diff --git a/cmake/modules/DumuxMacros.cmake b/cmake/modules/DumuxMacros.cmake
index a8d3041bff592689a9822d4cde8ba85d24d54d84..b3e7328fe322bd418bc3868ec9876ee20c19e031 100644
--- a/cmake/modules/DumuxMacros.cmake
+++ b/cmake/modules/DumuxMacros.cmake
@@ -9,3 +9,4 @@ find_package(Gnuplot)
set(HAVE_GNUPLOT ${GNUPLOT_FOUND})
find_package(Valgrind)
+find_package(PTScotch)
diff --git a/dumux/linear/CMakeLists.txt b/dumux/linear/CMakeLists.txt
index c8ce338dbc029c6e609463b284871fa8bb8ee5b3..38a751c16f370bdab9c6ba674b07681ed6904ef6 100644
--- a/dumux/linear/CMakeLists.txt
+++ b/dumux/linear/CMakeLists.txt
@@ -1,3 +1,4 @@
+add_subdirectory(reordering)
#install headers
install(FILES
diff --git a/dumux/linear/reordering/CMakeLists.txt b/dumux/linear/reordering/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a08d5315e27a198078bc6c0401d9167f80644a16
--- /dev/null
+++ b/dumux/linear/reordering/CMakeLists.txt
@@ -0,0 +1,4 @@
+#install headers
+install(FILES
+scotchbackend.hh
+DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dumux/linear/reordering)
diff --git a/dumux/linear/reordering/scotchbackend.hh b/dumux/linear/reordering/scotchbackend.hh
new file mode 100644
index 0000000000000000000000000000000000000000..d93c0f900dd911aa271202aa24ca6e5f2917fab9
--- /dev/null
+++ b/dumux/linear/reordering/scotchbackend.hh
@@ -0,0 +1,169 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ * See the file COPYING for full copying permissions. *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 2 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+
+/*!
+ * \file An interface to the scotch library for matrix reordering
+ * \brief An interface to the scotch library for matrix reordering
+ * \note This is adapted from the FEniCS implementation of the scotch interface
+ */
+#ifndef DUMUX_SCOTCH_BACKEND_HH
+#define DUMUX_SCOTCH_BACKEND_HH
+
+#include <string>
+#include <vector>
+#include <iostream>
+
+#if HAVE_PTSCOTCH
+extern "C"
+{
+#include <stdint.h>
+#include <ptscotch.h>
+}
+#endif
+
+namespace Dumux
+{
+
+template<class IndexType>
+class ScotchBackend
+{
+ using Graph = std::vector<std::vector<IndexType>>;
+
+public:
+ //! Compute reordering (map[old] -> new) using
+ //! Gibbs-Poole-Stockmeyer (GPS) re-ordering
+ static std::vector<int> computeGPSReordering(const Graph& graph,
+ std::size_t numPasses = 5)
+ {
+ // Create strategy string for Gibbs-Poole-Stockmeyer ordering
+ std::string strategy = "g{pass= " + std::to_string(numPasses) + "}";
+ return computeReordering(graph, strategy);
+ }
+
+ // Compute graph re-ordering
+ static std::vector<int> computeReordering(const Graph& graph,
+ std::string scotchStrategy = "")
+ {
+ std::vector<int> permutation, inversePermutation;
+ computeReordering(graph, permutation, inversePermutation, scotchStrategy);
+ return permutation;
+ }
+
+ // Compute graph re-ordering
+ static void computeReordering(const Graph& graph,
+ std::vector<int>& permutation,
+ std::vector<int>& inversePermutation,
+ std::string scotchStrategy = "")
+ {
+ // Number of local graph vertices (cells)
+ const SCOTCH_Num vertnbr = graph.size();
+
+ // Data structures for graph input to SCOTCH (add 1 for case that
+ // graph size is zero)
+ std::vector<SCOTCH_Num> verttab;
+ verttab.reserve(vertnbr + 1);
+ std::vector<SCOTCH_Num> edgetab;
+ edgetab.reserve(20*vertnbr);
+
+ // Build local graph input for SCOTCH
+ // (number of graph vertices (cells),
+ // number of edges connecting two vertices)
+ SCOTCH_Num edgenbr = 0;
+ verttab.push_back(0);
+ typename Graph::const_iterator vertex;
+ for (vertex = graph.begin(); vertex != graph.end(); ++vertex)
+ {
+ edgenbr += vertex->size();
+ verttab.push_back(verttab.back() + vertex->size());
+ edgetab.insert(edgetab.end(), vertex->begin(), vertex->end());
+ }
+
+ // Shrink vectors to hopefully recover an unused memory
+ verttab.shrink_to_fit();
+ edgetab.shrink_to_fit();
+
+ // Create SCOTCH graph
+ SCOTCH_Graph scotchGraph;
+
+ // C-style array indexing
+ const SCOTCH_Num baseval = 0;
+
+ // Create SCOTCH graph and initialise
+ if (SCOTCH_graphInit(&scotchGraph) != 0)
+ {
+ std::cerr << "Error initializing SCOTCH graph!" << std::endl;
+ exit(1);
+ }
+
+ // Build SCOTCH graph
+ if (SCOTCH_graphBuild(&scotchGraph, baseval,
+ vertnbr, &verttab[0], &verttab[1], NULL, NULL,
+ edgenbr, &edgetab[0], NULL))
+ {
+ std::cerr << "Error building SCOTCH graph!" << std::endl;
+ exit(1);
+ }
+
+ // Check graph data for consistency
+ // if (SCOTCH_graphCheck(&scotchGraph))
+ // {
+ // std::cerr << "Consistency error in SCOTCH graph!" << std::endl;
+ // exit(1);
+ // }
+
+ // Re-ordering strategy
+ SCOTCH_Strat strat;
+ SCOTCH_stratInit(&strat);
+
+ // Set SCOTCH strategy (if provided)
+ if (!scotchStrategy.empty())
+ SCOTCH_stratGraphOrder(&strat, scotchStrategy.c_str());
+
+ // Vector to hold permutation vectors
+ std::vector<SCOTCH_Num> permutationIndices(vertnbr);
+ std::vector<SCOTCH_Num> inversePermutationIndices(vertnbr);
+
+ // Reset SCOTCH random number generator to produce deterministic partitions
+ SCOTCH_randomReset();
+
+ // Compute re-ordering
+ if (SCOTCH_graphOrder(&scotchGraph, &strat, permutationIndices.data(),
+ inversePermutationIndices.data(), NULL, NULL, NULL))
+ {
+ std::cerr << "SCOTCH: Error during reordering graph!" << std::endl;
+ exit(1);
+ }
+
+ // Clean up SCOTCH objects
+ SCOTCH_graphExit(&scotchGraph);
+ SCOTCH_stratExit(&strat);
+
+ // Copy permutation vectors
+ permutation.resize(vertnbr);
+ inversePermutation.resize(vertnbr);
+ std::copy(permutationIndices.begin(), permutationIndices.end(),
+ permutation.begin());
+ std::copy(inversePermutationIndices.begin(), inversePermutationIndices.end(),
+ inversePermutation.begin());
+ }
+};
+
+} // end namespace Dumux
+
+#endif