Cylindrical2dMesh.cpp

/*
 
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*/
 
#include <map>
 
/* These lines are very useful for debugging (visualize with 'showme').
#include "TrianglesMeshWriter.hpp"
TrianglesMeshWriter<2,2> mesh_writer("Cylindrical2dMeshDebug", "mesh", false);
mesh_writer.WriteFilesUsingMesh(*this);
*/
#include "Cylindrical2dMesh.hpp"
#include "Exception.hpp"
#include "VtkMeshWriter.hpp"
 
Cylindrical2dMesh::Cylindrical2dMesh(double width)
  : MutableMesh<2,2>(),
    mWidth(width),
    mHaloScalingFactor(2.0), // Default value
    mHaloOffset(1.0) // Default value
{
    assert(width > 0.0);
}
 
Cylindrical2dMesh::~Cylindrical2dMesh()
{
}
 
Cylindrical2dMesh::Cylindrical2dMesh(double width, std::vector<Node<2>* > nodes)
  : MutableMesh<2,2>(),
    mWidth(width),
    mHaloScalingFactor(2.0), // Default value
    mHaloOffset(1.0) // Default value
{
    assert(width > 0.0);
//    mMismatchedBoundaryElements = false;
    for (unsigned index=0; index<nodes.size(); index++)
    {
        Node<2>* p_temp_node = nodes[index];
        double x = p_temp_node->rGetLocation()[0];
        UNUSED_OPT(x); // Fix optimised build
        assert( 0 <= x && x < width);
        mNodes.push_back(p_temp_node);
    }
    NodeMap node_map(nodes.size());
    ReMesh(node_map);
}
 
//bool Cylindrical2dMesh::GetInstanceOfMismatchedBoundaryNodes()
//{
//    return mMismatchedBoundaryElements;
//}
 
void Cylindrical2dMesh::UpdateTopAndBottom()
{
    ChasteCuboid<2> bounding_box = CalculateBoundingBox();
    mBottom = bounding_box.rGetLowerCorner()[1];
    mTop = bounding_box.rGetUpperCorner()[1];
}
 
void Cylindrical2dMesh::CreateMirrorNodes()
{
    double half_way = 0.5*mWidth;
 
    mLeftOriginals.clear();
    mLeftImages.clear();
    mImageToLeftOriginalNodeMap.clear();
    mRightOriginals.clear();
    mRightImages.clear();
    mImageToRightOriginalNodeMap.clear();
    mLeftPeriodicBoundaryElementIndices.clear();
    mRightPeriodicBoundaryElementIndices.clear();
 
    for (AbstractMesh<2,2>::NodeIterator node_iter = GetNodeIteratorBegin();
         node_iter != GetNodeIteratorEnd();
         ++node_iter)
    {
        c_vector<double, 2> location;
        location = node_iter->rGetLocation();
        unsigned this_node_index = node_iter->GetIndex();
        double this_node_x_location = location[0];
 
        // Check the mesh currently conforms to the dimensions given
        assert(0.0 <= location[0]);
        assert(location[0] <= mWidth);
 
        // Put the nodes which are to be mirrored in the relevant vectors
        if (this_node_x_location < half_way)
        {
            mLeftOriginals.push_back(this_node_index);
        }
        else
        {
            mRightOriginals.push_back(this_node_index);
        }
    }
 
    // For each left original node, create an image node and record its new index
    for (unsigned i=0; i<mLeftOriginals.size(); i++)
    {
        c_vector<double, 2> location;
        location = mNodes[mLeftOriginals[i]]->rGetLocation();
        location[0] = location[0] + mWidth;
 
        unsigned new_node_index = MutableMesh<2,2>::AddNode(new Node<2>(0, location));
        mLeftImages.push_back(new_node_index);
        mImageToLeftOriginalNodeMap[new_node_index] = mLeftOriginals[i];
    }
 
    // For each right original node, create an image node and record its new index
    for (unsigned i=0; i<mRightOriginals.size(); i++)
    {
        c_vector<double, 2> location;
        location = mNodes[mRightOriginals[i]]->rGetLocation();
        location[0] = location[0] - mWidth;
 
        unsigned new_node_index = MutableMesh<2,2>::AddNode(new Node<2>(0, location));
        mRightImages.push_back(new_node_index);
        mImageToRightOriginalNodeMap[new_node_index] = mRightOriginals[i];
    }
 
    assert(mRightOriginals.size() == mRightImages.size());
    assert(mLeftOriginals.size() == mLeftImages.size());
    assert(mImageToLeftOriginalNodeMap.size() == mLeftOriginals.size());
    assert(mImageToRightOriginalNodeMap.size() == mRightOriginals.size());
}
 
void Cylindrical2dMesh::CreateHaloNodes()
{
    UpdateTopAndBottom();
 
    mTopHaloNodes.clear();
    mBottomHaloNodes.clear();
 
    unsigned num_halo_nodes = static_cast<unsigned>(floor(mWidth * mHaloScalingFactor));
    double halo_node_separation = mWidth / (static_cast<double>(num_halo_nodes));
    double y_top_coordinate = mTop + mHaloOffset * halo_node_separation;
    double y_bottom_coordinate = mBottom - mHaloOffset * halo_node_separation;
 
    c_vector<double, 2> location;
    for (unsigned i=0; i<num_halo_nodes; i++)
    {
       double x_coordinate = 0.5 * halo_node_separation + static_cast<double>(i) * halo_node_separation;
 
       // Inserting top halo node in mesh
       location[0] = x_coordinate;
       location[1] = y_top_coordinate;
       unsigned new_node_index = MutableMesh<2,2>::AddNode(new Node<2>(0, location));
       mTopHaloNodes.push_back(new_node_index);
 
       location[1] = y_bottom_coordinate;
       new_node_index = MutableMesh<2,2>::AddNode(new Node<2>(0, location));
       mBottomHaloNodes.push_back(new_node_index);
    }
}
 
void Cylindrical2dMesh::ReMesh(NodeMap& rMap)
{
    unsigned old_num_all_nodes = GetNumAllNodes();
 
    rMap.Resize(old_num_all_nodes);
    rMap.ResetToIdentity();
 
    // Flag the deleted nodes as deleted in the map
    for (unsigned i=0; i<old_num_all_nodes; i++)
    {
        if (mNodes[i]->IsDeleted())
        {
            rMap.SetDeleted(i);
        }
    }
 
    CreateHaloNodes();
 
    // Create mirrored nodes for the normal remesher to work with
    CreateMirrorNodes();
 
    /*
     * The mesh now has messed up boundary elements, but this
     * doesn't matter as the ReMesh() below doesn't read them in
     * and reconstructs the boundary elements.
     *
     * Call ReMesh() on the parent class. Note that the mesh now has lots
     * of extra nodes which will be deleted, hence the name 'big_map'.
     */
    NodeMap big_map(GetNumAllNodes());
    MutableMesh<2,2>::ReMesh(big_map);
 
    /*
     * If the big_map isn't the identity map, the little map ('map') needs to be
     * altered accordingly before being passed to the user. Not sure how this all
     * works, so deal with this bridge when we get to it.
     */
    assert(big_map.IsIdentityMap());
 
    // Re-index the vectors according to the big nodemap, and set up the maps.
    mImageToLeftOriginalNodeMap.clear();
    mImageToRightOriginalNodeMap.clear();
 
    assert(mLeftOriginals.size() == mLeftImages.size());
    assert(mRightOriginals.size() == mRightImages.size());
 
    for (unsigned i=0; i<mLeftOriginals.size(); i++)
    {
        mLeftOriginals[i] = big_map.GetNewIndex(mLeftOriginals[i]);
        mLeftImages[i] = big_map.GetNewIndex(mLeftImages[i]);
        mImageToLeftOriginalNodeMap[mLeftImages[i]] = mLeftOriginals[i];
    }
 
    for (unsigned i=0; i<mRightOriginals.size(); i++)
    {
        mRightOriginals[i] = big_map.GetNewIndex(mRightOriginals[i]);
        mRightImages[i] = big_map.GetNewIndex(mRightImages[i]);
        mImageToRightOriginalNodeMap[mRightImages[i]] = mRightOriginals[i];
    }
 
    for (unsigned i=0; i<mTopHaloNodes.size(); i++)
    {
        mTopHaloNodes[i] = big_map.GetNewIndex(mTopHaloNodes[i]);
        mBottomHaloNodes[i] = big_map.GetNewIndex(mBottomHaloNodes[i]);
    }
 
    /*
     * Check that elements crossing the periodic boundary have been meshed
     * in the same way at each side.
     */
    CorrectNonPeriodicMesh();
 
    /*
     * Take the double-sized mesh, with its new boundary elements, and
     * remove the relevant nodes, elements and boundary elements to leave
     * a proper periodic mesh.
     */
    ReconstructCylindricalMesh();
 
    DeleteHaloNodes();
 
    /*
     * Create a random boundary element between two nodes of the first
     * element if it is not deleted. This is a temporary measure to get
     * around re-index crashing when there are no boundary elements.
     */
    unsigned num_elements = GetNumAllElements();
    bool boundary_element_made = false;
    unsigned elem_index = 0;
 
    while (elem_index<num_elements && !boundary_element_made)
    {
        Element<2,2>* p_element = GetElement(elem_index);
        if (!p_element->IsDeleted())
        {
            boundary_element_made = true;
            std::vector<Node<2>*> nodes;
            nodes.push_back(p_element->GetNode(0));
            nodes.push_back(p_element->GetNode(1));
            BoundaryElement<1,2>* p_boundary_element = new BoundaryElement<1,2>(0, nodes);
            p_boundary_element->RegisterWithNodes();
            mBoundaryElements.push_back(p_boundary_element);
            this->mBoundaryElementWeightedDirections.push_back(zero_vector<double>(2));
            this->mBoundaryElementJacobianDeterminants.push_back(0.0);
        }
        elem_index++;
    }
 
    // Now call ReIndex() to remove the temporary nodes which are marked as deleted
    NodeMap reindex_map(GetNumAllNodes());
    ReIndex(reindex_map);
    assert(!reindex_map.IsIdentityMap());  // maybe don't need this
 
    /*
     * Go through the reindex map and use it to populate the original NodeMap
     * (the one that is returned to the user).
     */
    for (unsigned i=0; i<rMap.GetSize(); i++) // only going up to be size of map, not size of reindex_map
    {
        if (reindex_map.IsDeleted(i))
        {
            /*
             * i < num_original_nodes and node is deleted, this should correspond to
             * a node that was labelled as before the remeshing, so should have already
             * been set as deleted in the map above.
             */
            assert(rMap.IsDeleted(i));
        }
        else
        {
            rMap.SetNewIndex(i, reindex_map.GetNewIndex(i));
        }
    }
 
    // We can now clear the index vectors and maps; they are only used for remeshing
    mLeftOriginals.clear();
    mLeftImages.clear();
    mImageToLeftOriginalNodeMap.clear();
    mRightOriginals.clear();
    mRightImages.clear();
    mImageToRightOriginalNodeMap.clear();
    mLeftPeriodicBoundaryElementIndices.clear();
    mRightPeriodicBoundaryElementIndices.clear();
}
 
void Cylindrical2dMesh::ReconstructCylindricalMesh()
{
    /*
     * Figure out which elements have real nodes and image nodes in them
     * and replace image nodes with corresponding real ones.
     */
    for (MutableMesh<2,2>::ElementIterator elem_iter = GetElementIteratorBegin();
         elem_iter != GetElementIteratorEnd();
         ++elem_iter)
    {
        // Left images are on the right of the mesh
        unsigned number_of_left_image_nodes = 0;
        unsigned number_of_right_image_nodes = 0;
 
        for (unsigned i=0; i<3; i++)
        {
            unsigned this_node_index = elem_iter->GetNodeGlobalIndex(i);
 
            if (mImageToLeftOriginalNodeMap.find(this_node_index) != mImageToLeftOriginalNodeMap.end())
            {
                number_of_left_image_nodes++;
            }
            else if (mImageToRightOriginalNodeMap.find(this_node_index) != mImageToRightOriginalNodeMap.end())
            {
                number_of_right_image_nodes++;
            }
        }
 
        // Delete all the elements on the left hand side (images of right)...
        if (number_of_right_image_nodes >= 1)
        {
            elem_iter->MarkAsDeleted();
            mDeletedElementIndices.push_back(elem_iter->GetIndex());
        }
 
        // Delete only purely imaginary elements on the right (images of left nodes)
        if (number_of_left_image_nodes == 3)
        {
            elem_iter->MarkAsDeleted();
            mDeletedElementIndices.push_back(elem_iter->GetIndex());
        }
 
        /*
         * If some are images then replace them with the real nodes. There
         * can be elements with either two image nodes on the right (and one
         * real) or one image node on the right (and two real).
         */
        if (number_of_left_image_nodes == 1 || number_of_left_image_nodes == 2)
        {
            for (unsigned i=0; i<3; i++)
            {
                unsigned this_node_index = elem_iter->GetNodeGlobalIndex(i);
                std::map<unsigned, unsigned>::iterator it = mImageToLeftOriginalNodeMap.find(this_node_index);
                if (it != mImageToLeftOriginalNodeMap.end())
                {
                    elem_iter->ReplaceNode(mNodes[this_node_index], mNodes[it->second]);
                }
            }
        }
    }
 
    /*
     * Figure out which boundary elements have real nodes and image nodes in them
     * and replace image nodes with corresponding real ones.
     */
    for (unsigned elem_index = 0; elem_index<GetNumAllBoundaryElements(); elem_index++)
    {
        BoundaryElement<1,2>* p_boundary_element = GetBoundaryElement(elem_index);
        if (!p_boundary_element->IsDeleted())
        {
            unsigned number_of_image_nodes = 0;
            for (unsigned i=0; i<2; i++)
            {
                unsigned this_node_index = p_boundary_element->GetNodeGlobalIndex(i);
 
                if (mImageToLeftOriginalNodeMap.find(this_node_index) != mImageToLeftOriginalNodeMap.end())
                {
                    number_of_image_nodes++;
                }
                else if (mImageToRightOriginalNodeMap.find(this_node_index) != mImageToRightOriginalNodeMap.end())
                {
                    number_of_image_nodes++;
                }
            }
 
            if (number_of_image_nodes == 2)
            {
                p_boundary_element->MarkAsDeleted();
                mDeletedBoundaryElementIndices.push_back(p_boundary_element->GetIndex());
            }
 
            /*
             * To avoid having two copies of the boundary elements on the periodic
             * boundaries we only deal with the elements on the left image and
             * delete the ones on the right image.
             */
            if (number_of_image_nodes == 1)
            {
                for (unsigned i=0; i<2; i++)
                {
                    unsigned this_node_index = p_boundary_element->GetNodeGlobalIndex(i);
                    std::map<unsigned, unsigned>::iterator it = mImageToLeftOriginalNodeMap.find(this_node_index);
                    if (it != mImageToLeftOriginalNodeMap.end())
                    {
                        p_boundary_element->ReplaceNode(mNodes[this_node_index], mNodes[it->second]);
                    }
                    else
                    {
                        it = mImageToRightOriginalNodeMap.find(this_node_index);
                        if (it != mImageToRightOriginalNodeMap.end())
                        {
                            p_boundary_element->MarkAsDeleted();
                            mDeletedBoundaryElementIndices.push_back(p_boundary_element->GetIndex());
                        }
                    }
                }
            }
        }
    }
 
    // Delete all image nodes unless they have already gone (halo nodes)
    for (unsigned i=0; i<mLeftImages.size(); i++)
    {
        mNodes[mLeftImages[i]]->MarkAsDeleted();
        mDeletedNodeIndices.push_back(mLeftImages[i]);
    }
 
    for (unsigned i=0; i<mRightImages.size(); i++)
    {
        mNodes[mRightImages[i]]->MarkAsDeleted();
        mDeletedNodeIndices.push_back(mRightImages[i]);
    }
}
 
void Cylindrical2dMesh::DeleteHaloNodes()
{
    assert(mTopHaloNodes.size() == mBottomHaloNodes.size());
    for (unsigned i=0; i<mTopHaloNodes.size(); i++)
    {
        DeleteBoundaryNodeAt(mTopHaloNodes[i]);
        DeleteBoundaryNodeAt(mBottomHaloNodes[i]);
    }
}
 
c_vector<double, 2> Cylindrical2dMesh::GetVectorFromAtoB(const c_vector<double, 2>& rLocation1, const c_vector<double, 2>& rLocation2)
{
    assert(mWidth > 0.0);
 
    c_vector<double, 2> vector = rLocation2 - rLocation1;
    vector[0] = fmod(vector[0], mWidth);
 
    /*
     * Handle the cylindrical condition here: if the points are more
     * than halfway around the cylinder apart, measure the other way.
     */
    if (vector[0] > 0.5*mWidth)
    {
        vector[0] -= mWidth;
    }
    else if (vector[0] < -0.5*mWidth)
    {
        vector[0] += mWidth;
    }
    return vector;
}
 
void Cylindrical2dMesh::SetNode(unsigned index, ChastePoint<2> point, bool concreteMove)
{
    // Perform a periodic movement if necessary
    if (point.rGetLocation()[0] >= mWidth)
    {
        // Move point to the left
        point.SetCoordinate(0, point.rGetLocation()[0] - mWidth);
    }
    else if (point.rGetLocation()[0] < 0.0)
    {
        // Move point to the right
        point.SetCoordinate(0, point.rGetLocation()[0] + mWidth);
    }
 
    // Update the node's location
    MutableMesh<2,2>::SetNode(index, point, concreteMove);
}
 
double Cylindrical2dMesh::GetWidth(const unsigned& rDimension) const
{
    double width = 0.0;
    assert(rDimension==0 || rDimension==1);
    if (rDimension==0)
    {
        width = mWidth;
    }
    else
    {
        width = MutableMesh<2,2>::GetWidth(rDimension);
    }
    return width;
}
 
unsigned Cylindrical2dMesh::AddNode(Node<2>* pNewNode)
{
    unsigned node_index = MutableMesh<2,2>::AddNode(pNewNode);
 
    // If necessary move it to be back on the cylinder
    ChastePoint<2> new_node_point = pNewNode->GetPoint();
    SetNode(node_index, new_node_point, false);
 
    return node_index;
}
 
void Cylindrical2dMesh::CorrectNonPeriodicMesh()
{
    GenerateVectorsOfElementsStraddlingPeriodicBoundaries();
 
    /*
     * Copy the member variables into new vectors, which we modify
     * by knocking out elements which pair up on each side.
     */
    std::set<unsigned> temp_left_hand_side_elements = mLeftPeriodicBoundaryElementIndices;
    std::set<unsigned> temp_right_hand_side_elements = mRightPeriodicBoundaryElementIndices;
 
//    if ((mLeftPeriodicBoundaryElementIndices.size()!=mRightPeriodicBoundaryElementIndices.size())
//            || (temp_left_hand_side_elements.size() <= 2)
//            || (temp_right_hand_side_elements.size() <= 2) )
//    {
//        mMismatchedBoundaryElements = true;
//    }
    assert(mLeftPeriodicBoundaryElementIndices.size()==mRightPeriodicBoundaryElementIndices.size());
 
    // Go through all of the elements on the left periodic boundary
    for (std::set<unsigned>::iterator left_iter = mLeftPeriodicBoundaryElementIndices.begin();
         left_iter != mLeftPeriodicBoundaryElementIndices.end();
         ++left_iter)
    {
        unsigned elem_index = *left_iter;
 
        Element<2,2>* p_element = GetElement(elem_index);
 
        /*
         * Make lists of the nodes which the elements on the left contain and
         * the nodes which should be in a corresponding element on the right.
         */
        c_vector<unsigned,3> original_element_node_indices;
        c_vector<unsigned,3> corresponding_element_node_indices;
        for (unsigned i=0; i<3; i++)
        {
            original_element_node_indices[i] = p_element->GetNodeGlobalIndex(i);
            corresponding_element_node_indices[i] = GetCorrespondingNodeIndex(original_element_node_indices[i]);
        }
 
        // Search the right hand side elements for the corresponding element
        for (std::set<unsigned>::iterator right_iter = mRightPeriodicBoundaryElementIndices.begin();
             right_iter != mRightPeriodicBoundaryElementIndices.end();
             ++right_iter)
        {
            unsigned corresponding_elem_index = *right_iter;
 
            Element<2,2>* p_corresponding_element = GetElement(corresponding_elem_index);
 
            bool is_corresponding_node = true;
 
            for (unsigned i=0; i<3; i++)
            {
                if ((corresponding_element_node_indices[i] != p_corresponding_element->GetNodeGlobalIndex(0)) &&
                    (corresponding_element_node_indices[i] != p_corresponding_element->GetNodeGlobalIndex(1)) &&
                    (corresponding_element_node_indices[i] != p_corresponding_element->GetNodeGlobalIndex(2)) )
                {
                    is_corresponding_node = false;
                    break;
                }
            }
 
            if (is_corresponding_node)
            {
                // Remove original and corresponding element from sets
                temp_left_hand_side_elements.erase(elem_index);
                temp_right_hand_side_elements.erase(corresponding_elem_index);
            }
        }
    }
 
    /*
     * If either of these ever throw you have more than one situation where the mesher has an option
     * of how to mesh. If it does ever throw you need to be cleverer and match up the
     * elements into as many pairs as possible on the left hand and right hand sides.
     */
 //    assert(temp_left_hand_side_elements.size() <= 2);
 //    assert(temp_right_hand_side_elements.size() <= 2);
 
    /*
     * Now we just have to use the first pair of elements and copy their info over to the other side.
     * First we need to get hold of both elements on either side.
     */
    if (temp_left_hand_side_elements.empty() || temp_right_hand_side_elements.empty())
    {
        assert(temp_right_hand_side_elements.empty());
        assert(temp_left_hand_side_elements.empty());
    }
    else
    {
        if (temp_right_hand_side_elements.size() == 2 && temp_left_hand_side_elements.size() == 2)
        {
            if (temp_right_hand_side_elements.size() == 2)
            {
                // Use the right hand side meshing and map to left
                UseTheseElementsToDecideMeshing(temp_right_hand_side_elements);
            }
            else
            {
                /*
                 * If you get here there are more than two mixed up elements on the periodic edge.
                 * We need to knock the pair out and then rerun this function. This shouldn't be
                 * too hard to do but is as yet unnecessary.
                 */
                NEVER_REACHED;
            }
        }
    }
}
 
void Cylindrical2dMesh::UseTheseElementsToDecideMeshing(std::set<unsigned>& rMainSideElements)
{
    assert(rMainSideElements.size() == 2);
 
    // We find the four nodes surrounding the dodgy meshing, on each side.
    std::set<unsigned> main_four_nodes;
    for (std::set<unsigned>::iterator left_iter = rMainSideElements.begin();
         left_iter != rMainSideElements.end();
         ++left_iter)
    {
        unsigned elem_index = *left_iter;
        Element<2,2>* p_element = GetElement(elem_index);
        for (unsigned i=0; i<3; i++)
        {
            unsigned index = p_element->GetNodeGlobalIndex(i);
            main_four_nodes.insert(index);
        }
    }
    assert(main_four_nodes.size() == 4);
 
    std::set<unsigned> other_four_nodes;
    for (std::set<unsigned>::iterator iter = main_four_nodes.begin();
         iter != main_four_nodes.end();
         ++iter)
    {
        other_four_nodes.insert(GetCorrespondingNodeIndex(*iter));
    }
    assert(other_four_nodes.size() == 4);
 
    /*
     * Find the elements surrounded by the nodes on the right
     * and change them to match the elements on the left.
     */
    std::vector<unsigned> corresponding_elements;
 
    // Loop over all elements
    for (MutableMesh<2,2>::ElementIterator elem_iter = GetElementIteratorBegin();
         elem_iter != GetElementIteratorEnd();
         ++elem_iter)
    {
        // Loop over the nodes of the element
        if (!(other_four_nodes.find(elem_iter->GetNodeGlobalIndex(0))==other_four_nodes.end()) &&
            !(other_four_nodes.find(elem_iter->GetNodeGlobalIndex(1))==other_four_nodes.end()) &&
            !(other_four_nodes.find(elem_iter->GetNodeGlobalIndex(2))==other_four_nodes.end()) )
        {
            corresponding_elements.push_back(elem_iter->GetIndex());
            elem_iter->MarkAsDeleted();
            mDeletedElementIndices.push_back(elem_iter->GetIndex());
        }
    }
    assert(corresponding_elements.size() == 2);
 
    // Now corresponding_elements contains the two elements which are going to be replaced by rMainSideElements
    unsigned num_elements = GetNumAllElements();
    for (std::set<unsigned>::iterator iter = rMainSideElements.begin();
         iter != rMainSideElements.end();
         ++iter)
    {
        Element<2,2>* p_main_element = GetElement(*iter);
        std::vector<Node<2>*> nodes;
 
        // Put corresponding nodes into a std::vector
        for (unsigned i=0; i<3; i++)
        {
            unsigned main_node = p_main_element->GetNodeGlobalIndex(i);
            nodes.push_back(this->GetNode(GetCorrespondingNodeIndex(main_node)));
        }
 
        // Make a new element
        Element<2,2>* p_new_element = new Element<2,2>(num_elements, nodes);
        this->mElements.push_back(p_new_element);
        this->mElementJacobians.push_back(zero_matrix<double>(2,2));
        this->mElementInverseJacobians.push_back(zero_matrix<double>(2,2));
        this->mElementJacobianDeterminants.push_back(0.0);
        num_elements++;
    }
 
    // Reindex to get rid of extra elements indices
    NodeMap map(GetNumAllNodes());
    this->ReIndex(map);
}
 
void Cylindrical2dMesh::GenerateVectorsOfElementsStraddlingPeriodicBoundaries()
{
    mLeftPeriodicBoundaryElementIndices.clear();
    mRightPeriodicBoundaryElementIndices.clear();
 
    unsigned incidences_of_zero_left_image_nodes = 0;
    unsigned incidences_of_zero_right_image_nodes = 0;
 
    for (MutableMesh<2,2>::ElementIterator elem_iter = GetElementIteratorBegin();
         elem_iter != GetElementIteratorEnd();
         ++elem_iter)
    {
        // Left images are on the right of the mesh
        unsigned number_of_left_image_nodes = 0;
        unsigned number_of_right_image_nodes = 0;
 
        for (unsigned i=0; i<3; i++)
        {
            unsigned this_node_index = elem_iter->GetNodeGlobalIndex(i);
 
            if (mImageToLeftOriginalNodeMap.find(this_node_index) != mImageToLeftOriginalNodeMap.end())
            {
                number_of_left_image_nodes++;
            }
            else if (mImageToRightOriginalNodeMap.find(this_node_index) != mImageToRightOriginalNodeMap.end())
            {
                number_of_right_image_nodes++;
            }
        }
 
        if ((number_of_left_image_nodes == 0) && (number_of_right_image_nodes == 1 || number_of_right_image_nodes == 2) )
        {
            incidences_of_zero_left_image_nodes++;
        }
        if ((number_of_right_image_nodes == 0) && (number_of_left_image_nodes == 1 || number_of_left_image_nodes == 2) )
        {
            incidences_of_zero_right_image_nodes++;
        }
 
        /* SJ - Have checked the following:
         * - It is never the case that number_of_left_image_nodes + number_of_right_image_nodes > 3
         * - There are 1264 incidences of zero left image nodes, and 1252 incidences of zero right image nodes
         * - There are 450 incidences of zero left image nodes and non-zero right image nodes; 438 incidences of zero right image nodes and non-zero left
         *   image nodes
         * - There are 40 incidences of 0 left image nodes, and 1/2 right image nodes; 39 incidences of 0 right image nodes and 1/2 left image nodes
         * As this corresponds to 40 left-hand boundary elements and 39 right-hand boundary elements, then it is this extra occurrence of a 0 left
         * image node with 1/2 right image nodes that is responsible for the extra element.
         */
 
        // Elements on the left hand side (images of right nodes)
        if (number_of_right_image_nodes == 1 || number_of_right_image_nodes == 2)
        {
            mLeftPeriodicBoundaryElementIndices.insert(elem_iter->GetIndex());
        }
 
        // Elements on the right (images of left nodes)
        if (number_of_left_image_nodes == 1 || number_of_left_image_nodes == 2)
        {
            mRightPeriodicBoundaryElementIndices.insert(elem_iter->GetIndex());
        }
    }
 
//    if (mLeftPeriodicBoundaryElementIndices.size() != mRightPeriodicBoundaryElementIndices.size())
//    {
//        mMismatchedBoundaryElements = true;
//        // In here - if you hit this case, we want to stop the test and move on, so we work with a stopping event
//    }
 
    // Every boundary element on the left must have a corresponding element on the right
    assert(mLeftPeriodicBoundaryElementIndices.size() == mRightPeriodicBoundaryElementIndices.size());
}
 
unsigned Cylindrical2dMesh::GetCorrespondingNodeIndex(unsigned nodeIndex)
{
    unsigned corresponding_node_index = UINT_MAX;
 
    // If nodeIndex is a member of mRightOriginals, then find the corresponding node index in mRightImages
    std::vector<unsigned>::iterator right_orig_iter = std::find(mRightOriginals.begin(), mRightOriginals.end(), nodeIndex);
    if (right_orig_iter != mRightOriginals.end())
    {
        corresponding_node_index = mRightImages[right_orig_iter - mRightOriginals.begin()];
    }
    else
    {
        // If nodeIndex is a member of mRightImages, then find the corresponding node index in mRightOriginals
        std::vector<unsigned>::iterator right_im_iter = std::find(mRightImages.begin(), mRightImages.end(), nodeIndex);
        if (right_im_iter != mRightImages.end())
        {
            corresponding_node_index = mRightOriginals[right_im_iter - mRightImages.begin()];
        }
        else
        {
            // If nodeIndex is a member of mLeftOriginals, then find the corresponding node index in mLeftImages
            std::vector<unsigned>::iterator left_orig_iter = std::find(mLeftOriginals.begin(), mLeftOriginals.end(), nodeIndex);
            if (left_orig_iter != mLeftOriginals.end())
            {
                corresponding_node_index = mLeftImages[left_orig_iter - mLeftOriginals.begin()];
            }
            else
            {
                // If nodeIndex is a member of mLeftImages, then find the corresponding node index in mLeftOriginals
                std::vector<unsigned>::iterator left_im_iter = std::find(mLeftImages.begin(), mLeftImages.end(), nodeIndex);
                if (left_im_iter != mLeftImages.end())
                {
                     corresponding_node_index = mLeftOriginals[left_im_iter - mLeftImages.begin()];
                }
            }
        }
    }
 
    // We must have found the corresponding node index
    assert(corresponding_node_index != UINT_MAX);
    return corresponding_node_index;
}
 
double Cylindrical2dMesh::GetHaloScalingFactor() const
{
    return mHaloScalingFactor;
}
 
void Cylindrical2dMesh::SetHaloScalingFactor(double haloScalingFactor)
{
    assert(haloScalingFactor >= 0.0);
    mHaloScalingFactor = haloScalingFactor;
}
 
double Cylindrical2dMesh::GetHaloOffset() const
{
    return mHaloOffset;
}
 
void Cylindrical2dMesh::SetHaloOffset(double haloOffset)
{
    assert(haloOffset >= 0.0);
    mHaloOffset = haloOffset;
}
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(Cylindrical2dMesh)