DistributedTetrahedralMesh.cpp

/*

Copyright (c) 2005-2015, University of Oxford.
All rights reserved.

University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
 * Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.
 * Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.
 * Neither the name of the University of Oxford nor the names of its
   contributors may be used to endorse or promote products derived from this
   software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

*/

#include "DistributedTetrahedralMesh.hpp"

#include <cassert>
#include <sstream>
#include <string>
#include <iterator>
#include <algorithm>
#include <boost/scoped_array.hpp>

#include "Exception.hpp"
#include "Element.hpp"
#include "BoundaryElement.hpp"

#include "PetscTools.hpp"
#include "DistributedVectorFactory.hpp"
#include "OutputFileHandler.hpp"
#include "NodePartitioner.hpp"

#include "RandomNumberGenerator.hpp"

#include "Timer.hpp"
#include "TetrahedralMesh.hpp"

#include "petscao.h"
#include <parmetis.h>
#if (PARMETIS_MAJOR_VERSION >= 4) //ParMETIS 4.x and above
//Redefine the index type so that we can still use the old name "idxtype"
#define idxtype idx_t
#else
//Old version of ParMETIS used "float" which may appear elsewhere in, for example, tetgen
#define real_t float
#endif

//   IMPLEMENTATION

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::DistributedTetrahedralMesh(DistributedTetrahedralMeshPartitionType::type partitioningMethod)
    :
      mTotalNumElements(0u),
      mTotalNumBoundaryElements(0u),
      mTotalNumNodes(0u),
      mpSpaceRegion(NULL),
      mMetisPartitioning(partitioningMethod)
{
    if (ELEMENT_DIM == 1 && (partitioningMethod != DistributedTetrahedralMeshPartitionType::GEOMETRIC))
    {
        //No METIS partition is possible - revert to DUMB
        mMetisPartitioning = DistributedTetrahedralMeshPartitionType::DUMB;
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::~DistributedTetrahedralMesh()
{
    for (unsigned i=0; i<this->mHaloNodes.size(); i++)
    {
        delete this->mHaloNodes[i];
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SetDistributedVectorFactory(DistributedVectorFactory* pFactory)
{
    AbstractMesh<ELEMENT_DIM,SPACE_DIM>::SetDistributedVectorFactory(pFactory);
    mMetisPartitioning = DistributedTetrahedralMeshPartitionType::DUMB;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ComputeMeshPartitioning(
    AbstractMeshReader<ELEMENT_DIM, SPACE_DIM>& rMeshReader,
    std::set<unsigned>& rNodesOwned,
    std::set<unsigned>& rHaloNodesOwned,
    std::set<unsigned>& rElementsOwned,
    std::vector<unsigned>& rProcessorsOffset)
{
    if (mMetisPartitioning==DistributedTetrahedralMeshPartitionType::PARMETIS_LIBRARY && PetscTools::IsParallel())
    {
        /*
         *  With ParMetisLibraryNodeAndElementPartitioning we compute the element partition first
         *  and then we work out the node ownership.
         */
        ParMetisLibraryNodeAndElementPartitioning(rMeshReader, rElementsOwned, rNodesOwned, rHaloNodesOwned, rProcessorsOffset);
    }
    else
    {
        /*
         *  Otherwise we compute the node partition and then we work out element distribution
         */
        if (mMetisPartitioning==DistributedTetrahedralMeshPartitionType::METIS_LIBRARY && PetscTools::IsParallel())
        {
            NodePartitioner<ELEMENT_DIM, SPACE_DIM>::MetisLibraryPartitioning(rMeshReader, this->mNodePermutation, rNodesOwned, rProcessorsOffset);
        }
        else if (mMetisPartitioning==DistributedTetrahedralMeshPartitionType::PETSC_MAT_PARTITION && PetscTools::IsParallel())
        {
            NodePartitioner<ELEMENT_DIM, SPACE_DIM>::PetscMatrixPartitioning(rMeshReader, this->mNodePermutation, rNodesOwned, rProcessorsOffset);
        }
        else if (mMetisPartitioning==DistributedTetrahedralMeshPartitionType::GEOMETRIC && PetscTools::IsParallel())
        {
            if (!mpSpaceRegion)
            {
                EXCEPTION("Using GEOMETRIC partition for DistributedTetrahedralMesh with local regions not set. Call SetProcessRegion(ChasteCuboid)");
            }
            NodePartitioner<ELEMENT_DIM, SPACE_DIM>::GeometricPartitioning(rMeshReader, this->mNodePermutation, rNodesOwned, rProcessorsOffset, mpSpaceRegion);
        }
        else
        {
            NodePartitioner<ELEMENT_DIM, SPACE_DIM>::DumbPartitioning(*this, rNodesOwned);
        }

        if ( rMeshReader.HasNclFile() )
        {
            // Form a set of all the element indices we are going to own
            // (union of the sets from the lines in the NCL file)
            for ( std::set<unsigned>::iterator iter=rNodesOwned.begin();
                  iter!=rNodesOwned.end();
                  ++iter )
            {
                std::vector<unsigned> containing_elements = rMeshReader.GetContainingElementIndices( *iter );
                rElementsOwned.insert( containing_elements.begin(), containing_elements.end() );
            }

            // Iterate through that set rather than mTotalNumElements (knowing that we own a least one node in each line)
            // Then read all the data into a node_index set
            std::set<unsigned> node_index_set;

            for ( std::set<unsigned>::iterator iter=rElementsOwned.begin();
                  iter!=rElementsOwned.end();
                  ++iter )
            {
                ElementData element_data = rMeshReader.GetElementData( *iter );
                node_index_set.insert( element_data.NodeIndices.begin(), element_data.NodeIndices.end() );
            }

            // Subtract off the rNodesOwned set to produce rHaloNodesOwned.
            // Note that rNodesOwned is a subset of node_index_set.
            std::set_difference(node_index_set.begin(), node_index_set.end(),
                                rNodesOwned.begin(), rNodesOwned.end(),
                                std::inserter(rHaloNodesOwned, rHaloNodesOwned.begin()));
        }
        else
        {
            for (unsigned element_number = 0; element_number < mTotalNumElements; element_number++)
            {
                ElementData element_data = rMeshReader.GetNextElementData();

                bool element_owned = false;
                std::set<unsigned> temp_halo_nodes;

                for (std::vector<unsigned>::const_iterator it = element_data.NodeIndices.begin();
                     it != element_data.NodeIndices.end();
                     ++it)
                {
                    if (rNodesOwned.find(*it) != rNodesOwned.end())
                    {
                        element_owned = true;
                        rElementsOwned.insert(element_number);
                    }
                    else
                    {
                        temp_halo_nodes.insert(*it);
                    }
                }

                if (element_owned)
                {
                    rHaloNodesOwned.insert(temp_halo_nodes.begin(), temp_halo_nodes.end());
                }
            }
        }

        if (mMetisPartitioning==DistributedTetrahedralMeshPartitionType::PETSC_MAT_PARTITION && PetscTools::IsParallel())
        {
            PetscTools::Barrier();
            if (PetscTools::AmMaster())
            {
                Timer::PrintAndReset("Element and halo node assignation");
            }
        }
    }
    rMeshReader.Reset();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructFromMeshReader(
    AbstractMeshReader<ELEMENT_DIM, SPACE_DIM>& rMeshReader)
{
    std::set<unsigned> nodes_owned;
    std::set<unsigned> halo_nodes_owned;
    std::set<unsigned> elements_owned;
    std::vector<unsigned> proc_offsets;//(PetscTools::GetNumProcs());

    this->mMeshFileBaseName = rMeshReader.GetMeshFileBaseName();
    mTotalNumElements = rMeshReader.GetNumElements();
    mTotalNumBoundaryElements = rMeshReader.GetNumFaces();
    mTotalNumNodes = rMeshReader.GetNumNodes();


    PetscTools::Barrier();
    Timer::Reset();
    ComputeMeshPartitioning(rMeshReader, nodes_owned, halo_nodes_owned, elements_owned, proc_offsets);
    PetscTools::Barrier();
    //Timer::Print("partitioning");

    // Reserve memory
    this->mElements.reserve(elements_owned.size());
    this->mNodes.reserve(nodes_owned.size());

    if ( rMeshReader.IsFileFormatBinary() )
    {
        std::vector<double> coords;
        // Binary : load only the nodes which are needed
        for (typename AbstractMeshReader<ELEMENT_DIM, SPACE_DIM>::NodeIterator node_it = rMeshReader.GetNodeIteratorBegin(nodes_owned);
                      node_it != rMeshReader.GetNodeIteratorEnd();
                      ++node_it)
        {
            //Loop over wholly-owned nodes
            unsigned global_node_index = node_it.GetIndex();
            coords = *node_it;
            RegisterNode(global_node_index);
            Node<SPACE_DIM>* p_node = new Node<SPACE_DIM>(global_node_index, coords, false);

//Node attributes in binary format are not yet supported, see #1730
//            for (unsigned i = 0; i < rMeshReader.GetNodeAttributes().size(); i++)
//            {
//                double attribute = rMeshReader.GetNodeAttributes()[i];
//                p_node->AddNodeAttribute(attribute);
//            }

            this->mNodes.push_back(p_node);
        }
        for (typename AbstractMeshReader<ELEMENT_DIM, SPACE_DIM>::NodeIterator node_it = rMeshReader.GetNodeIteratorBegin(halo_nodes_owned);
                      node_it != rMeshReader.GetNodeIteratorEnd();
                      ++node_it)
        {
            //Loop over halo-owned nodes
            unsigned global_node_index = node_it.GetIndex();
            coords = *node_it;
            RegisterHaloNode(global_node_index);
            mHaloNodes.push_back(new Node<SPACE_DIM>(global_node_index, coords, false));
        }
    }
    else
    {
        // Ascii : Sequentially load all the nodes and store those owned (or halo-owned) by the process
        for (unsigned node_index=0; node_index < mTotalNumNodes; node_index++)
        {
            std::vector<double> coords;
            coords = rMeshReader.GetNextNode();

            // The node is owned by the processor
            if (nodes_owned.find(node_index) != nodes_owned.end())
            {
                RegisterNode(node_index);
                Node<SPACE_DIM>* p_node =  new Node<SPACE_DIM>(node_index, coords, false);

                for (unsigned i = 0; i < rMeshReader.GetNodeAttributes().size(); i++)
                {
                    double attribute = rMeshReader.GetNodeAttributes()[i];
                    p_node->AddNodeAttribute(attribute);
                }

                this->mNodes.push_back(p_node);
            }

            // The node is a halo node in this processor
            if (halo_nodes_owned.find(node_index) != halo_nodes_owned.end())
            {
                RegisterHaloNode(node_index);
                mHaloNodes.push_back(new Node<SPACE_DIM>(node_index, coords, false));
            }
        }
    }

    for (typename AbstractMeshReader<ELEMENT_DIM, SPACE_DIM>::ElementIterator elem_it
             = rMeshReader.GetElementIteratorBegin(elements_owned);
         elem_it != rMeshReader.GetElementIteratorEnd();
         ++elem_it)
    {
        ElementData element_data = *elem_it;
        unsigned global_element_index = elem_it.GetIndex();

        std::vector<Node<SPACE_DIM>*> nodes;
        for (unsigned j=0; j<ELEMENT_DIM+1; j++)
        {
            // Because we have populated mNodes and mHaloNodes above, we can now use this method, which should never throw
            nodes.push_back(this->GetNodeOrHaloNode(element_data.NodeIndices[j]));
        }

        RegisterElement(global_element_index);
        Element<ELEMENT_DIM,SPACE_DIM>* p_element = new Element<ELEMENT_DIM,SPACE_DIM>(global_element_index, nodes);
        this->mElements.push_back(p_element);

        if (rMeshReader.GetNumElementAttributes() > 0)
        {
            assert(rMeshReader.GetNumElementAttributes() == 1);
            double attribute_value = element_data.AttributeValue;
            p_element->SetAttribute(attribute_value);
        }
    }

    // Boundary nodes and elements
    try
    {
        for (unsigned face_index=0; face_index<mTotalNumBoundaryElements; face_index++)
        {
            ElementData face_data = rMeshReader.GetNextFaceData();
            std::vector<unsigned> node_indices = face_data.NodeIndices;

            bool own = false;

            for (unsigned node_index=0; node_index<node_indices.size(); node_index++)
            {
                // if I own this node
                if (mNodesMapping.find(node_indices[node_index]) != mNodesMapping.end())
                {
                    own = true;
                    break;
                }
            }

            if (!own)
            {
                continue;
            }

            // Determine if this is a boundary face
            //std::set<unsigned> containing_element_indices; // Elements that contain this face
            std::vector<Node<SPACE_DIM>*> nodes;

            for (unsigned node_index=0; node_index<node_indices.size(); node_index++)
            {
                //because we have populated mNodes and mHaloNodes above, we can now use this method,
                //which SHOULD never throw (but it does).
                try
                {
                    nodes.push_back(this->GetNodeOrHaloNode(node_indices[node_index]));
                }
                catch (Exception &)
                {
                    EXCEPTION("Face does not appear in element file (Face " << face_index << " in "<<this->mMeshFileBaseName<< ")");
                }
            }

            // This is a boundary face
            // Ensure all its nodes are marked as boundary nodes
            for (unsigned j=0; j<nodes.size(); j++)
            {
                if (!nodes[j]->IsBoundaryNode())
                {
                    nodes[j]->SetAsBoundaryNode();
                    this->mBoundaryNodes.push_back(nodes[j]);
                }
                // Register the index that this boundary element will have with the node
                nodes[j]->AddBoundaryElement(face_index);
            }

            RegisterBoundaryElement(face_index);
            BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>* p_boundary_element = new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(face_index, nodes);
            this->mBoundaryElements.push_back(p_boundary_element);

            if (rMeshReader.GetNumFaceAttributes() > 0)
            {
                assert(rMeshReader.GetNumFaceAttributes() == 1);
                p_boundary_element->SetAttribute(face_data.AttributeValue);
            }
        }
    }
    catch (Exception &e)
    {
        PetscTools::ReplicateException(true); //Bad face exception
        throw e;
    }
    PetscTools::ReplicateException(false);

    if (mMetisPartitioning != DistributedTetrahedralMeshPartitionType::DUMB && PetscTools::IsParallel())
    {
        assert(this->mNodePermutation.size() != 0);
        // If we are partitioning (and permuting) a mesh, we need to be certain that we aren't doing it twice
        assert(rMeshReader.HasNodePermutation() == false);

        // We reorder so that each process owns a contiguous set of the indices and we can then build a distributed vector factory.
        ReorderNodes();

        unsigned num_owned;
        unsigned rank = PetscTools::GetMyRank();
        if ( !PetscTools::AmTopMost() )
        {
            num_owned =  proc_offsets[rank+1]-proc_offsets[rank];
        }
        else
        {
            num_owned = mTotalNumNodes - proc_offsets[rank];
        }

        assert(!this->mpDistributedVectorFactory);
        this->mpDistributedVectorFactory = new DistributedVectorFactory(this->GetNumNodes(), num_owned);
    }
    else
    {
        // Dumb or sequential partition
        assert(this->mpDistributedVectorFactory);

        if (rMeshReader.HasNodePermutation())
        {
            // This is probably an unarchiving operation where the original run applied a permutation to the mesh
            // We need to re-record that the permutation has happened (so that we can archive it correctly later).
            this->mNodePermutation = rMeshReader.rGetNodePermutation();
        }
    }
    rMeshReader.Reset();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumLocalNodes() const
{
    return this->mNodes.size();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumHaloNodes() const
{
    return this->mHaloNodes.size();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumLocalElements() const
{
    return this->mElements.size();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumLocalBoundaryElements() const
{
    return this->mBoundaryElements.size();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumNodes() const
{
    return mTotalNumNodes;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumAllNodes() const
{
    return mTotalNumNodes;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumElements() const
{
    return mTotalNumElements;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
DistributedTetrahedralMeshPartitionType::type DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetPartitionType() const
{
    return mMetisPartitioning;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumBoundaryElements() const
{
    return mTotalNumBoundaryElements;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetHaloNodeIndices(std::vector<unsigned>& rHaloIndices) const
{
    //Make sure the output vector is empty
    rHaloIndices.clear();
    for (unsigned i=0; i<mHaloNodes.size(); i++)
    {
        rHaloIndices.push_back(mHaloNodes[i]->GetIndex());
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
ChasteCuboid<SPACE_DIM>*  DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetProcessRegion()
{
    if (mpSpaceRegion == NULL)
    {
        EXCEPTION("Trying to get unset mpSpaceRegion");
    }
    return mpSpaceRegion;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SetElementOwnerships()
{
    // All the local elements are owned by the processor (obviously...)
    //Does nothing - unlike the non-distributed version
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SetProcessRegion(ChasteCuboid<SPACE_DIM>* pRegion)
{
    mpSpaceRegion = pRegion;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
bool DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateDesignatedOwnershipOfElement( unsigned elementIndex )
{
    try
    {
        return(AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateDesignatedOwnershipOfElement(elementIndex));
    }
    catch(Exception&)      // we don't own the element
    {
        return false;
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
bool DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateDesignatedOwnershipOfBoundaryElement( unsigned faceIndex )
{
    try
    {
        return(AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateDesignatedOwnershipOfBoundaryElement(faceIndex));
    }
    catch(Exception&)      //  we don't own the face
    {
        return false;
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::RegisterNode(unsigned index)
{
    mNodesMapping[index] = this->mNodes.size();
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::RegisterHaloNode(unsigned index)
{
    mHaloNodesMapping[index] = mHaloNodes.size();
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::RegisterElement(unsigned index)
{
    mElementsMapping[index] = this->mElements.size();
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::RegisterBoundaryElement(unsigned index)
{
    mBoundaryElementsMapping[index] = this->mBoundaryElements.size();
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SolveNodeMapping(unsigned index) const
{
    std::map<unsigned, unsigned>::const_iterator node_position = mNodesMapping.find(index);

    if (node_position == mNodesMapping.end())
    {
        EXCEPTION("Requested node " << index << " does not belong to processor " << PetscTools::GetMyRank());
    }
    return node_position->second;
}

//template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
//unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SolveHaloNodeMapping(unsigned index)
//{
//    assert(mHaloNodesMapping.find(index) != mHaloNodesMapping.end());
//    return mHaloNodesMapping[index];
//}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SolveElementMapping(unsigned index) const
{
    std::map<unsigned, unsigned>::const_iterator element_position = mElementsMapping.find(index);

    if (element_position == mElementsMapping.end())
    {
        EXCEPTION("Requested element " << index << " does not belong to processor " << PetscTools::GetMyRank());
    }

    return element_position->second;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SolveBoundaryElementMapping(unsigned index) const
{
    std::map<unsigned, unsigned>::const_iterator boundary_element_position = mBoundaryElementsMapping.find(index);

    if (boundary_element_position == mBoundaryElementsMapping.end())
    {
        EXCEPTION("Requested boundary element " << index << " does not belong to processor " << PetscTools::GetMyRank());
    }

    return boundary_element_position->second;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
Node<SPACE_DIM> * DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNodeOrHaloNode(unsigned index) const
{
    std::map<unsigned, unsigned>::const_iterator node_position;
    // First search the halo (expected to be a smaller map so quicker)
    if ((node_position=mHaloNodesMapping.find(index)) != mHaloNodesMapping.end())
    {
        return mHaloNodes[node_position->second];
    }
    // Next search the owned node
    if ((node_position=mNodesMapping.find(index)) != mNodesMapping.end())
    {
        //Found an owned node
        return this->mNodes[node_position->second];
    }
    // Not here
    EXCEPTION("Requested node/halo " << index << " does not belong to processor " << PetscTools::GetMyRank());
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ReorderNodes()
{
    assert(PetscTools::IsParallel());

    // Need to rebuild global-local maps
    mNodesMapping.clear();
    mHaloNodesMapping.clear();

    // Update indices
    for (unsigned index=0; index<this->mNodes.size(); index++)
    {
        unsigned old_index = this->mNodes[index]->GetIndex();
        unsigned new_index = this->mNodePermutation[old_index];

        this->mNodes[index]->SetIndex(new_index);
        mNodesMapping[new_index] = index;
    }

    for (unsigned index=0; index<mHaloNodes.size(); index++)
    {
        unsigned old_index = mHaloNodes[index]->GetIndex();
        unsigned new_index = this->mNodePermutation[old_index];

        mHaloNodes[index]->SetIndex(new_index);
        mHaloNodesMapping[new_index] = index;
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructLinearMesh(unsigned width)
{
    assert(ELEMENT_DIM == 1);

     //Check that there are enough nodes to make the parallelisation worthwhile
    if (width==0)
    {
        EXCEPTION("There aren't enough nodes to make parallelisation worthwhile");
    }

    // Hook to pick up when we are using a geometric partition.
    if(mMetisPartitioning == DistributedTetrahedralMeshPartitionType::GEOMETRIC)
    {
        if (!mpSpaceRegion)
        {
            EXCEPTION("Space region not set for GEOMETRIC partition of DistributedTetrahedralMesh");
        }

        // Write a serial file, the load on distributed processors.
        {
            TrianglesMeshWriter<ELEMENT_DIM,SPACE_DIM> mesh_writer("", "temp_linear_mesh");
            TetrahedralMesh<ELEMENT_DIM,SPACE_DIM> base_mesh;
            base_mesh.ConstructLinearMesh(width);
            mesh_writer.WriteFilesUsingMesh(base_mesh);
        }
        PetscTools::Barrier();

        OutputFileHandler output_handler("", false);

        std::string output_dir = output_handler.GetOutputDirectoryFullPath();
        TrianglesMeshReader<ELEMENT_DIM,SPACE_DIM> mesh_reader(output_dir+"temp_linear_mesh");

        this->ConstructFromMeshReader(mesh_reader);
    }
    else    // use a default partition.
    {
        //Use dumb partition so that archiving doesn't permute anything
        mMetisPartitioning=DistributedTetrahedralMeshPartitionType::DUMB;
        mTotalNumNodes=width+1;
        mTotalNumBoundaryElements=2u;
        mTotalNumElements=width;

        //Use DistributedVectorFactory to make a dumb partition of the nodes
        assert(!this->mpDistributedVectorFactory);
        this->mpDistributedVectorFactory = new DistributedVectorFactory(mTotalNumNodes);
        if (this->mpDistributedVectorFactory->GetLocalOwnership() == 0)
        {
            //It's a short mesh and this process owns no nodes
            return;
        }

        /* am_top_most is like PetscTools::AmTopMost() but accounts for the fact that a
         * higher numbered process may have dropped out of this construction altogether
         * (because is has no local ownership)
         */
        bool am_top_most = (this->mpDistributedVectorFactory->GetHigh() == mTotalNumNodes);

        unsigned lo_node=this->mpDistributedVectorFactory->GetLow();
        unsigned hi_node=this->mpDistributedVectorFactory->GetHigh();
        if (!PetscTools::AmMaster())
        {
            //Allow for a halo node
            lo_node--;
        }
        if (!am_top_most)
        {
            //Allow for a halo node
            hi_node++;
        }
        Node<SPACE_DIM>* p_old_node=NULL;
        for (unsigned node_index=lo_node; node_index<hi_node; node_index++)
        {
            // create node or halo-node
            Node<SPACE_DIM>* p_node = new Node<SPACE_DIM>(node_index, node_index==0 || node_index==width, node_index);
            if (node_index<this->mpDistributedVectorFactory->GetLow() ||
                node_index==this->mpDistributedVectorFactory->GetHigh() )
            {
                //Beyond left or right it's a halo node
                RegisterHaloNode(node_index);
                mHaloNodes.push_back(p_node);
            }
            else
            {
                RegisterNode(node_index);
                this->mNodes.push_back(p_node); // create node

                //A boundary face has to be wholely owned by the process
                //Since, when ELEMENT_DIM>1 we have *at least* boundary node as a non-halo
                if (node_index==0) // create left boundary node and boundary element
                {
                    this->mBoundaryNodes.push_back(p_node);
                    RegisterBoundaryElement(0);
                    this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(0, p_node) );
                }
                if (node_index==width) // create right boundary node and boundary element
                {
                    this->mBoundaryNodes.push_back(p_node);
                    RegisterBoundaryElement(1);
                    this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(1, p_node) );
                }
                }
            if (node_index>lo_node) // create element
            {
                std::vector<Node<SPACE_DIM>*> nodes;
                nodes.push_back(p_old_node);
                nodes.push_back(p_node);
                RegisterElement(node_index-1);
                this->mElements.push_back(new Element<ELEMENT_DIM,SPACE_DIM>(node_index-1, nodes) );
            }
            //Keep track of the node which we've just created
            p_old_node=p_node;
        }
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructRectangularMesh(unsigned width, unsigned height, bool stagger)
{
    assert(SPACE_DIM == 2);
    assert(ELEMENT_DIM == 2);
    //Check that there are enough nodes to make the parallelisation worthwhile
    if (height==0)
    {
        EXCEPTION("There aren't enough nodes to make parallelisation worthwhile");
    }

    // Hook to pick up when we are using a geometric partition.
    if(mMetisPartitioning == DistributedTetrahedralMeshPartitionType::GEOMETRIC)
    {
        if (!mpSpaceRegion)
        {
            EXCEPTION("Space region not set for GEOMETRIC partition of DistributedTetrahedralMesh");
        }

        // Write a serial file, the load on distributed processors.
        {
            TrianglesMeshWriter<ELEMENT_DIM,SPACE_DIM> mesh_writer("", "temp_rectangular_mesh");
            TetrahedralMesh<ELEMENT_DIM,SPACE_DIM> base_mesh;
            base_mesh.ConstructRectangularMesh(width, height);
            mesh_writer.WriteFilesUsingMesh(base_mesh);
        }
        PetscTools::Barrier();

        OutputFileHandler output_handler("", false);

        std::string output_dir = output_handler.GetOutputDirectoryFullPath();
        TrianglesMeshReader<ELEMENT_DIM,SPACE_DIM> mesh_reader(output_dir+"temp_rectangular_mesh");

        this->ConstructFromMeshReader(mesh_reader);
    }
    else
    {
        //Use dumb partition so that archiving doesn't permute anything
        mMetisPartitioning=DistributedTetrahedralMeshPartitionType::DUMB;

        mTotalNumNodes=(width+1)*(height+1);
        mTotalNumBoundaryElements=(width+height)*2;
        mTotalNumElements=width*height*2;

        //Use DistributedVectorFactory to make a dumb partition of space
        DistributedVectorFactory y_partition(height+1);
        unsigned lo_y = y_partition.GetLow();
        unsigned hi_y = y_partition.GetHigh();
        //Dumb partition of nodes has to be such that each process gets complete slices
        assert(!this->mpDistributedVectorFactory);
        this->mpDistributedVectorFactory = new DistributedVectorFactory(mTotalNumNodes, (width+1)*y_partition.GetLocalOwnership());
        if (this->mpDistributedVectorFactory->GetLocalOwnership() == 0)
        {
            //It's a short mesh and this process owns no nodes
            return;
        }
        /* am_top_most is like PetscTools::AmTopMost() but accounts for the fact that a
         * higher numbered process may have dropped out of this construction altogether
         * (because is has no local ownership)
         */
        bool am_top_most = (this->mpDistributedVectorFactory->GetHigh() == mTotalNumNodes);


        if (!PetscTools::AmMaster())
        {
            //Allow for a halo node
            lo_y--;
        }
        if (!am_top_most)
        {
            //Allow for a halo node
            hi_y++;
        }

        //Construct the nodes
        for (unsigned j=lo_y; j<hi_y; j++)
        {
            for (unsigned i=0; i<width+1; i++)
            {
                bool is_boundary=false;
                if (i==0 || j==0 || i==width || j==height)
                {
                    is_boundary=true;
                }
                unsigned global_node_index=((width+1)*(j) + i); //Verified from sequential
                Node<SPACE_DIM>* p_node = new Node<SPACE_DIM>(global_node_index, is_boundary, i, j);
                if (j<y_partition.GetLow() || j==y_partition.GetHigh() )
                {
                    //Beyond left or right it's a halo node
                    RegisterHaloNode(global_node_index);
                    mHaloNodes.push_back(p_node);
                }
                else
                {
                    RegisterNode(global_node_index);
                    this->mNodes.push_back(p_node);
                }
                if (is_boundary)
                {
                    this->mBoundaryNodes.push_back(p_node);
                }
            }
        }

        //Construct the boundary elements
        unsigned belem_index;
        //Top
        if (am_top_most)
        {
           for (unsigned i=0; i<width; i++)
           {
                std::vector<Node<SPACE_DIM>*> nodes;
                nodes.push_back(GetNodeOrHaloNode( height*(width+1)+i+1 ));
                nodes.push_back(GetNodeOrHaloNode( height*(width+1)+i ));
                belem_index=i;
                RegisterBoundaryElement(belem_index);
                this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index,nodes));
            }
        }

        //Right
        for (unsigned j=lo_y+1; j<hi_y; j++)
        {
            std::vector<Node<SPACE_DIM>*> nodes;
            nodes.push_back(GetNodeOrHaloNode( (width+1)*j-1 ));
            nodes.push_back(GetNodeOrHaloNode( (width+1)*(j+1)-1 ));
            belem_index=width+j-1;
            RegisterBoundaryElement(belem_index);
            this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index,nodes));
        }

        //Bottom
        if (PetscTools::AmMaster())
        {
            for (unsigned i=0; i<width; i++)
            {
                std::vector<Node<SPACE_DIM>*> nodes;
                nodes.push_back(GetNodeOrHaloNode( i ));
                nodes.push_back(GetNodeOrHaloNode( i+1 ));
                belem_index=width+height+i;
                RegisterBoundaryElement(belem_index);
                this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index,nodes));
            }
        }

        //Left
        for (unsigned j=lo_y; j<hi_y-1; j++)
        {
            std::vector<Node<SPACE_DIM>*> nodes;
            nodes.push_back(GetNodeOrHaloNode( (width+1)*(j+1) ));
            nodes.push_back(GetNodeOrHaloNode( (width+1)*(j) ));
            belem_index=2*width+height+j;
            RegisterBoundaryElement(belem_index);
            this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index,nodes));
        }


        //Construct the elements
        unsigned elem_index;
        for (unsigned j=lo_y; j<hi_y-1; j++)
        {
            for (unsigned i=0; i<width; i++)
            {
                unsigned parity=(i+(height-j))%2;//Note that parity is measured from the top-left (not bottom left) for historical reasons
                unsigned nw=(j+1)*(width+1)+i; //ne=nw+1
                unsigned sw=(j)*(width+1)+i;   //se=sw+1
                std::vector<Node<SPACE_DIM>*> upper_nodes;
                upper_nodes.push_back(GetNodeOrHaloNode( nw ));
                upper_nodes.push_back(GetNodeOrHaloNode( nw+1 ));
                if (stagger==false  || parity == 1)
                {
                    upper_nodes.push_back(GetNodeOrHaloNode( sw+1 ));
                }
                else
                {
                    upper_nodes.push_back(GetNodeOrHaloNode( sw ));
                }
                elem_index=2*(j*width+i);
                RegisterElement(elem_index);
                this->mElements.push_back(new Element<ELEMENT_DIM,SPACE_DIM>(elem_index,upper_nodes));
                std::vector<Node<SPACE_DIM>*> lower_nodes;
                lower_nodes.push_back(GetNodeOrHaloNode( sw+1 ));
                lower_nodes.push_back(GetNodeOrHaloNode( sw ));
                if (stagger==false  ||parity == 1)
                {
                    lower_nodes.push_back(GetNodeOrHaloNode( nw ));
                }
                else
                {
                    lower_nodes.push_back(GetNodeOrHaloNode( nw+1 ));
                }
                elem_index++;
                RegisterElement(elem_index);
                this->mElements.push_back(new Element<ELEMENT_DIM,SPACE_DIM>(elem_index,lower_nodes));
            }
        }
    }
}


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructCuboid(unsigned width,
        unsigned height,
        unsigned depth)
{
    assert(SPACE_DIM == 3);
    assert(ELEMENT_DIM == 3);
    //Check that there are enough nodes to make the parallelisation worthwhile
    if (depth==0)
    {
        EXCEPTION("There aren't enough nodes to make parallelisation worthwhile");
    }

    // Hook to pick up when we are using a geometric partition.
    if(mMetisPartitioning == DistributedTetrahedralMeshPartitionType::GEOMETRIC)
    {
        if (!mpSpaceRegion)
        {
            EXCEPTION("Space region not set for GEOMETRIC partition of DistributedTetrahedralMesh");
        }

        // Write a serial file, the load on distributed processors.
        {
            TrianglesMeshWriter<ELEMENT_DIM,SPACE_DIM> mesh_writer("", "temp_cuboid_mesh");
            TetrahedralMesh<ELEMENT_DIM,SPACE_DIM> base_mesh;
            base_mesh.ConstructCuboid(width, height, depth);
            mesh_writer.WriteFilesUsingMesh(base_mesh);
        }
        PetscTools::Barrier();

        OutputFileHandler output_handler("", false);

        std::string output_dir = output_handler.GetOutputDirectoryFullPath();
        TrianglesMeshReader<ELEMENT_DIM,SPACE_DIM> mesh_reader(output_dir+"temp_cuboid_mesh");

        this->ConstructFromMeshReader(mesh_reader);
    }
    else
    {
        //Use dumb partition so that archiving doesn't permute anything
        mMetisPartitioning=DistributedTetrahedralMeshPartitionType::DUMB;

        mTotalNumNodes=(width+1)*(height+1)*(depth+1);
        mTotalNumBoundaryElements=((width*height)+(width*depth)+(height*depth))*4;//*2 for top-bottom, *2 for tessellating each unit square
        mTotalNumElements=width*height*depth*6;

        //Use DistributedVectorFactory to make a dumb partition of space
        DistributedVectorFactory z_partition(depth+1);
        unsigned lo_z = z_partition.GetLow();
        unsigned hi_z = z_partition.GetHigh();

        //Dumb partition of nodes has to be such that each process gets complete slices
        assert(!this->mpDistributedVectorFactory);
        this->mpDistributedVectorFactory = new DistributedVectorFactory(mTotalNumNodes, (width+1)*(height+1)*z_partition.GetLocalOwnership());
        if (this->mpDistributedVectorFactory->GetLocalOwnership() == 0)
        {
            return;
        }
        /* am_top_most is like PetscTools::AmTopMost() but accounts for the fact that a
         * higher numbered process may have dropped out of this construction altogether
         * (because is has no local ownership)
         */
        bool am_top_most = (this->mpDistributedVectorFactory->GetHigh() == mTotalNumNodes);



        if (!PetscTools::AmMaster())
        {
            //Allow for a halo node
            lo_z--;
        }
        if (!am_top_most)
        {
            //Allow for a halo node
            hi_z++;
        }

        //Construct the nodes
        unsigned global_node_index;
        for (unsigned k=lo_z; k<hi_z; k++)
        {
            for (unsigned j=0; j<height+1; j++)
            {
                for (unsigned i=0; i<width+1; i++)
                {
                    bool is_boundary = false;
                    if (i==0 || j==0 || k==0 || i==width || j==height || k==depth)
                    {
                        is_boundary = true;
                    }
                    global_node_index = (k*(height+1)+j)*(width+1)+i;

                    Node<SPACE_DIM>* p_node = new Node<SPACE_DIM>(global_node_index, is_boundary, i, j, k);

                    if (k<z_partition.GetLow() || k==z_partition.GetHigh() )
                    {
                        //Beyond left or right it's a halo node
                        RegisterHaloNode(global_node_index);
                        mHaloNodes.push_back(p_node);
                    }
                    else
                    {
                        RegisterNode(global_node_index);
                        this->mNodes.push_back(p_node);
                    }

                    if (is_boundary)
                    {
                        this->mBoundaryNodes.push_back(p_node);
                    }
                }
            }
        }

        // Construct the elements

        unsigned element_nodes[6][4] = {{0, 1, 5, 7}, {0, 1, 3, 7},
                                            {0, 2, 3, 7}, {0, 2, 6, 7},
                                            {0, 4, 6, 7}, {0, 4, 5, 7}};
        std::vector<Node<SPACE_DIM>*> tetrahedra_nodes;

        for (unsigned k=lo_z; k<hi_z-1; k++)
        {
            unsigned belem_index = 0;
            if (k != 0)
            {
                // height*width squares on upper face, k layers of 2*height+2*width square aroun
                belem_index =   2*(height*width+k*2*(height+width));
            }

            for (unsigned j=0; j<height; j++)
            {
                for (unsigned i=0; i<width; i++)
                {
                    // Compute the nodes' index
                    unsigned global_node_indices[8];
                    unsigned local_node_index = 0;

                    for (unsigned z = 0; z < 2; z++)
                    {
                        for (unsigned y = 0; y < 2; y++)
                        {
                            for (unsigned x = 0; x < 2; x++)
                            {
                                global_node_indices[local_node_index] = i+x+(width+1)*(j+y+(height+1)*(k+z));

                                local_node_index++;
                            }
                        }
                    }

                    for (unsigned m = 0; m < 6; m++)
                    {
                        // Tetrahedra #m

                        tetrahedra_nodes.clear();

                        for (unsigned n = 0; n < 4; n++)
                        {
                            tetrahedra_nodes.push_back(GetNodeOrHaloNode( global_node_indices[element_nodes[m][n]] ));
                        }
                        unsigned elem_index = 6 * ((k*height+j)*width+i)+m;
                        RegisterElement(elem_index);
                        this->mElements.push_back(new Element<ELEMENT_DIM,SPACE_DIM>(elem_index, tetrahedra_nodes));
                    }

                    //Are we at a boundary?
                    std::vector<Node<SPACE_DIM>*> triangle_nodes;

                    if (i == 0) //low face at x==0
                    {
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[0] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[2] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[6] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[0] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[6] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[4] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    }
                    if (i == width-1) //high face at x=width
                    {
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[1] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[5] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[7] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[1] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[7] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[3] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    }
                    if (j == 0) //low face at y==0
                    {
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[0] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[5] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[1] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[0] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[4] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[5] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    }
                    if (j == height-1) //high face at y=height
                    {
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[2] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[3] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[7] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[2] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[7] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[6] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    }
                    if (k == 0) //low face at z==0
                    {
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[0] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[3] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[2] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[0] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[1] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[3] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    }
                    if (k == depth-1) //high face at z=depth
                    {
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[4] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[7] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[5] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                        triangle_nodes.clear();
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[4] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[6] ));
                        triangle_nodes.push_back(GetNodeOrHaloNode( global_node_indices[7] ));
                        RegisterBoundaryElement(belem_index);
                        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    }
                }//i
            }//j
        }//k
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::Scale(const double xFactor, const double yFactor, const double zFactor)
{
    //Base class scale (scales node positions)
    AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::Scale(xFactor, yFactor, zFactor);
    //Scales halos
    for (unsigned i=0; i<mHaloNodes.size(); i++)
    {
        c_vector<double, SPACE_DIM>& r_location = mHaloNodes[i]->rGetModifiableLocation();
        if (SPACE_DIM>=3)
        {
            r_location[2] *= zFactor;
        }
        if (SPACE_DIM>=2)
        {
            r_location[1] *= yFactor;
        }
        r_location[0] *= xFactor;
    }

}


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ParMetisLibraryNodeAndElementPartitioning(
        AbstractMeshReader<ELEMENT_DIM, SPACE_DIM>& rMeshReader,
        std::set<unsigned>& rElementsOwned,
        std::set<unsigned>& rNodesOwned,
        std::set<unsigned>& rHaloNodesOwned,
        std::vector<unsigned>& rProcessorsOffset)
{
    assert(PetscTools::IsParallel());
    assert(ELEMENT_DIM==2 || ELEMENT_DIM==3); // Metis works with triangles and tetras

    const unsigned num_elements = rMeshReader.GetNumElements();
    const unsigned num_procs = PetscTools::GetNumProcs();
    const unsigned local_proc_index = PetscTools::GetMyRank();

    /*
     *  Work out initial element distribution
     */
    boost::scoped_array<idxtype> element_distribution(new idxtype[num_procs+1]);
    boost::scoped_array<int> element_counts(new int[num_procs]);

    element_distribution[0] = 0;

    for (unsigned proc_index=1; proc_index<num_procs; proc_index++)
    {
        element_distribution[proc_index] = element_distribution[proc_index-1] + num_elements/num_procs;
        element_counts[proc_index-1] = element_distribution[proc_index] - element_distribution[proc_index-1];
    }

    element_distribution[num_procs] = num_elements;
    element_counts[num_procs-1] = element_distribution[num_procs] - element_distribution[num_procs-1];

    /*
     *  Create distributed mesh data structure
     */
    idxtype first_local_element = element_distribution[local_proc_index];
    idxtype last_plus_one_element = element_distribution[local_proc_index+1];
    idxtype num_local_elements = last_plus_one_element - first_local_element;

    boost::scoped_array<idxtype> eind(new idxtype[num_local_elements*(ELEMENT_DIM+1)]);
    boost::scoped_array<idxtype> eptr(new idxtype[num_local_elements+1]);

    if ( rMeshReader.IsFileFormatBinary() && first_local_element > 0)
    {
        // Advance the file pointer to the first element before the ones I own.
        rMeshReader.GetElementData(first_local_element - 1);
    }
    else
    {
        // Advance the file pointer to the first element before the ones I own.
        for (idxtype element_index = 0; element_index < first_local_element; element_index++)
        {
            rMeshReader.GetNextElementData();
        }
    }

    unsigned counter = 0;
    for (idxtype element_index = 0; element_index < num_local_elements; element_index++)
    {
        ElementData element_data;

        element_data = rMeshReader.GetNextElementData();

        eptr[element_index] = counter;
        for (unsigned i=0; i<ELEMENT_DIM+1; i++)
        {
            eind[counter++] = element_data.NodeIndices[i];
        }
    }
    eptr[num_local_elements] = counter;

    rMeshReader.Reset();

    idxtype numflag = 0; // METIS speak for C-style numbering
    /* Connectivity degree.
     * Specifically, an GRAPH EDGE is placed between any two elements if and only if they share
     * at least this many nodes.
     *
     * Manual recommends "for meshes containing only triangular, tetrahedral,
     * hexahedral, or rectangular elements, this parameter can be set to two, three, four, or two, respectively.
     */
    idxtype ncommonnodes = 3; //Linear tetrahedra
    if (ELEMENT_DIM == 2)
    {
        ncommonnodes = 2;
    }

    MPI_Comm communicator = PETSC_COMM_WORLD;

    idxtype* xadj;
    idxtype* adjncy;

    Timer::Reset();
    ParMETIS_V3_Mesh2Dual(element_distribution.get(), eptr.get(), eind.get(),
                          &numflag, &ncommonnodes, &xadj, &adjncy, &communicator);
    //Timer::Print("ParMETIS Mesh2Dual");

    // Be more memory efficient, and get rid of (maybe large) arrays as soon as they're no longer needed, rather than at end of scope
    eind.reset();
    eptr.reset();

    idxtype weight_flag = 0; // unweighted graph
    idxtype n_constraints = 1; // number of weights that each vertex has (number of balance constraints)
    idxtype n_subdomains = PetscTools::GetNumProcs();
    idxtype options[3]; // extra options
    options[0] = 0; // ignore extra options
    idxtype edgecut;
    boost::scoped_array<real_t> tpwgts(new real_t[n_subdomains]);
    real_t ubvec_value = (real_t)1.05;
    for (unsigned proc=0; proc<PetscTools::GetNumProcs(); proc++)
    {
        tpwgts[proc] = ((real_t)1.0)/n_subdomains;
    }
    boost::scoped_array<idxtype> local_partition(new idxtype[num_local_elements]);

/*
 *  In order to use ParMETIS_V3_PartGeomKway, we need to sort out how to compute the coordinates of the
 *  centers of each element efficiently.
 *
 *  In the meantime use ParMETIS_V3_PartKway.
 */
//    int n_dimensions = ELEMENT_DIM;
//    float node_coordinates[num_local_elements*SPACE_DIM];
//
//    ParMETIS_V3_PartGeomKway(element_distribution, xadj, adjncy, NULL, NULL, &weight_flag, &numflag,
//                             &n_dimensions, node_coordinates, &n_constraints, &n_subdomains, NULL, NULL,
//                             options, &edgecut, local_partition, &communicator);

    Timer::Reset();
    ParMETIS_V3_PartKway(element_distribution.get(), xadj, adjncy, NULL, NULL, &weight_flag, &numflag,
                         &n_constraints, &n_subdomains, tpwgts.get(), &ubvec_value,
                         options, &edgecut, local_partition.get(), &communicator);
    //Timer::Print("ParMETIS PartKway");
    tpwgts.reset();

    boost::scoped_array<idxtype> global_element_partition(new idxtype[num_elements]);

    //idxtype is normally int (see metis-4.0/Lib/struct.h 17-22) but is 64bit on Windows
    MPI_Datatype mpi_idxtype = MPI_LONG_LONG_INT;
    if (sizeof(idxtype) == sizeof(int))
    {
        mpi_idxtype = MPI_INT;
    }
    boost::scoped_array<int> int_element_distribution(new int[num_procs+1]);
    for (unsigned i=0; i<num_procs+1; ++i)
    {
        int_element_distribution[i] = element_distribution[i];
    }
    MPI_Allgatherv(local_partition.get(), num_local_elements, mpi_idxtype,
                   global_element_partition.get(), element_counts.get(), int_element_distribution.get(), mpi_idxtype, PETSC_COMM_WORLD);

    local_partition.reset();

    for (unsigned elem_index=0; elem_index<num_elements; elem_index++)
    {
        if ((unsigned) global_element_partition[elem_index] == local_proc_index)
        {
            rElementsOwned.insert(elem_index);
        }
    }

    rMeshReader.Reset();
    free(xadj);
    free(adjncy);

    unsigned num_nodes = rMeshReader.GetNumNodes();

    // Initialise with no nodes known
    std::vector<unsigned> global_node_partition(num_nodes, UNASSIGNED_NODE);

    assert(rProcessorsOffset.size() == 0); // Making sure the vector is empty. After calling resize() only newly created memory will be initialised to 0.
    rProcessorsOffset.resize(PetscTools::GetNumProcs(), 0);

    /*
     *  Work out node distribution based on initial element distribution returned by ParMETIS
     *
     *  In this loop we handle 4 different data structures:
     *      global_node_partition and rProcessorsOffset are global,
     *      rNodesOwned and rHaloNodesOwned are local.
     */

    /*
     * Note that at this point each process has to read the entire element file in order to compute
     * the node partition form the initial element distribution.
     *  * Previously we randomly permuted the BIN file element access order on each process so that the processes
     *    weren't reading the same file sectors at the same time
     *  * We noted that with large files (above about 0.5 GigaByte) on HECToR the random access file reader
     *    was spending all its time in fseekg.  This is presumably because each fseekg from the start of the file
     *    involves multiple levels of indirect file block pointers.
     *  * Hence the use of random element reading is only useful for the niche of moderately large meshes with
     *    process counts in the thousands.
     *  Hence BIN file element permuting is deprecated - we just read the file in order.
     *  See
     *  https://chaste.cs.ox.ac.uk/trac/browser/trunk/mesh/src/common/DistributedTetrahedralMesh.cpp?rev=19291#L1459
     */

    for (unsigned element_number = 0; element_number < mTotalNumElements; element_number++)
    {
        unsigned element_owner = global_element_partition[element_number];

        ElementData element_data;

        element_data = rMeshReader.GetNextElementData();

        for (std::vector<unsigned>::const_iterator node_it = element_data.NodeIndices.begin();
             node_it != element_data.NodeIndices.end();
             ++node_it)
        {
            /*
             * For each node in this element, check whether it hasn't been assigned to another processor yet.
             * If so, assign it to the owner of the element. Otherwise, consider it halo.
             */
            if ( global_node_partition[*node_it] == UNASSIGNED_NODE )
            {
                if (element_owner == local_proc_index)
                {
                    rNodesOwned.insert(*node_it);
                }

                global_node_partition[*node_it] = element_owner;

                // Offset is defined as the first node owned by a processor. We compute it incrementally.
                // i.e. if node_index belongs to proc 3 (of 6) we have to shift the processors 4, 5, and 6
                // offset a position.
                for (unsigned proc=element_owner+1; proc<PetscTools::GetNumProcs(); proc++)
                {
                    rProcessorsOffset[proc]++;
                }
            }
            else
            {
                if (element_owner == local_proc_index)
                {
                    //if (rNodesOwned.find(*node_it) == rNodesOwned.end())
                    if (global_node_partition[*node_it] != local_proc_index)
                    {
                        rHaloNodesOwned.insert(*node_it);
                    }
                }
            }
        }
    }


    /*
     * Refine element distribution. Add extra elements that parMETIS didn't consider initially but
     * include any node owned by the processor. This ensures that all the system matrix rows are
     * assembled locally.
     * It may be that some of these elements are in the set of owned nodes erroneously.
     * The original set of owned elements (from the k-way partition) informed a
     * node partition.  It may be that an element near the edge of this new node
     * partition may no longer be needed.
     *
     * Note that rather than clearing the set we could remove elements to the original element partition set
     * with erase(), if (!element_owned) below.
     */
    rElementsOwned.clear();
    rMeshReader.Reset();
    for (unsigned element_number = 0; element_number < mTotalNumElements; element_number++)
    {
        ElementData element_data = rMeshReader.GetNextElementData();

        bool element_owned = false;
        std::set<unsigned> temp_halo_nodes;

        for (std::vector<unsigned>::const_iterator node_it = element_data.NodeIndices.begin();
             node_it != element_data.NodeIndices.end();
             ++node_it)
        {
            if (rNodesOwned.find(*node_it) != rNodesOwned.end())
            {
                element_owned = true;
                rElementsOwned.insert(element_number);
            }
            else
            {
                temp_halo_nodes.insert(*node_it);
            }
        }

        if (element_owned)
        {
            rHaloNodesOwned.insert(temp_halo_nodes.begin(), temp_halo_nodes.end());
        }
    }

    rMeshReader.Reset();

    /*
     *  Once we know the offsets we can compute the permutation vector
     */
    std::vector<unsigned> local_index(PetscTools::GetNumProcs(), 0);

    this->mNodePermutation.resize(this->GetNumNodes());

    for (unsigned node_index=0; node_index<this->GetNumNodes(); node_index++)
    {
        unsigned partition = global_node_partition[node_index];
        assert(partition != UNASSIGNED_NODE);

        this->mNodePermutation[node_index] = rProcessorsOffset[partition] + local_index[partition];

        local_index[partition]++;
    }
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
ChasteCuboid<SPACE_DIM> DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateBoundingBox() const
{
    ChastePoint<SPACE_DIM> my_minimum_point;
    ChastePoint<SPACE_DIM> my_maximum_point;

    try
    {
        ChasteCuboid<SPACE_DIM> my_box=AbstractMesh<ELEMENT_DIM, SPACE_DIM>::CalculateBoundingBox();
        my_minimum_point=my_box.rGetLowerCorner();
        my_maximum_point=my_box.rGetUpperCorner();
    }
    catch (Exception& e)
    {
#define COVERAGE_IGNORE
        PetscTools::ReplicateException(true);
        throw e;
#undef COVERAGE_IGNORE
    }

    PetscTools::ReplicateException(false);

    c_vector<double, SPACE_DIM> global_minimum_point;
    c_vector<double, SPACE_DIM> global_maximum_point;
    MPI_Allreduce(&my_minimum_point.rGetLocation()[0], &global_minimum_point[0], SPACE_DIM, MPI_DOUBLE, MPI_MIN, PETSC_COMM_WORLD);
    MPI_Allreduce(&my_maximum_point.rGetLocation()[0], &global_maximum_point[0], SPACE_DIM, MPI_DOUBLE, MPI_MAX, PETSC_COMM_WORLD);

    ChastePoint<SPACE_DIM> min(global_minimum_point);
    ChastePoint<SPACE_DIM> max(global_maximum_point);

    return ChasteCuboid<SPACE_DIM>(min, max);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNearestNodeIndex(const ChastePoint<SPACE_DIM>& rTestPoint)
{
    // Call base method to find closest on local processor
    unsigned best_node_index = AbstractMesh<ELEMENT_DIM, SPACE_DIM>::GetNearestNodeIndex(rTestPoint);

    // Recalculate the distance to the best node (if this process has one)
    double best_node_point_distance = DBL_MAX;
    if (best_node_index != UINT_MAX)
    {
        best_node_point_distance = norm_2(this->GetNode(best_node_index)->rGetLocation() - rTestPoint.rGetLocation());
    }


    // This is a handy data structure that will work with MPI_DOUBLE_INT data type.
    // There is no MPI_DOUBLE_UNSIGNED
    struct
    {
        double distance;
        int node_index;
    } value, minval;

    value.node_index = best_node_index;
    value.distance = best_node_point_distance;

    MPI_Allreduce( &value, &minval, 1, MPI_DOUBLE_INT, MPI_MINLOC, MPI_COMM_WORLD );

    return minval.node_index;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
c_vector<double, 2> DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateMinMaxEdgeLengths()
{
    c_vector<double, 2> local_min_max =  AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateMinMaxEdgeLengths();
    c_vector<double, 2> global_min_max;

    MPI_Allreduce(&local_min_max[0], &global_min_max[0], 1, MPI_DOUBLE, MPI_MIN, PETSC_COMM_WORLD);
    MPI_Allreduce(&local_min_max[1], &global_min_max[1], 1, MPI_DOUBLE, MPI_MAX, PETSC_COMM_WORLD);

    return global_min_max;
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
typename DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::HaloNodeIterator DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetHaloNodeIteratorBegin() const
{
    return mHaloNodes.begin();
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
typename DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::HaloNodeIterator DistributedTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetHaloNodeIteratorEnd() const
{
    return mHaloNodes.end();
}

// Explicit instantiation

template class DistributedTetrahedralMesh<1,1>;
template class DistributedTetrahedralMesh<1,2>;
template class DistributedTetrahedralMesh<1,3>;
template class DistributedTetrahedralMesh<2,2>;
template class DistributedTetrahedralMesh<2,3>;
template class DistributedTetrahedralMesh<3,3>;


// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
EXPORT_TEMPLATE_CLASS_ALL_DIMS(DistributedTetrahedralMesh)