if (comm_size == 1)
+      data = {{0}, {0}, {0}, {0}};
+    else if (comm_size == 2)
+      data = {{0}, {0}, {0}, {0}, {0, 1}, {1, 0}, {1}, {1}, {1}};
+    else if (comm_size == 3)
+      data = {{1}, {1},    {1},    {1}, {1, 2}, {2, 1}, {2},
+              {2}, {2, 0}, {0, 2}, {0}, {0},    {0},    {0}};
+    else
+      FAIL("Test only supports <= 3 processes");
+    return graph::AdjacencyList<std::int32_t>(std::move(data));
+  };
+
+  auto mesh_coarse = std::make_shared<mesh::Mesh<T>>(
+      mesh::create_interval<T>(MPI_COMM_WORLD, 5 * comm_size - 1, {0., 1.},
+                               mesh::GhostMode::shared_facet, part));
+
+  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
+      *mesh_coarse, std::nullopt, part, mesh::GhostMode::shared_facet,
+      refinement::Option::none);
+
+  auto element = basix::create_element<T>(
+      basix::element::family::P, basix::cell::type::interval, 1,
+      basix::element::lagrange_variant::unset,
+      basix::element::dpc_variant::unset, false);
+
+  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
+      fem::create_functionspace<T>(mesh_coarse, element, {}));
+  auto V_fine
+      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
+          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
+
+  mesh_fine.topology()->create_connectivity(1, 0);
+  mesh_fine.topology()->create_connectivity(0, 1);
+
+  std::vector<int64_t> from_to_map;
+  switch (comm_size)
+  {
+  case 1:
+    from_to_map = {0, 2, 4, 6, 8};
+    break;
+  case 2:
+    from_to_map = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18};
+    break;
+  case 3:
+    from_to_map = {0, 2, 4, 6, 8, 9, 11, 13, 15, 17, 19, 28, 26, 24, 22};
+    break;
+  }
+
+  la::MatrixCSR<T> transfer_matrix = transfer::create_transfer_matrix(
+      *V_coarse, *V_fine, from_to_map, weight<T>);
+
+  std::array<std::vector<T>, 3> expected;
+  if (comm_size == 1)
+  {
+    // clang-format off
+    expected[0] = {
+        /* row_0 */ 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0
+    };
+    // clang-format on
+  }
+  else if (comm_size == 2)
+  {
+    // clang-format off
+    expected[0] = {
+        /* row_0 */ 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
+    };
+    expected[1] = {
+        /* row_0 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
+    };
+    // clang-format on
+  }
+  else if (comm_size == 3)
+  {
+    // clang-format off
+    expected[0] = {
+        /* row_0 */ 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+    };
+    expected[1] = {
+        /* row_0 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5,
+        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+    };
+    expected[2] = {
+        /* row_0 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0,
+        /* row_1 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+    };
+    // clang-format on
+  }
+  else
+  {
+    CHECK(false);
+  }
+
+  CHECK_THAT(transfer_matrix.to_dense(),
+             RangeEquals(expected[rank], [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+}
+
+TEMPLATE_TEST_CASE("Transfer Matrix 2D", "[transfer_matrix]", double)
+{
+  using T = TestType;
+
+  auto mesh_coarse
+      = std::make_shared<mesh::Mesh<T>>(dolfinx::mesh::create_rectangle<T>(
+          MPI_COMM_SELF, {{{0, 0}, {1, 1}}}, {1, 1}, mesh::CellType::triangle));
+  mesh_coarse->topology()->create_entities(1);
+
+  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
+      *mesh_coarse, std::nullopt, &refinement::maintain_coarse_partitioner, mesh::GhostMode::none,
+      refinement::Option::parent_cell);
+
+  auto element = basix::create_element<T>(
+      basix::element::family::P, basix::cell::type::triangle, 1,
+      basix::element::lagrange_variant::unset,
+      basix::element::dpc_variant::unset, false);
+
+  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
+      fem::create_functionspace<T>(mesh_coarse, element, {}));
+  auto V_fine
+      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
+          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
+
+  mesh_fine.topology()->create_connectivity(1, 0);
+  mesh_fine.topology()->create_connectivity(0, 1);
+
+  std::vector<std::int64_t> from_to_map{4, 1, 5,
+                                        8}; // TODO: general computation!
+
+  la::MatrixCSR<T> transfer_matrix = transfer::create_transfer_matrix(
+      *V_coarse, *V_fine, from_to_map, weight<T>);
+
+  std::vector<T> expected{0.5, 0.0, 0.5, 0.0, 1.0, 0.0, 0.5, 0.0, 0.0,
+                          0.5, 1.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
+                          0.5, 0.0, 0.0, 0.5, 0.0, 1.0, 0.0, 0.5, 0.0,
+                          0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 1.0};
+  CHECK_THAT(transfer_matrix.to_dense(),
+             RangeEquals(expected, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+}
+
+TEMPLATE_TEST_CASE("Transfer Matrix 3D", "[transfer_matrix]", double)
+{
+  using T = TestType;
+
+  auto mesh_coarse = std::make_shared<mesh::Mesh<T>>(
+      dolfinx::mesh::create_box<T>(MPI_COMM_SELF, {{{0, 0, 0}, {1, 1, 1}}},
+                                   {1, 1, 1}, mesh::CellType::tetrahedron));
+  mesh_coarse->topology()->create_entities(1);
+
+  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
+      *mesh_coarse, std::nullopt, &refinement::maintain_coarse_partitioner, mesh::GhostMode::none,
+      refinement::Option::parent_cell);
+
+  auto element = basix::create_element<T>(
+      basix::element::family::P, basix::cell::type::tetrahedron, 1,
+      basix::element::lagrange_variant::unset,
+      basix::element::dpc_variant::unset, false);
+
+  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
+      fem::create_functionspace<T>(mesh_coarse, element, {}));
+  auto V_fine
+      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
+          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
+
+  mesh_fine.topology()->create_connectivity(1, 0);
+  mesh_fine.topology()->create_connectivity(0, 1);
+
+  std::vector<std::int64_t> from_to_map{
+      0, 6, 15, 25, 17, 9, 11, 22}; // TODO: general computation!
+
+  la::MatrixCSR<T> transfer_matrix = transfer::create_transfer_matrix(
+      *V_coarse, *V_fine, from_to_map, weight<T>);
+
+  std::vector<T> expected{
+      1.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5,
+      0.5, 0.5, 0.0, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.5, 0.0, 0.5, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.5, 0.5, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0,
+      0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.5, 0.0, 0.5,
+      0.5, 1.0, 0.5, 0.0, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+      0.5, 0.0, 0.5, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0,
+      0.0, 0.5, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0,
+      0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0,
+      0.0, 0.5, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0,
+      0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5,
+      0.5, 1.0, 0.0, 0.0, 0.0, 0.5};
+  CHECK_THAT(transfer_matrix.to_dense(),
+             RangeEquals(expected, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+}
diff --git a/python/dolfinx/mesh.py b/python/dolfinx/mesh.py
index b9cefce09b3..46fec0bed34 100644
--- a/python/dolfinx/mesh.py
+++ b/python/dolfinx/mesh.py
@@ -370,8 +370,7 @@ def transfer_meshtag(
 def refine(
     mesh: Mesh,
     edges: typing.Optional[np.ndarray] = None,
-    redistribute: bool = True,
-    ghost_mode: GhostMode = GhostMode.shared_facet,
+    partitioner: typing.Optional[typing.Callable] = None,
     option: RefinementOption = RefinementOption.none,
 ) -> tuple[Mesh, npt.NDArray[np.int32], npt.NDArray[np.int8]]:
     """Refine a mesh.
@@ -380,17 +379,16 @@ def refine(
         mesh: Mesh from which to create the refined mesh.
         edges: Indices of edges to split during refinement. If ``None``,
             mesh refinement is uniform.
-        redistribute:
-            Refined mesh is re-partitioned if ``True``.
-        ghost_mode: Ghost mode to use for the refined mesh.
+        partitioner:
+            partitioner to use for the refined mesh, If ``None`` no redistribution is performed,
+            i.e. previous local mesh is equally parallelized now with new vertices.s
         option: Controls whether parent cells and/or parent facets are computed.
 
-
     Returns:
        Refined mesh, (optional) parent cells, (optional) parent facets
     """
     mesh1, parent_cell, parent_facet = _cpp.refinement.refine(
-        mesh._cpp_object, edges, redistribute, ghost_mode, option
+        mesh._cpp_object, edges, partitioner, option
     )
     return Mesh(mesh1, mesh._ufl_domain), parent_cell, parent_facet
 
diff --git a/python/dolfinx/wrappers/refinement.cpp b/python/dolfinx/wrappers/refinement.cpp
index 37ca3937992..7921ffb22e5 100644
--- a/python/dolfinx/wrappers/refinement.cpp
+++ b/python/dolfinx/wrappers/refinement.cpp
@@ -4,9 +4,20 @@
 //
 // SPDX-License-Identifier:    LGPL-3.0-or-later
 
-#include "array.h"
 #include <concepts>
 #include <cstdint>
+#include <functional>
+#include <optional>
+#include <span>
+
+#include <nanobind/nanobind.h>
+#include <nanobind/ndarray.h>
+#include <nanobind/stl/array.h>
+#include <nanobind/stl/optional.h>
+#include <nanobind/stl/shared_ptr.h>
+#include <nanobind/stl/tuple.h>
+#include <nanobind/stl/vector.h>
+
 #include <dolfinx/mesh/Mesh.h>
 #include <dolfinx/mesh/MeshTags.h>
 #include <dolfinx/refinement/interval.h>
@@ -14,30 +25,67 @@
 #include <dolfinx/refinement/plaza.h>
 #include <dolfinx/refinement/refine.h>
 #include <dolfinx/refinement/utils.h>
-#include <nanobind/nanobind.h>
-#include <nanobind/ndarray.h>
-#include <nanobind/stl/optional.h>
-#include <nanobind/stl/shared_ptr.h>
-#include <nanobind/stl/tuple.h>
-#include <nanobind/stl/vector.h>
-#include <optional>
-#include <span>
+
+#include "MPICommWrapper.h"
+#include "array.h"
 
 namespace nb = nanobind;
 
 namespace dolfinx_wrappers
 {
 
+namespace
+{
+
+using PythonCellPartitionFunction
+    = std::function<dolfinx::graph::AdjacencyList<std::int32_t>(
+        dolfinx_wrappers::MPICommWrapper, int,
+        const std::vector<dolfinx::mesh::CellType>&,
+        std::vector<nb::ndarray<const std::int64_t, nb::numpy>>)>;
+
+using CppCellPartitionFunction
+    = std::function<dolfinx::graph::AdjacencyList<std::int32_t>(
+        MPI_Comm, int, const std::vector<dolfinx::mesh::CellType>& q,
+        const std::vector<std::span<const std::int64_t>>&)>;
+
+/// Wrap a Python graph partitioning function as a C++ function
+CppCellPartitionFunction
+create_cell_partitioner_cpp(const PythonCellPartitionFunction& p)
+{
+  if (p)
+  {
+    return [p](MPI_Comm comm, int n,
+               const std::vector<dolfinx::mesh::CellType>& cell_types,
+               const std::vector<std::span<const std::int64_t>>& cells)
+    {
+      std::vector<nb::ndarray<const std::int64_t, nb::numpy>> cells_nb;
+      std::ranges::transform(
+          cells, std::back_inserter(cells_nb),
+          [](auto c)
+          {
+            return nb::ndarray<const std::int64_t, nb::numpy>(
+                c.data(), {c.size()}, nb::handle());
+          });
+
+      return p(dolfinx_wrappers::MPICommWrapper(comm), n, cell_types, cells_nb);
+    };
+  }
+  else
+    return nullptr;
+}
+} // namespace
+
 template <std::floating_point T>
 void export_refinement_with_variable_mesh_type(nb::module_& m)
 {
+
   m.def(
       "refine",
       [](const dolfinx::mesh::Mesh<T>& mesh,
          std::optional<
              nb::ndarray<const std::int32_t, nb::ndim<1>, nb::c_contig>>
              edges,
-         bool redistribute, dolfinx::mesh::GhostMode ghost_mode,
+         std::optional<PythonCellPartitionFunction> partitioner,
          dolfinx::refinement::Option option)
       {
         std::optional<std::span<const std::int32_t>> cpp_edges(std::nullopt);
@@ -47,8 +95,12 @@ void export_refinement_with_variable_mesh_type(nb::module_& m)
               std::span(edges.value().data(), edges.value().size()));
         }
 
+        CppCellPartitionFunction cpp_partitioner
+            = partitioner.has_value()
+                  ? create_cell_partitioner_cpp(partitioner.value())
+                  : dolfinx::refinement::maintain_coarse_partitioner;
         auto [mesh1, cell, facet] = dolfinx::refinement::refine(
-            mesh, cpp_edges, redistribute, ghost_mode, option);
+            mesh, cpp_edges, cpp_partitioner, option);
 
         std::optional<nb::ndarray<std::int32_t, nb::numpy>> python_cell(
             std::nullopt);
@@ -63,8 +115,8 @@ void export_refinement_with_variable_mesh_type(nb::module_& m)
         return std::tuple{std::move(mesh1), std::move(python_cell),
                           std::move(python_facet)};
       },
-      nb::arg("mesh"), nb::arg("edges") = nb::none(), nb::arg("redistribute"),
-      nb::arg("ghost_mode"), nb::arg("option"));
+      nb::arg("mesh"), nb::arg("edges") = nb::none(),
+      nb::arg("partitioner") = nb::none(), nb::arg("option"));
 }
 
 void refinement(nb::module_& m)
diff --git a/python/test/unit/refinement/test_interval.py b/python/test/unit/refinement/test_interval.py
index 28779644840..27040fb0b90 100644
--- a/python/test/unit/refinement/test_interval.py
+++ b/python/test/unit/refinement/test_interval.py
@@ -20,16 +20,14 @@
     "ghost_mode_refined",
     [mesh.GhostMode.none, mesh.GhostMode.shared_vertex, mesh.GhostMode.shared_facet],
 )
-@pytest.mark.parametrize("redistribute", [True, False])
 @pytest.mark.parametrize("option", [mesh.RefinementOption.none, mesh.RefinementOption.parent_cell])
-def test_refine_interval(n, ghost_mode, redistribute, ghost_mode_refined, option):
+def test_refine_interval(n, ghost_mode, ghost_mode_refined, option):
     msh = mesh.create_interval(MPI.COMM_WORLD, n, [0, 1], ghost_mode=ghost_mode)
     msh_refined, edges, vertices = mesh.refine(
         msh,
-        redistribute=redistribute,
-        ghost_mode=ghost_mode_refined,
         option=option,
     )
+    # TODO: add create_cell_partitioner(ghost_mode) when works
 
     # vertex count
     assert msh_refined.topology.index_map(0).size_global == 2 * n + 1
@@ -52,16 +50,14 @@ def test_refine_interval(n, ghost_mode, redistribute, ghost_mode_refined, option
     "ghost_mode_refined",
     [mesh.GhostMode.none, mesh.GhostMode.shared_vertex, mesh.GhostMode.shared_facet],
 )
-@pytest.mark.parametrize("redistribute", [True, False])
-def test_refine_interval_adaptive(n, ghost_mode, redistribute, ghost_mode_refined):
+def test_refine_interval_adaptive(n, ghost_mode, ghost_mode_refined):
     msh = mesh.create_interval(MPI.COMM_WORLD, n, [0, 1], ghost_mode=ghost_mode)
     msh_refined, edges, vertices = mesh.refine(
         msh,
         np.arange(10, dtype=np.int32),
-        redistribute=redistribute,
-        ghost_mode=ghost_mode_refined,
         option=mesh.RefinementOption.parent_cell,
     )
+    # TODO: add create_cell_partitioner(ghost_mode) when works
 
     # vertex count
     assert msh_refined.topology.index_map(0).size_global == n + 1 + 10 * MPI.COMM_WORLD.size
diff --git a/python/test/unit/refinement/test_refinement.py b/python/test/unit/refinement/test_refinement.py
index 440057ce265..eb5188d5bf1 100644
--- a/python/test/unit/refinement/test_refinement.py
+++ b/python/test/unit/refinement/test_refinement.py
@@ -32,7 +32,7 @@ def test_refine_create_unit_square():
     """Refine mesh of unit square."""
     mesh = create_unit_square(MPI.COMM_WORLD, 5, 7, ghost_mode=GhostMode.none)
     mesh.topology.create_entities(1)
-    mesh_refined, _, _ = refine(mesh, redistribute=False)
+    mesh_refined, _, _ = refine(mesh)
     assert mesh_refined.topology.index_map(0).size_global == 165
     assert mesh_refined.topology.index_map(2).size_global == 280
 
@@ -46,7 +46,7 @@ def test_refine_create_unit_cube(ghost_mode, redistribute):
     """Refine mesh of unit cube."""
     mesh = create_unit_cube(MPI.COMM_WORLD, 5, 7, 9, ghost_mode=ghost_mode)
     mesh.topology.create_entities(1)
-    mesh, _, _ = refine(mesh, redistribute=redistribute)
+    mesh, _, _ = refine(mesh)  # , partitioner=create_cell_partitioner(ghost_mode))
     assert mesh.topology.index_map(0).size_global == 3135
     assert mesh.topology.index_map(3).size_global == 15120
 
@@ -58,7 +58,7 @@ def test_refine_create_form():
     """Check that forms can be assembled on refined mesh"""
     mesh = create_unit_cube(MPI.COMM_WORLD, 3, 3, 3)
     mesh.topology.create_entities(1)
-    mesh, _, _ = refine(mesh, redistribute=True)
+    mesh, _, _ = refine(mesh)  # TODO: recover redistribute=True behavior
 
     V = functionspace(mesh, ("Lagrange", 1))
 
@@ -83,7 +83,7 @@ def left_corner_edge(x, tol=1e-7):
     if MPI.COMM_WORLD.size == 0:
         assert edges == 1
 
-    mesh2, _, _ = refine(mesh, edges, redistribute=False)
+    mesh2, _, _ = refine(mesh, edges)
     assert mesh.topology.index_map(2).size_global + 3 == mesh2.topology.index_map(2).size_global
 
 
@@ -105,7 +105,7 @@ def left_side(x, tol=1e-16):
     edges = compute_incident_entities(msh.topology, cells, 2, 1)
     if MPI.COMM_WORLD.size == 0:
         assert edges.__len__() == Nx // 2 * (2 * Ny + 1) + (Nx // 2 + 1) * Ny
-    mesh2, _, _ = refine(msh, edges, redistribute=True)
+    mesh2, _, _ = refine(msh, edges)  # TODO: redistribute=True
 
     num_cells_global = mesh2.topology.index_map(2).size_global
     actual_cells = 3 * (Nx * Ny) + 3 * Ny + 2 * Nx * Ny
@@ -116,13 +116,10 @@ def left_side(x, tol=1e-16):
 @pytest.mark.parametrize(
     "refine_plaza_wrapper",
     [
-        lambda mesh: refine(
-            mesh, redistribute=False, option=RefinementOption.parent_cell_and_facet
-        ),
+        lambda mesh: refine(mesh, option=RefinementOption.parent_cell_and_facet),
         lambda mesh: refine(
             mesh,
             np.arange(mesh.topology.index_map(1).size_local),
-            redistribute=False,
             option=RefinementOption.parent_cell_and_facet,
         ),
     ],
@@ -178,13 +175,10 @@ def test_refine_facet_meshtag(tdim, refine_plaza_wrapper):
 @pytest.mark.parametrize(
     "refine_plaza_wrapper",
     [
-        lambda mesh: refine(
-            mesh, redistribute=False, option=RefinementOption.parent_cell_and_facet
-        ),
+        lambda mesh: refine(mesh, option=RefinementOption.parent_cell_and_facet),
         lambda mesh: refine(
             mesh,
             np.arange(mesh.topology.index_map(1).size_local),
-            redistribute=False,
             option=RefinementOption.parent_cell_and_facet,
         ),
     ],

From 32fca7cb63bbf64732a24541066f61ca254f20df Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Tue, 17 Sep 2024 22:43:48 +0200
Subject: [PATCH 02/10] Remove wrongly added transfer_matrix -> later PR

---
 cpp/test/transfer/transfer_matrix.cpp | 315 --------------------------
 1 file changed, 315 deletions(-)
 delete mode 100644 cpp/test/transfer/transfer_matrix.cpp

diff --git a/cpp/test/transfer/transfer_matrix.cpp b/cpp/test/transfer/transfer_matrix.cpp
deleted file mode 100644
index 9747e776fcb..00000000000
--- a/cpp/test/transfer/transfer_matrix.cpp
+++ /dev/null
@@ -1,315 +0,0 @@
-// Copyright (C) 2024 Paul Kühner
-//
-// This file is part of DOLFINX (https://www.fenicsproject.org)
-//
-// SPDX-License-Identifier:    LGPL-3.0-or-later
-
-#include <concepts>
-#include <cstdint>
-#include <memory>
-#include <optional>
-
-#include <mpi.h>
-
-#include <catch2/catch_template_test_macros.hpp>
-#include <catch2/catch_test_macros.hpp>
-#include <catch2/matchers/catch_matchers.hpp>
-#include <catch2/matchers/catch_matchers_floating_point.hpp>
-#include <catch2/matchers/catch_matchers_range_equals.hpp>
-
-#include <dolfinx/fem/FunctionSpace.h>
-#include <dolfinx/fem/utils.h>
-#include <dolfinx/la/MatrixCSR.h>
-#include <dolfinx/la/SparsityPattern.h>
-#include <dolfinx/mesh/cell_types.h>
-#include <dolfinx/mesh/generation.h>
-#include <dolfinx/mesh/utils.h>
-#include <dolfinx/refinement/plaza.h>
-#include <dolfinx/refinement/refine.h>
-#include <dolfinx/transfer/transfer_matrix.h>
-
-#include "../mesh/util.h"
-
-using namespace dolfinx;
-using namespace Catch::Matchers;
-
-template <std::floating_point T>
-constexpr auto weight = [](std::int32_t d) -> T { return d == 0 ? 1. : .5; };
-
-TEMPLATE_TEST_CASE("Transfer Matrix 1D", "[transfer_matrix]",
-                   double) // TODO: float
-{
-  using T = TestType;
-
-  auto mesh_coarse
-      = std::make_shared<mesh::Mesh<T>>(dolfinx::mesh::create_interval<T>(
-          MPI_COMM_SELF, 2, {0.0, 1.0}, mesh::GhostMode::none));
-
-  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
-      *mesh_coarse, std::nullopt, &refinement::maintain_coarse_partitioner, mesh::GhostMode::none,
-      refinement::Option::parent_cell);
-
-  auto element = basix::create_element<T>(
-      basix::element::family::P, basix::cell::type::interval, 1,
-      basix::element::lagrange_variant::unset,
-      basix::element::dpc_variant::unset, false);
-
-  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
-      fem::create_functionspace<T>(mesh_coarse, element, {}));
-  auto V_fine
-      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
-          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
-
-  mesh_fine.topology()->create_connectivity(1, 0);
-  mesh_fine.topology()->create_connectivity(0, 1);
-
-  std::vector<std::int64_t> from_to_map{0, 2, 4}; // TODO: general computation!
-
-  la::MatrixCSR<T> transfer_matrix = transfer::create_transfer_matrix<T>(
-      *V_coarse, *V_fine, from_to_map, weight<T>);
-
-  std::vector<T> expected{1.0, .5, 0, 0, 0, 0, .5, 1, .5, 0, 0, 0, 0, .5, 1};
-  CHECK_THAT(transfer_matrix.to_dense(),
-             RangeEquals(expected, [](auto a, auto b)
-                         { return std::abs(a - b) <= EPS<T>; }));
-}
-
-TEMPLATE_TEST_CASE("Transfer Matrix 1D (parallel)", "[transfer_matrix]",
-                   double) // TODO: float
-{
-  using T = TestType;
-
-  int comm_size = dolfinx::MPI::size(MPI_COMM_WORLD);
-  int rank = dolfinx::MPI::rank(MPI_COMM_WORLD);
-
-  // TODO: see https://github.com/FEniCS/dolfinx/issues/3358
-  // auto part = mesh::create_cell_partitioner(mesh::GhostMode::shared_facet);
-  mesh::CellPartitionFunction part
-      = [&](MPI_Comm /* comm */, int /* nparts */,
-            const std::vector<mesh::CellType>& /* cell_types */,
-            const std::vector<std::span<const std::int64_t>>& /* cells */)
-  {
-    std::vector<std::vector<std::int32_t>> data;
-    if (comm_size == 1)
-      data = {{0}, {0}, {0}, {0}};
-    else if (comm_size == 2)
-      data = {{0}, {0}, {0}, {0}, {0, 1}, {1, 0}, {1}, {1}, {1}};
-    else if (comm_size == 3)
-      data = {{1}, {1},    {1},    {1}, {1, 2}, {2, 1}, {2},
-              {2}, {2, 0}, {0, 2}, {0}, {0},    {0},    {0}};
-    else
-      FAIL("Test only supports <= 3 processes");
-    return graph::AdjacencyList<std::int32_t>(std::move(data));
-  };
-
-  auto mesh_coarse = std::make_shared<mesh::Mesh<T>>(
-      mesh::create_interval<T>(MPI_COMM_WORLD, 5 * comm_size - 1, {0., 1.},
-                               mesh::GhostMode::shared_facet, part));
-
-  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
-      *mesh_coarse, std::nullopt, part, mesh::GhostMode::shared_facet,
-      refinement::Option::none);
-
-  auto element = basix::create_element<T>(
-      basix::element::family::P, basix::cell::type::interval, 1,
-      basix::element::lagrange_variant::unset,
-      basix::element::dpc_variant::unset, false);
-
-  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
-      fem::create_functionspace<T>(mesh_coarse, element, {}));
-  auto V_fine
-      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
-          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
-
-  mesh_fine.topology()->create_connectivity(1, 0);
-  mesh_fine.topology()->create_connectivity(0, 1);
-
-  std::vector<int64_t> from_to_map;
-  switch (comm_size)
-  {
-  case 1:
-    from_to_map = {0, 2, 4, 6, 8};
-    break;
-  case 2:
-    from_to_map = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18};
-    break;
-  case 3:
-    from_to_map = {0, 2, 4, 6, 8, 9, 11, 13, 15, 17, 19, 28, 26, 24, 22};
-    break;
-  }
-
-  la::MatrixCSR<T> transfer_matrix = transfer::create_transfer_matrix(
-      *V_coarse, *V_fine, from_to_map, weight<T>);
-
-  std::array<std::vector<T>, 3> expected;
-  if (comm_size == 1)
-  {
-    // clang-format off
-    expected[0] = {
-        /* row_0 */ 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_1 */ 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_2 */ 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0,
-        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0,
-        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0
-    };
-    // clang-format on
-  }
-  else if (comm_size == 2)
-  {
-    // clang-format off
-    expected[0] = {
-        /* row_0 */ 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_1 */ 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_2 */ 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
-    };
-    expected[1] = {
-        /* row_0 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_1 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0,
-        /* row_2 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0,
-        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0,
-        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
-    };
-    // clang-format on
-  }
-  else if (comm_size == 3)
-  {
-    // clang-format off
-    expected[0] = {
-        /* row_0 */ 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_1 */ 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_2 */ 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-    };
-    expected[1] = {
-        /* row_0 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_1 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_2 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5,
-        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-    };
-    expected[2] = {
-        /* row_0 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0,
-        /* row_1 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0,
-        /* row_2 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0,
-        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-    };
-    // clang-format on
-  }
-  else
-  {
-    CHECK(false);
-  }
-
-  CHECK_THAT(transfer_matrix.to_dense(),
-             RangeEquals(expected[rank], [](auto a, auto b)
-                         { return std::abs(a - b) <= EPS<T>; }));
-}
-
-TEMPLATE_TEST_CASE("Transfer Matrix 2D", "[transfer_matrix]", double)
-{
-  using T = TestType;
-
-  auto mesh_coarse
-      = std::make_shared<mesh::Mesh<T>>(dolfinx::mesh::create_rectangle<T>(
-          MPI_COMM_SELF, {{{0, 0}, {1, 1}}}, {1, 1}, mesh::CellType::triangle));
-  mesh_coarse->topology()->create_entities(1);
-
-  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
-      *mesh_coarse, std::nullopt, &refinement::maintain_coarse_partitioner, mesh::GhostMode::none,
-      refinement::Option::parent_cell);
-
-  auto element = basix::create_element<T>(
-      basix::element::family::P, basix::cell::type::triangle, 1,
-      basix::element::lagrange_variant::unset,
-      basix::element::dpc_variant::unset, false);
-
-  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
-      fem::create_functionspace<T>(mesh_coarse, element, {}));
-  auto V_fine
-      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
-          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
-
-  mesh_fine.topology()->create_connectivity(1, 0);
-  mesh_fine.topology()->create_connectivity(0, 1);
-
-  std::vector<std::int64_t> from_to_map{4, 1, 5,
-                                        8}; // TODO: general computation!
-
-  la::MatrixCSR<T> transfer_matrix = transfer::create_transfer_matrix(
-      *V_coarse, *V_fine, from_to_map, weight<T>);
-
-  std::vector<T> expected{0.5, 0.0, 0.5, 0.0, 1.0, 0.0, 0.5, 0.0, 0.0,
-                          0.5, 1.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
-                          0.5, 0.0, 0.0, 0.5, 0.0, 1.0, 0.0, 0.5, 0.0,
-                          0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 1.0};
-  CHECK_THAT(transfer_matrix.to_dense(),
-             RangeEquals(expected, [](auto a, auto b)
-                         { return std::abs(a - b) <= EPS<T>; }));
-}
-
-TEMPLATE_TEST_CASE("Transfer Matrix 3D", "[transfer_matrix]", double)
-{
-  using T = TestType;
-
-  auto mesh_coarse = std::make_shared<mesh::Mesh<T>>(
-      dolfinx::mesh::create_box<T>(MPI_COMM_SELF, {{{0, 0, 0}, {1, 1, 1}}},
-                                   {1, 1, 1}, mesh::CellType::tetrahedron));
-  mesh_coarse->topology()->create_entities(1);
-
-  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
-      *mesh_coarse, std::nullopt, &refinement::maintain_coarse_partitioner, mesh::GhostMode::none,
-      refinement::Option::parent_cell);
-
-  auto element = basix::create_element<T>(
-      basix::element::family::P, basix::cell::type::tetrahedron, 1,
-      basix::element::lagrange_variant::unset,
-      basix::element::dpc_variant::unset, false);
-
-  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
-      fem::create_functionspace<T>(mesh_coarse, element, {}));
-  auto V_fine
-      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
-          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
-
-  mesh_fine.topology()->create_connectivity(1, 0);
-  mesh_fine.topology()->create_connectivity(0, 1);
-
-  std::vector<std::int64_t> from_to_map{
-      0, 6, 15, 25, 17, 9, 11, 22}; // TODO: general computation!
-
-  la::MatrixCSR<T> transfer_matrix = transfer::create_transfer_matrix(
-      *V_coarse, *V_fine, from_to_map, weight<T>);
-
-  std::vector<T> expected{
-      1.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5,
-      0.5, 0.5, 0.0, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.5, 0.0, 0.5, 0.0, 0.0, 0.0,
-      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0,
-      0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.5, 0.5, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0,
-      0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-      0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.5, 0.0, 0.5,
-      0.5, 1.0, 0.5, 0.0, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-      0.5, 0.0, 0.5, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0,
-      0.0, 0.5, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0,
-      0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0,
-      0.0, 0.5, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0,
-      0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0,
-      0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5,
-      0.5, 1.0, 0.0, 0.0, 0.0, 0.5};
-  CHECK_THAT(transfer_matrix.to_dense(),
-             RangeEquals(expected, [](auto a, auto b)
-                         { return std::abs(a - b) <= EPS<T>; }));
-}

From 5bd8ba5387c894bd993c2de87747baca345394cf Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Tue, 17 Sep 2024 22:46:02 +0200
Subject: [PATCH 03/10] Add author name

---
 cpp/dolfinx/refinement/refine.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/cpp/dolfinx/refinement/refine.h b/cpp/dolfinx/refinement/refine.h
index 50d2181207c..12d5ccce196 100644
--- a/cpp/dolfinx/refinement/refine.h
+++ b/cpp/dolfinx/refinement/refine.h
@@ -1,4 +1,4 @@
-// Copyright (C) 2010-2023 Garth N. Wells
+// Copyright (C) 2010-2024 Garth N. Wells and Paul T. Kühner
 //
 // This file is part of DOLFINx (https://www.fenicsproject.org)
 //

From 124630aea480a1823c43e1dcc51371bba1c5efec Mon Sep 17 00:00:00 2001
From: "Garth N. Wells" <gnw20@cam.ac.uk>
Date: Wed, 18 Sep 2024 11:49:28 +0100
Subject: [PATCH 04/10] Doc fix

---
 cpp/dolfinx/refinement/refine.h | 29 ++++++++++-------------------
 1 file changed, 10 insertions(+), 19 deletions(-)

diff --git a/cpp/dolfinx/refinement/refine.h b/cpp/dolfinx/refinement/refine.h
index 12d5ccce196..4e72c35837c 100644
--- a/cpp/dolfinx/refinement/refine.h
+++ b/cpp/dolfinx/refinement/refine.h
@@ -6,6 +6,7 @@
 
 #pragma once
 
+#include "dolfinx/graph/AdjacencyList.h"
 #include "dolfinx/mesh/Mesh.h"
 #include "dolfinx/mesh/Topology.h"
 #include "dolfinx/mesh/cell_types.h"
@@ -17,25 +18,16 @@
 #include <optional>
 #include <utility>
 
-#include "dolfinx/graph/AdjacencyList.h"
-#include "dolfinx/mesh/Mesh.h"
-#include "dolfinx/mesh/Topology.h"
-#include "dolfinx/mesh/cell_types.h"
-#include "dolfinx/mesh/utils.h"
-
-#include "interval.h"
-#include "plaza.h"
-
 namespace dolfinx::refinement
 {
 
-// TODO: move to cpp?
+/// TODO: Document function
 inline graph::AdjacencyList<std::int32_t> maintain_coarse_partitioner(
     MPI_Comm comm, int, const std::vector<mesh::CellType>& cell_types,
     const std::vector<std::span<const std::int64_t>>& cell_topology)
 {
-  std::int32_t mpi_rank = MPI::rank(comm);
-  std::int32_t num_cell_vertices = mesh::num_cell_vertices(cell_types.front());
+  int mpi_rank = MPI::rank(comm);
+  int num_cell_vertices = mesh::num_cell_vertices(cell_types.front());
   std::int32_t num_cells = cell_topology.front().size() / num_cell_vertices;
   std::vector<std::int32_t> destinations(num_cells, mpi_rank);
   std::vector<std::int32_t> dest_offsets(num_cells + 1);
@@ -46,10 +38,10 @@ inline graph::AdjacencyList<std::int32_t> maintain_coarse_partitioner(
 /// @brief Refine with markers, optionally redistributing, and
 /// optionally calculating the parent-child relationships.
 ///
-/// @param[in] mesh Input mesh to be refined
-/// @param[in] edges Optional indices of the edges that should be split by this
-/// refinement, if optional is not set, a uniform refinement is performend, same
-/// behavior as passing a list of all indices.
+/// @param[in] mesh Input mesh to be refined.
+/// @param[in] edges Optional indices of the edges that should be split
+/// by this refinement, if optional is not set, a uniform refinement is
+/// performed, same behavior as passing a list of all indices.
 /// @param[in] partitioner partitioner to be used for the refined mesh
 /// @param[in] option Control the computation of parent facets, parent
 /// cells. If an option is unselected, an empty list is returned.
@@ -65,10 +57,9 @@ refine(const mesh::Mesh<T>& mesh,
 {
   auto topology = mesh.topology();
   assert(topology);
-
-  mesh::CellType cell_t = topology->cell_type();
-  if (!mesh::is_simplex(cell_t))
+  if (!mesh::is_simplex(topology->cell_type()))
     throw std::runtime_error("Refinement only defined for simplices");
+
   bool oned = topology->cell_type() == mesh::CellType::interval;
   auto [cell_adj, new_vertex_coords, xshape, parent_cell, parent_facet]
       = oned ? interval::compute_refinement_data(mesh, edges, option)

From 8a706621c4c064a6b2d66b74e1bab206ac8c8764 Mon Sep 17 00:00:00 2001
From: "Garth N. Wells" <gnw20@cam.ac.uk>
Date: Wed, 18 Sep 2024 11:49:58 +0100
Subject: [PATCH 05/10] Fix typi

---
 cpp/dolfinx/refinement/refine.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/cpp/dolfinx/refinement/refine.h b/cpp/dolfinx/refinement/refine.h
index 4e72c35837c..1473a4db4e0 100644
--- a/cpp/dolfinx/refinement/refine.h
+++ b/cpp/dolfinx/refinement/refine.h
@@ -70,7 +70,7 @@ refine(const mesh::Mesh<T>& mesh,
                           mesh.geometry().cmap(), mesh.comm(),
                           std::move(new_vertex_coords), xshape, partitioner);
 
-  // Report the number of refined cellse
+  // Report the number of refined cells
   const int D = topology->dim();
   const std::int64_t n0 = topology->index_map(D)->size_global();
   const std::int64_t n1 = refined_mesh.topology()->index_map(D)->size_global();

From 973f16dca8705a87c23cbbbc5d4e0401520ad139 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Thu, 19 Sep 2024 07:44:53 +0200
Subject: [PATCH 06/10] Move maintain_coarse_partitioner to refine.cpp

---
 cpp/dolfinx/refinement/CMakeLists.txt |  1 +
 cpp/dolfinx/refinement/refine.h       | 13 ++-----------
 2 files changed, 3 insertions(+), 11 deletions(-)

diff --git a/cpp/dolfinx/refinement/CMakeLists.txt b/cpp/dolfinx/refinement/CMakeLists.txt
index 9560e45c823..b11546361db 100644
--- a/cpp/dolfinx/refinement/CMakeLists.txt
+++ b/cpp/dolfinx/refinement/CMakeLists.txt
@@ -11,4 +11,5 @@ set(HEADERS_refinement
 target_sources(
   dolfinx PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}/plaza.cpp
                   ${CMAKE_CURRENT_SOURCE_DIR}/utils.cpp
+                  ${CMAKE_CURRENT_SOURCE_DIR}/refine.cpp
 )
diff --git a/cpp/dolfinx/refinement/refine.h b/cpp/dolfinx/refinement/refine.h
index 1473a4db4e0..e55245d4750 100644
--- a/cpp/dolfinx/refinement/refine.h
+++ b/cpp/dolfinx/refinement/refine.h
@@ -22,18 +22,9 @@ namespace dolfinx::refinement
 {
 
 /// TODO: Document function
-inline graph::AdjacencyList<std::int32_t> maintain_coarse_partitioner(
+graph::AdjacencyList<std::int32_t> maintain_coarse_partitioner(
     MPI_Comm comm, int, const std::vector<mesh::CellType>& cell_types,
-    const std::vector<std::span<const std::int64_t>>& cell_topology)
-{
-  int mpi_rank = MPI::rank(comm);
-  int num_cell_vertices = mesh::num_cell_vertices(cell_types.front());
-  std::int32_t num_cells = cell_topology.front().size() / num_cell_vertices;
-  std::vector<std::int32_t> destinations(num_cells, mpi_rank);
-  std::vector<std::int32_t> dest_offsets(num_cells + 1);
-  std::iota(dest_offsets.begin(), dest_offsets.end(), 0);
-  return graph::AdjacencyList(std::move(destinations), std::move(dest_offsets));
-}
+    const std::vector<std::span<const std::int64_t>>& cell_topology);
 
 /// @brief Refine with markers, optionally redistributing, and
 /// optionally calculating the parent-child relationships.

From face987aba59853b04a65bf65459da9057a1f76c Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Thu, 19 Sep 2024 07:47:41 +0200
Subject: [PATCH 07/10] Works better with the actual file

---
 cpp/dolfinx/refinement/refine.cpp | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)
 create mode 100644 cpp/dolfinx/refinement/refine.cpp

diff --git a/cpp/dolfinx/refinement/refine.cpp b/cpp/dolfinx/refinement/refine.cpp
new file mode 100644
index 00000000000..961f5cb98fc
--- /dev/null
+++ b/cpp/dolfinx/refinement/refine.cpp
@@ -0,0 +1,25 @@
+// Copyright (C) 2024 Paul T. Kühner
+//
+// This file is part of DOLFINx (https://www.fenicsproject.org)
+//
+// SPDX-License-Identifier:    LGPL-3.0-or-later
+
+#include "refine.h"
+
+namespace dolfinx::refinement
+{
+
+graph::AdjacencyList<std::int32_t> maintain_coarse_partitioner(
+    MPI_Comm comm, int, const std::vector<mesh::CellType>& cell_types,
+    const std::vector<std::span<const std::int64_t>>& cell_topology)
+{
+  int mpi_rank = MPI::rank(comm);
+  int num_cell_vertices = mesh::num_cell_vertices(cell_types.front());
+  std::int32_t num_cells = cell_topology.front().size() / num_cell_vertices;
+  std::vector<std::int32_t> destinations(num_cells, mpi_rank);
+  std::vector<std::int32_t> dest_offsets(num_cells + 1);
+  std::iota(dest_offsets.begin(), dest_offsets.end(), 0);
+  return graph::AdjacencyList(std::move(destinations), std::move(dest_offsets));
+}
+
+} // namespace dolfinx::refinement

From 965c28bdcb59166da33a36a2cb51efffe044c39c Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Thu, 19 Sep 2024 07:53:48 +0200
Subject: [PATCH 08/10] Add doc string to partitioner

---
 cpp/dolfinx/refinement/refine.h | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/cpp/dolfinx/refinement/refine.h b/cpp/dolfinx/refinement/refine.h
index e55245d4750..4d1420e7460 100644
--- a/cpp/dolfinx/refinement/refine.h
+++ b/cpp/dolfinx/refinement/refine.h
@@ -21,7 +21,15 @@
 namespace dolfinx::refinement
 {
 
-/// TODO: Document function
+/// @brief Partitioner that maintains the regional destribution for a refined
+/// mesh. Meaning, process local data is just maintained and no redistribution
+/// happens.
+///
+/// @param[in] comm MPI Communicator
+/// @param[in] nparts Number of partitions (input has no effect)
+/// @param[in] cell_types Cell types in the mesh
+/// @param[in] cells Lists of cells of each cell type.
+/// @return Destination ranks for each cell on this process
 graph::AdjacencyList<std::int32_t> maintain_coarse_partitioner(
     MPI_Comm comm, int, const std::vector<mesh::CellType>& cell_types,
     const std::vector<std::span<const std::int64_t>>& cell_topology);

From ba75f6afd86dd897bcfcd6a7aa595d0be789ee0b Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Thu, 19 Sep 2024 08:01:37 +0200
Subject: [PATCH 09/10] Make doxygen happy

---
 cpp/dolfinx/refinement/refine.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/cpp/dolfinx/refinement/refine.h b/cpp/dolfinx/refinement/refine.h
index 4d1420e7460..dddfa908104 100644
--- a/cpp/dolfinx/refinement/refine.h
+++ b/cpp/dolfinx/refinement/refine.h
@@ -31,7 +31,7 @@ namespace dolfinx::refinement
 /// @param[in] cells Lists of cells of each cell type.
 /// @return Destination ranks for each cell on this process
 graph::AdjacencyList<std::int32_t> maintain_coarse_partitioner(
-    MPI_Comm comm, int, const std::vector<mesh::CellType>& cell_types,
+    MPI_Comm comm, int nparts, const std::vector<mesh::CellType>& cell_types,
     const std::vector<std::span<const std::int64_t>>& cell_topology);
 
 /// @brief Refine with markers, optionally redistributing, and

From 33a3fd4deaaab72bf0d7518783bd57d5c11866d4 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Thu, 1 Aug 2024 15:22:49 +0200
Subject: [PATCH 10/10] Introduce transfer matrix operation

---
 cpp/dolfinx/CMakeLists.txt                 |   1 +
 cpp/dolfinx/transfer/CMakeLists.txt        |   4 +
 cpp/dolfinx/transfer/transfer_matrix.h     | 236 +++++++++++++
 cpp/test/CMakeLists.txt                    |   1 +
 cpp/test/transfer/transfer_matrix.cpp      | 377 +++++++++++++++++++++
 python/CMakeLists.txt                      |   1 +
 python/dolfinx/transfer.py                 |  23 ++
 python/dolfinx/wrappers/dolfinx.cpp        |   6 +
 python/dolfinx/wrappers/transfer.cpp       |  67 ++++
 python/test/unit/transfer/test_transfer.py |  22 ++
 10 files changed, 738 insertions(+)
 create mode 100644 cpp/dolfinx/transfer/CMakeLists.txt
 create mode 100644 cpp/dolfinx/transfer/transfer_matrix.h
 create mode 100644 cpp/test/transfer/transfer_matrix.cpp
 create mode 100644 python/dolfinx/transfer.py
 create mode 100644 python/dolfinx/wrappers/transfer.cpp
 create mode 100644 python/test/unit/transfer/test_transfer.py

diff --git a/cpp/dolfinx/CMakeLists.txt b/cpp/dolfinx/CMakeLists.txt
index 63d941fef51..d86501af4cc 100644
--- a/cpp/dolfinx/CMakeLists.txt
+++ b/cpp/dolfinx/CMakeLists.txt
@@ -18,6 +18,7 @@ set(DOLFINX_DIRS
     mesh
     nls
     refinement
+    transfer
 )
 
 # Add source to dolfinx target, and get sets of header files
diff --git a/cpp/dolfinx/transfer/CMakeLists.txt b/cpp/dolfinx/transfer/CMakeLists.txt
new file mode 100644
index 00000000000..68bcddd738e
--- /dev/null
+++ b/cpp/dolfinx/transfer/CMakeLists.txt
@@ -0,0 +1,4 @@
+set(HEADERS_transfer
+    ${CMAKE_CURRENT_SOURCE_DIR}/transfer_matrix.h
+    PARENT_SCOPE
+)
diff --git a/cpp/dolfinx/transfer/transfer_matrix.h b/cpp/dolfinx/transfer/transfer_matrix.h
new file mode 100644
index 00000000000..add92cdc9d1
--- /dev/null
+++ b/cpp/dolfinx/transfer/transfer_matrix.h
@@ -0,0 +1,236 @@
+// Copyright (C) 2024 Paul T. Kühner
+//
+// This file is part of DOLFINX (https://www.fenicsproject.org)
+//
+// SPDX-License-Identifier:    LGPL-3.0-or-later
+
+#pragma once
+
+#include <algorithm>
+#include <concepts>
+#include <cstdint>
+#include <iterator>
+#include <vector>
+
+#include "dolfinx/common/IndexMap.h"
+#include "dolfinx/fem/FunctionSpace.h"
+#include "dolfinx/la/SparsityPattern.h"
+#include "dolfinx/la/utils.h"
+#include "dolfinx/mesh/Mesh.h"
+
+namespace dolfinx::transfer
+{
+
+template <std::floating_point T>
+std::vector<std::int64_t>
+inclusion_mapping(const dolfinx::mesh::Mesh<T>& mesh_from,
+                  const dolfinx::mesh::Mesh<T>& mesh_to)
+{
+
+  const common::IndexMap& im_from = *mesh_from.topology()->index_map(0);
+  const common::IndexMap& im_to = *mesh_to.topology()->index_map(0);
+
+  std::vector<std::int64_t> map(im_from.size_global(), -1);
+
+  std::span<const T> x_from = mesh_from.geometry().x();
+  std::span<const T> x_to = mesh_to.geometry().x();
+
+  auto build_global_to_local = [&](const auto& im)
+  {
+    return [&](std::int32_t idx)
+    {
+      std::array<std::int64_t, 1> tmp;
+      im.local_to_global(std::vector<std::int32_t>{idx}, tmp);
+      return tmp[0];
+    };
+  };
+
+  auto to_global_to = build_global_to_local(im_to);
+  auto to_global_from = build_global_to_local(im_from);
+
+  for (std::int32_t i = 0; i < im_from.size_local(); i++)
+  {
+    std::ranges::subrange vertex_from(std::next(x_from.begin(), 3 * i),
+                                      std::next(x_from.begin(), 3 * (i + 1)));
+    for (std::int64_t j = 0; j < im_to.size_local() + im_to.num_ghosts(); j++)
+    {
+      std::ranges::subrange vertex_to(std::next(x_to.begin(), 3 * j),
+                                      std::next(x_to.begin(), 3 * (j + 1)));
+
+      if (std::ranges::equal(
+              vertex_from, vertex_to, [](T a, T b)
+              { return std::abs(a - b) <= std::numeric_limits<T>::epsilon(); }))
+      {
+        map[to_global_from(i)] = to_global_to(j);
+        break;
+      }
+    }
+  }
+
+  if (dolfinx::MPI::size(mesh_to.comm()) == 1)
+  {
+    // no communication required
+    assert(std::ranges::all_of(map, [](auto e) { return e >= 0; }));
+    return map;
+  }
+
+  // map holds at this point for every original local index the corresponding
+  // mapped global index. All other entries are still -1, but are available on
+  // other processes.
+  std::vector<std::int64_t> result(map.size(), -1);
+  MPI_Allreduce(map.data(), result.data(), map.size(),
+                dolfinx::MPI::mpi_type<std::int64_t>(), MPI_MAX,
+                mesh_from.comm());
+
+  assert(std::ranges::all_of(result, [](auto e) { return e >= 0; }));
+  return result;
+}
+
+template <std::floating_point T>
+la::SparsityPattern
+create_sparsity_pattern(const dolfinx::fem::FunctionSpace<T>& V_from,
+                        const dolfinx::fem::FunctionSpace<T>& V_to,
+                        const std::vector<std::int64_t>& inclusion_map)
+{
+  // TODO: P1 and which elements supported?
+  auto mesh_from = V_from.mesh();
+  auto mesh_to = V_to.mesh();
+  assert(mesh_from);
+  assert(mesh_to);
+
+  MPI_Comm comm = mesh_from->comm();
+  {
+    // Check comms equal
+    int result;
+    MPI_Comm_compare(comm, mesh_to->comm(), &result);
+    assert(result == MPI_CONGRUENT);
+  }
+  assert(mesh_from->topology()->dim() == mesh_to->topology()->dim());
+
+  auto to_v_to_f = mesh_to->topology()->connectivity(0, 1);
+  auto to_f_to_v = mesh_to->topology()->connectivity(1, 0);
+  assert(to_v_to_f);
+  assert(to_f_to_v);
+
+  auto dofmap_from = V_from.dofmap();
+  auto dofmap_to = V_to.dofmap();
+  assert(dofmap_from);
+  assert(dofmap_to);
+
+  assert(mesh_to->topology()->index_map(0));
+  assert(mesh_from->topology()->index_map(0));
+  const common::IndexMap& im_to = *mesh_to->topology()->index_map(0);
+  const common::IndexMap& im_from = *mesh_from->topology()->index_map(0);
+
+  dolfinx::la::SparsityPattern sp(
+      comm, {dofmap_from->index_map, dofmap_to->index_map},
+      {dofmap_from->index_map_bs(), dofmap_to->index_map_bs()});
+
+  assert(inclusion_map.size() == im_from.size_global());
+  for (int dof_from_global = 0; dof_from_global < im_from.size_global();
+       dof_from_global++)
+  {
+    std::int64_t dof_to_global = inclusion_map[dof_from_global];
+
+    std::vector<std::int32_t> local_dof_to_v{0};
+    im_to.global_to_local(std::vector<std::int64_t>{dof_to_global},
+                          local_dof_to_v);
+
+    auto local_dof_to = local_dof_to_v[0];
+
+    bool is_remote = (local_dof_to == -1);
+    bool is_ghost = local_dof_to >= im_to.size_local();
+    if (is_remote || is_ghost)
+      continue;
+
+    std::vector<std::int32_t> dof_from_v{0};
+    im_from.global_to_local(std::vector<std::int64_t>{dof_from_global},
+                            dof_from_v);
+
+    std::ranges::for_each(
+        to_v_to_f->links(local_dof_to),
+        [&](auto e)
+        {
+          sp.insert(
+              std::vector<int32_t>(to_f_to_v->links(e).size(), dof_from_v[0]),
+              to_f_to_v->links(e));
+        });
+  }
+  sp.finalize();
+  return sp;
+}
+
+template <std::floating_point T>
+void assemble_transfer_matrix(la::MatSet<T> auto mat_set,
+                              const dolfinx::fem::FunctionSpace<T>& V_from,
+                              const dolfinx::fem::FunctionSpace<T>& V_to,
+                              const std::vector<std::int64_t>& inclusion_map,
+                              std::function<T(std::int32_t)> weight)
+{
+  // TODO: P1 and which elements supported?
+  auto mesh_from = V_from.mesh();
+  auto mesh_to = V_to.mesh();
+  assert(mesh_from);
+  assert(mesh_to);
+
+  MPI_Comm comm = mesh_from->comm();
+  {
+    // Check comms equal
+    int result;
+    MPI_Comm_compare(comm, mesh_to->comm(), &result);
+    assert(result == MPI_CONGRUENT);
+  }
+  assert(mesh_from->topology()->dim() == mesh_to->topology()->dim());
+
+  auto to_v_to_f = mesh_to->topology()->connectivity(0, 1);
+  auto to_f_to_v = mesh_to->topology()->connectivity(1, 0);
+  assert(to_v_to_f);
+  assert(to_f_to_v);
+
+  auto dofmap_from = V_from.dofmap();
+  auto dofmap_to = V_to.dofmap();
+  assert(dofmap_from);
+  assert(dofmap_to);
+
+  assert(mesh_to->topology()->index_map(0));
+  assert(mesh_from->topology()->index_map(0));
+  const common::IndexMap& im_to = *mesh_to->topology()->index_map(0);
+  const common::IndexMap& im_from = *mesh_from->topology()->index_map(0);
+
+  assert(inclusion_map.size() == im_from.size_global());
+
+  for (int dof_from_global = 0; dof_from_global < im_from.size_global();
+       dof_from_global++)
+  {
+    std::int64_t dof_to_global = inclusion_map[dof_from_global];
+
+    std::vector<std::int32_t> local_dof_to_v{0};
+    im_to.global_to_local(std::vector<std::int64_t>{dof_to_global},
+                          local_dof_to_v);
+
+    auto local_dof_to = local_dof_to_v[0];
+
+    bool is_remote = (local_dof_to == -1);
+    bool is_ghost = local_dof_to >= im_to.size_local();
+    if (is_remote || is_ghost)
+      continue;
+
+    std::vector<std::int32_t> dof_from_v{0};
+    im_from.global_to_local(std::vector<std::int64_t>{dof_from_global},
+                            dof_from_v);
+
+    for (auto e : to_v_to_f->links(local_dof_to))
+    {
+      for (auto n : to_f_to_v->links(e))
+      {
+        // For now we only support distance <= 1 -> this should be somehow
+        // asserted.
+        std::int32_t distance = (n == local_dof_to) ? 0 : 1;
+        mat_set(std::vector<int32_t>{dof_from_v[0]}, std::vector<int32_t>{n},
+                std::vector<double>{weight(distance)});
+      }
+    }
+  }
+}
+
+} // namespace dolfinx::transfer
\ No newline at end of file
diff --git a/cpp/test/CMakeLists.txt b/cpp/test/CMakeLists.txt
index 4a3dd8f3817..64315eada0e 100644
--- a/cpp/test/CMakeLists.txt
+++ b/cpp/test/CMakeLists.txt
@@ -47,6 +47,7 @@ add_executable(
   mesh/refinement/interval.cpp
   mesh/refinement/option.cpp
   mesh/refinement/rectangle.cpp
+  transfer/transfer_matrix.cpp
   ${CMAKE_CURRENT_BINARY_DIR}/poisson.c
 )
 target_link_libraries(unittests PRIVATE Catch2::Catch2WithMain dolfinx)
diff --git a/cpp/test/transfer/transfer_matrix.cpp b/cpp/test/transfer/transfer_matrix.cpp
new file mode 100644
index 00000000000..3487090d01b
--- /dev/null
+++ b/cpp/test/transfer/transfer_matrix.cpp
@@ -0,0 +1,377 @@
+// Copyright (C) 2024 Paul T. Kühner
+//
+// This file is part of DOLFINX (https://www.fenicsproject.org)
+//
+// SPDX-License-Identifier:    LGPL-3.0-or-later
+
+#include <concepts>
+#include <cstdint>
+#include <memory>
+#include <optional>
+#include <vector>
+
+#include <mpi.h>
+
+#include <catch2/catch_template_test_macros.hpp>
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/matchers/catch_matchers.hpp>
+#include <catch2/matchers/catch_matchers_floating_point.hpp>
+#include <catch2/matchers/catch_matchers_range_equals.hpp>
+
+#include <dolfinx/common/IndexMap.h>
+#include <dolfinx/common/MPI.h>
+#include <dolfinx/fem/FunctionSpace.h>
+#include <dolfinx/fem/utils.h>
+#include <dolfinx/la/MatrixCSR.h>
+#include <dolfinx/la/SparsityPattern.h>
+#include <dolfinx/mesh/cell_types.h>
+#include <dolfinx/mesh/generation.h>
+#include <dolfinx/mesh/utils.h>
+#include <dolfinx/refinement/plaza.h>
+#include <dolfinx/refinement/refine.h>
+#include <dolfinx/transfer/transfer_matrix.h>
+
+using namespace dolfinx;
+using namespace Catch::Matchers;
+
+namespace
+{
+template <typename T>
+constexpr auto EPS = std::numeric_limits<T>::epsilon();
+} // namespace
+
+template <std::floating_point T>
+constexpr auto weight = [](std::int32_t d) -> T { return d == 0 ? 1. : .5; };
+
+TEMPLATE_TEST_CASE("Transfer Matrix 1D", "[transfer_matrix]",
+                   double) // TODO: float
+{
+  using T = TestType;
+
+  auto mesh_coarse
+      = std::make_shared<mesh::Mesh<T>>(dolfinx::mesh::create_interval<T>(
+          MPI_COMM_SELF, 2, {0.0, 1.0}, mesh::GhostMode::none));
+
+  auto [mesh_fine, parent_cell, parent_facet]
+      = refinement::refine(*mesh_coarse, std::nullopt);
+
+  auto element = basix::create_element<T>(
+      basix::element::family::P, basix::cell::type::interval, 1,
+      basix::element::lagrange_variant::unset,
+      basix::element::dpc_variant::unset, false);
+
+  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
+      fem::create_functionspace<T>(mesh_coarse, element, {}));
+  auto V_fine
+      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
+          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
+
+  mesh_fine.topology()->create_connectivity(1, 0);
+  mesh_fine.topology()->create_connectivity(0, 1);
+
+  std::vector<std::int64_t> inclusion_map
+      = transfer::inclusion_mapping(*mesh_coarse, mesh_fine);
+
+  CHECK_THAT(inclusion_map, RangeEquals(std::vector<std::int64_t>{0, 2, 4}));
+
+  la::SparsityPattern sp
+      = transfer::create_sparsity_pattern(*V_coarse, *V_fine, inclusion_map);
+
+  la::MatrixCSR<T> transfer_matrix(std::move(sp), la::BlockMode::compact);
+  transfer::assemble_transfer_matrix<T>(transfer_matrix.mat_set_values(),
+                                        *V_coarse, *V_fine, inclusion_map,
+                                        weight<T>);
+
+  std::vector<T> expected{1.0, .5, 0, 0, 0, 0, .5, 1, .5, 0, 0, 0, 0, .5, 1};
+  CHECK_THAT(transfer_matrix.to_dense(),
+             RangeEquals(expected, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+}
+
+TEMPLATE_TEST_CASE("Transfer Matrix 1D (parallel)", "[transfer_matrix]",
+                   double) // TODO: float
+{
+  using T = TestType;
+
+  int comm_size = dolfinx::MPI::size(MPI_COMM_WORLD);
+  int rank = dolfinx::MPI::rank(MPI_COMM_WORLD);
+
+  // TODO: see https://github.com/FEniCS/dolfinx/issues/3358
+  //   auto part = mesh::create_cell_partitioner(mesh::GhostMode::shared_facet);
+  mesh::CellPartitionFunction part
+      = [&](MPI_Comm /* comm */, int /* nparts */,
+            const std::vector<mesh::CellType>& /* cell_types */,
+            const std::vector<std::span<const std::int64_t>>& /* cells */)
+  {
+    std::vector<std::vector<std::int32_t>> data;
+    if (comm_size == 1)
+      data = {{0}, {0}, {0}, {0}};
+    else if (comm_size == 2)
+      data = {{0}, {0}, {0}, {0}, {0, 1}, {1, 0}, {1}, {1}, {1}};
+    else if (comm_size == 3)
+      data = {{1}, {1},    {1},    {1}, {1, 2}, {2, 1}, {2},
+              {2}, {2, 0}, {0, 2}, {0}, {0},    {0},    {0}};
+    else
+      FAIL("Test only supports <= 3 processes");
+    return graph::AdjacencyList<std::int32_t>(std::move(data));
+  };
+
+  auto mesh_coarse = std::make_shared<mesh::Mesh<T>>(
+      mesh::create_interval<T>(MPI_COMM_WORLD, 5 * comm_size - 1, {0., 1.},
+                               mesh::GhostMode::shared_facet, part));
+
+  // TODO: see https://github.com/FEniCS/dolfinx/issues/3358
+  //   auto part_refine
+  //       = mesh::create_cell_partitioner(mesh::GhostMode::shared_facet);
+  mesh::CellPartitionFunction part_refine
+      = [&](MPI_Comm comm, int /* nparts */,
+            const std::vector<mesh::CellType>& /* cell_types */,
+            const std::vector<std::span<const std::int64_t>>& /* cells */)
+  {
+    std::vector<std::vector<std::int32_t>> data;
+    if (dolfinx::MPI::size(comm) == 1)
+      data = {{0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}};
+    else if (dolfinx::MPI::size(comm) == 2)
+    {
+      if (rank == 0)
+        data = {{0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0, 1}, {1, 0}};
+      else
+        data = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}};
+    }
+    else if (dolfinx::MPI::size(comm) == 3)
+    {
+      if (rank == 0)
+        data = {{2, 0}, {0, 2}, {0}, {0}, {0}, {0}, {0}, {0}, {0}, {0}};
+      else if (rank == 1)
+        data = {{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1, 2}};
+      else
+        data = {{2, 1}, {2}, {2}, {2}, {2}, {2}, {2}, {2}};
+    }
+    else
+      FAIL("Test only supports <= 3 processes");
+    return graph::AdjacencyList<std::int32_t>(std::move(data));
+  };
+
+  auto [mesh_fine, parent_cell, parent_facet] = refinement::refine(
+      *mesh_coarse, std::nullopt, part_refine, refinement::Option::none);
+
+  auto element = basix::create_element<T>(
+      basix::element::family::P, basix::cell::type::interval, 1,
+      basix::element::lagrange_variant::unset,
+      basix::element::dpc_variant::unset, false);
+
+  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
+      fem::create_functionspace<T>(mesh_coarse, element, {}));
+  auto V_fine
+      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
+          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
+
+  mesh_fine.topology()->create_connectivity(1, 0);
+  mesh_fine.topology()->create_connectivity(0, 1);
+
+  std::vector<int64_t> inclusion_map;
+  switch (comm_size)
+  {
+  case 1:
+    inclusion_map = {0, 2, 4, 6, 8};
+    break;
+  case 2:
+    inclusion_map = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18};
+    break;
+  case 3:
+    inclusion_map = {0, 2, 4, 6, 8, 9, 11, 13, 15, 17, 19, 27, 25, 23, 20};
+    break;
+  }
+
+  CHECK_THAT(transfer::inclusion_mapping(*mesh_coarse, mesh_fine),
+             RangeEquals(inclusion_map));
+
+  la::SparsityPattern sp
+      = transfer::create_sparsity_pattern(*V_coarse, *V_fine, inclusion_map);
+
+  la::MatrixCSR<T> transfer_matrix(std::move(sp), la::BlockMode::compact);
+  transfer::assemble_transfer_matrix<T>(transfer_matrix.mat_set_values(),
+                                        *V_coarse, *V_fine, inclusion_map,
+                                        weight<T>);
+
+  std::array<std::vector<T>, 3> expected;
+  if (comm_size == 1)
+  {
+    // clang-format off
+    expected[0] = {
+        /* row_0 */ 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0
+    };
+    // clang-format on
+  }
+  else if (comm_size == 2)
+  {
+    // clang-format off
+    expected[0] = {
+        /* row_0 */ 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
+    };
+    expected[1] = {
+        /* row_0 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
+    };
+    // clang-format on
+  }
+  else if (comm_size == 3)
+  {
+    // clang-format off
+    expected[0] = {
+        /* row_0 */ 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+    };
+    expected[1] = {
+        /* row_0 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_1 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5,
+        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+    };
+    expected[2] = {
+        /* row_0 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5,
+        /* row_1 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0,
+        /* row_2 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 1.0, 0.5, 0.0, 0.0, 0.0, 0.0,
+        /* row_3 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_4 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_5 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+        /* row_6 */ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
+    };
+    // clang-format on
+  }
+  else
+  {
+    CHECK(false);
+  }
+
+  CHECK_THAT(transfer_matrix.to_dense(),
+             RangeEquals(expected[rank], [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+}
+
+TEMPLATE_TEST_CASE("Transfer Matrix 2D", "[transfer_matrix]", double)
+{
+  using T = TestType;
+
+  auto mesh_coarse
+      = std::make_shared<mesh::Mesh<T>>(dolfinx::mesh::create_rectangle<T>(
+          MPI_COMM_SELF, {{{0, 0}, {1, 1}}}, {1, 1}, mesh::CellType::triangle));
+  mesh_coarse->topology()->create_entities(1);
+
+  auto [mesh_fine, parent_cell, parent_facet]
+      = refinement::refine(*mesh_coarse, std::nullopt);
+
+  auto element = basix::create_element<T>(
+      basix::element::family::P, basix::cell::type::triangle, 1,
+      basix::element::lagrange_variant::unset,
+      basix::element::dpc_variant::unset, false);
+
+  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
+      fem::create_functionspace<T>(mesh_coarse, element, {}));
+  auto V_fine
+      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
+          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
+
+  mesh_fine.topology()->create_connectivity(1, 0);
+  mesh_fine.topology()->create_connectivity(0, 1);
+
+  std::vector<std::int64_t> inclusion_map
+      = transfer::inclusion_mapping(*mesh_coarse, mesh_fine);
+  CHECK_THAT(inclusion_map, RangeEquals(std::vector<std::int64_t>{4, 1, 5, 8}));
+
+  la::SparsityPattern sp
+      = transfer::create_sparsity_pattern(*V_coarse, *V_fine, inclusion_map);
+  la::MatrixCSR<T> transfer_matrix(std::move(sp), la::BlockMode::compact);
+  transfer::assemble_transfer_matrix<T>(transfer_matrix.mat_set_values(),
+                                        *V_coarse, *V_fine, inclusion_map,
+                                        weight<T>);
+  transfer_matrix.scatter_rev();
+  std::vector<T> expected{0.5, 0.0, 0.5, 0.0, 1.0, 0.0, 0.5, 0.0, 0.0,
+                          0.5, 1.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0,
+                          0.5, 0.0, 0.0, 0.5, 0.0, 1.0, 0.0, 0.5, 0.0,
+                          0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 1.0};
+  CHECK_THAT(transfer_matrix.to_dense(),
+             RangeEquals(expected, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+}
+
+TEMPLATE_TEST_CASE("Transfer Matrix 3D", "[transfer_matrix]", double)
+{
+  using T = TestType;
+
+  auto mesh_coarse = std::make_shared<mesh::Mesh<T>>(
+      dolfinx::mesh::create_box<T>(MPI_COMM_SELF, {{{0, 0, 0}, {1, 1, 1}}},
+                                   {1, 1, 1}, mesh::CellType::tetrahedron));
+  mesh_coarse->topology()->create_entities(1);
+
+  auto [mesh_fine, parent_cell, parent_facet]
+      = refinement::refine(*mesh_coarse, std::nullopt);
+
+  auto element = basix::create_element<T>(
+      basix::element::family::P, basix::cell::type::tetrahedron, 1,
+      basix::element::lagrange_variant::unset,
+      basix::element::dpc_variant::unset, false);
+
+  auto V_coarse = std::make_shared<fem::FunctionSpace<T>>(
+      fem::create_functionspace<T>(mesh_coarse, element, {}));
+  auto V_fine
+      = std::make_shared<fem::FunctionSpace<T>>(fem::create_functionspace<T>(
+          std::make_shared<mesh::Mesh<T>>(mesh_fine), element, {}));
+
+  mesh_fine.topology()->create_connectivity(1, 0);
+  mesh_fine.topology()->create_connectivity(0, 1);
+
+  std::vector<std::int64_t> inclusion_map
+      = transfer::inclusion_mapping(*mesh_coarse, mesh_fine);
+  CHECK_THAT(inclusion_map, RangeEquals(std::vector<std::int64_t>{
+                                0, 6, 15, 25, 17, 9, 11, 22}));
+
+  la::SparsityPattern sp
+      = transfer::create_sparsity_pattern(*V_coarse, *V_fine, inclusion_map);
+  la::MatrixCSR<T> transfer_matrix(std::move(sp), la::BlockMode::compact);
+  transfer::assemble_transfer_matrix<T>(transfer_matrix.mat_set_values(),
+                                        *V_coarse, *V_fine, inclusion_map,
+                                        weight<T>);
+
+  std::vector<T> expected{
+      1.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5,
+      0.5, 0.5, 0.0, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.5, 0.0, 0.5, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.5, 0.5, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0,
+      0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.5, 0.0, 0.5,
+      0.5, 1.0, 0.5, 0.0, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
+      0.5, 0.0, 0.5, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0,
+      0.0, 0.5, 0.5, 0.0, 0.0, 0.5, 0.0, 0.0, 0.5, 1.0, 0.0, 0.0, 0.0, 0.5, 0.0,
+      0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0,
+      0.0, 0.5, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0,
+      0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0,
+      0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.5,
+      0.5, 1.0, 0.0, 0.0, 0.0, 0.5};
+  CHECK_THAT(transfer_matrix.to_dense(),
+             RangeEquals(expected, [](auto a, auto b)
+                         { return std::abs(a - b) <= EPS<T>; }));
+}
diff --git a/python/CMakeLists.txt b/python/CMakeLists.txt
index 2a9f9de56ee..90dce7571e8 100644
--- a/python/CMakeLists.txt
+++ b/python/CMakeLists.txt
@@ -46,6 +46,7 @@ nanobind_add_module(
   dolfinx/wrappers/mesh.cpp
   dolfinx/wrappers/petsc.cpp
   dolfinx/wrappers/refinement.cpp
+  dolfinx/wrappers/transfer.cpp
 )
 target_compile_definitions(cpp PRIVATE cxx_std_20)
 
diff --git a/python/dolfinx/transfer.py b/python/dolfinx/transfer.py
new file mode 100644
index 00000000000..4e2a7670f3b
--- /dev/null
+++ b/python/dolfinx/transfer.py
@@ -0,0 +1,23 @@
+import numpy as np
+from numpy.typing import NDArray
+
+from dolfinx.cpp.la import SparsityPattern
+from dolfinx.cpp.transfer import (
+    assemble_transfer_matrix,
+)
+from dolfinx.cpp.transfer import create_sparsity_pattern as _create_sparsity_pattern
+from dolfinx.cpp.transfer import inclusion_mapping as _inclusion_mapping
+from dolfinx.fem import FunctionSpace
+from dolfinx.mesh import Mesh
+
+__all__ = ["inclusion_mapping", "create_sparsity_pattern", "assemble_transfer_matrix"]
+
+
+def inclusion_mapping(mesh_from: Mesh, mesh_to: Mesh) -> NDArray[np.int64]:
+    return _inclusion_mapping(mesh_from._cpp_object, mesh_to._cpp_object)
+
+
+def create_sparsity_pattern(
+    V_from: FunctionSpace, V_to: FunctionSpace, inclusion_map: NDArray[np.int64]
+) -> SparsityPattern:
+    return _create_sparsity_pattern(V_from._cpp_object, V_to._cpp_object, inclusion_map)
diff --git a/python/dolfinx/wrappers/dolfinx.cpp b/python/dolfinx/wrappers/dolfinx.cpp
index 9c0864f9ef1..9d2ca3e716d 100644
--- a/python/dolfinx/wrappers/dolfinx.cpp
+++ b/python/dolfinx/wrappers/dolfinx.cpp
@@ -25,6 +25,8 @@ void la(nb::module_& m);
 void mesh(nb::module_& m);
 void nls(nb::module_& m);
 void refinement(nb::module_& m);
+void transfer(nb::module_& m);
+
 } // namespace dolfinx_wrappers
 
 NB_MODULE(cpp, m)
@@ -74,6 +76,10 @@ NB_MODULE(cpp, m)
   nb::module_ refinement = m.def_submodule("refinement", "Refinement module");
   dolfinx_wrappers::refinement(refinement);
 
+  // Create transfer submodule
+  nb::module_ transfer = m.def_submodule("transfer", "Transfer module");
+  dolfinx_wrappers::transfer(transfer);
+
 #if defined(HAS_PETSC) && defined(HAS_PETSC4PY)
   // PETSc-specific wrappers
   nb::module_ nls = m.def_submodule("nls", "Nonlinear solver module");
diff --git a/python/dolfinx/wrappers/transfer.cpp b/python/dolfinx/wrappers/transfer.cpp
new file mode 100644
index 00000000000..16ffc4cbe5a
--- /dev/null
+++ b/python/dolfinx/wrappers/transfer.cpp
@@ -0,0 +1,67 @@
+// Copyright (C) 2024 Paul T. Kühner
+//
+// This file is part of DOLFINX (https://www.fenicsproject.org)
+//
+// SPDX-License-Identifier:    LGPL-3.0-or-later
+
+#include <cstdint>
+#include <vector>
+
+#include <nanobind/nanobind.h>
+#include <nanobind/stl/vector.h>
+
+#include <dolfinx/la/MatrixCSR.h>
+#include <dolfinx/transfer/transfer_matrix.h>
+
+#include "array.h"
+
+namespace nb = nanobind;
+
+namespace dolfinx_wrappers
+{
+
+void transfer(nb::module_& m)
+{
+  m.def(
+      "inclusion_mapping",
+      [](const dolfinx::mesh::Mesh<double>& mesh_from,
+         const dolfinx::mesh::Mesh<double>& mesh_to)
+      {
+        std::vector<std::int64_t> map
+            = dolfinx::transfer::inclusion_mapping<double>(mesh_from, mesh_to);
+        return dolfinx_wrappers::as_nbarray(map);
+      },
+      nb::arg("mesh_from"), nb::arg("mesh_to"),
+      "Computes inclusion mapping between two meshes");
+
+  m.def(
+      "create_sparsity_pattern",
+      [](const dolfinx::fem::FunctionSpace<double>& V_from,
+         const dolfinx::fem::FunctionSpace<double>& V_to,
+         nb::ndarray<const std::int64_t, nb::numpy>& inclusion_map)
+      {
+        // TODO: cahnge to accepting range;
+        auto vec = std::vector(inclusion_map.data(),
+                               inclusion_map.data() + inclusion_map.size());
+        return dolfinx::transfer::create_sparsity_pattern<double>(V_from, V_to,
+                                                                  vec);
+      },
+      nb::arg("V_from"), nb::arg("V_to"), nb::arg("inclusion_map"));
+
+  m.def(
+      "assemble_transfer_matrix",
+      [](dolfinx::la::MatrixCSR<double>& A,
+         const dolfinx::fem::FunctionSpace<double>& V_from,
+         const dolfinx::fem::FunctionSpace<double>& V_to,
+         const std::vector<std::int64_t>& inclusion_map,
+         std::function<double(std::int32_t)> weight)
+      {
+        dolfinx::transfer::assemble_transfer_matrix(
+            A.mat_set_values(), V_from, V_to, inclusion_map, weight);
+      },
+      nb::arg("A"), nb::arg("V_from"), nb::arg("V_to"),
+      nb::arg("inclusion_map"), nb::arg("weight"),
+      "Assembles a transfer matrix between two function spaces.");
+}
+
+} // namespace dolfinx_wrappers
diff --git a/python/test/unit/transfer/test_transfer.py b/python/test/unit/transfer/test_transfer.py
new file mode 100644
index 00000000000..93c260442da
--- /dev/null
+++ b/python/test/unit/transfer/test_transfer.py
@@ -0,0 +1,22 @@
+from mpi4py import MPI
+
+import pytest
+
+from dolfinx.fem import functionspace
+from dolfinx.mesh import GhostMode, create_interval, refine
+from dolfinx.transfer import create_sparsity_pattern, inclusion_mapping
+
+
+@pytest.mark.parametrize(
+    "ghost_mode", [GhostMode.none, GhostMode.shared_vertex, GhostMode.shared_facet]
+)
+def test_1d(ghost_mode):
+    mesh = create_interval(MPI.COMM_WORLD, 10, (0, 1), ghost_mode=ghost_mode)
+    mesh_fine, _, _ = refine(mesh)
+    inclusion_map = inclusion_mapping(mesh, mesh_fine)
+    V = functionspace(mesh, ("Lagrange", 1, (1,)))
+    V_fine = functionspace(mesh_fine, ("Lagrange", 1, (1,)))
+    V_fine.mesh.topology.create_connectivity(1, 0)
+    V_fine.mesh.topology.create_connectivity(0, 1)
+    create_sparsity_pattern(V, V_fine, inclusion_map)
+    # continue with assembly of matrix