AbstractTetrahedralMesh.cpp

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*/
 
#include <limits>
#include "AbstractTetrahedralMesh.hpp"
 
// Implementation
 
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::SetElementOwnerships()
{
    unsigned lo=this->GetDistributedVectorFactory()->GetLow();
    unsigned hi=this->GetDistributedVectorFactory()->GetHigh();
    for (unsigned element_index=0; element_index<mElements.size(); element_index++)
    {
        Element<ELEMENT_DIM, SPACE_DIM>* p_element = mElements[element_index];
        p_element->SetOwnership(false);
        for (unsigned local_node_index=0; local_node_index< p_element->GetNumNodes(); local_node_index++)
        {
            unsigned global_node_index = p_element->GetNodeGlobalIndex(local_node_index);
            if (lo<=global_node_index && global_node_index<hi)
            {
                p_element->SetOwnership(true);
                break;
            }
        }
    }
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::AbstractTetrahedralMesh()
    : mMeshIsLinear(true)
{
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::~AbstractTetrahedralMesh()
{
    // Iterate over elements and free the memory
    for (unsigned i=0; i<mElements.size(); i++)
    {
        delete mElements[i];
    }
    // Iterate over boundary elements and free the memory
    for (unsigned i=0; i<mBoundaryElements.size(); i++)
    {
        delete mBoundaryElements[i];
    }
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumElements() const
{
    return mElements.size();
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumLocalElements() const
{
    return GetNumElements();
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumAllElements() const
{
    return mElements.size();
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumBoundaryElements() const
{
    return mBoundaryElements.size();
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumLocalBoundaryElements() const
{
    return GetNumBoundaryElements();
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumAllBoundaryElements() const
{
    return mBoundaryElements.size();
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumCableElements() const
{
    return 0u;
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNumVertices() const
{
    return this->GetNumNodes();
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetMaximumNodeIndex()
{
    return this->GetNumAllNodes();
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
Element<ELEMENT_DIM, SPACE_DIM>* AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetElement(unsigned index) const
{
    unsigned local_index = SolveElementMapping(index);
    return mElements[local_index];
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
BoundaryElement<ELEMENT_DIM-1, SPACE_DIM>* AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetBoundaryElement(unsigned index) const
{
    unsigned local_index = SolveBoundaryElementMapping(index);
    return mBoundaryElements[local_index];
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::BoundaryElementIterator AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetBoundaryElementIteratorBegin() const
{
    return mBoundaryElements.begin();
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::BoundaryElementIterator AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetBoundaryElementIteratorEnd() const
{
    return mBoundaryElements.end();
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetInverseJacobianForElement(
        unsigned elementIndex,
        c_matrix<double, SPACE_DIM, ELEMENT_DIM>& rJacobian,
        double& rJacobianDeterminant,
        c_matrix<double, ELEMENT_DIM, SPACE_DIM>& rInverseJacobian) const
{
    mElements[SolveElementMapping(elementIndex)]->CalculateInverseJacobian(rJacobian, rJacobianDeterminant, rInverseJacobian);
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetWeightedDirectionForBoundaryElement(
        unsigned elementIndex,
        c_vector<double, SPACE_DIM>& rWeightedDirection,
        double& rJacobianDeterminant) const
{
    mBoundaryElements[SolveBoundaryElementMapping(elementIndex)]->CalculateWeightedDirection(rWeightedDirection, rJacobianDeterminant );
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CheckOutwardNormals()
{
    if (ELEMENT_DIM <= 1)
    {
        //If the ELEMENT_DIM of the mesh is 1 then the boundary will have ELEMENT_DIM = 0
        EXCEPTION("1-D mesh has no boundary normals");
    }
    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::BoundaryElementIterator face_iter = this->GetBoundaryElementIteratorBegin();
         face_iter != this->GetBoundaryElementIteratorEnd();
         ++face_iter)
    {
        //Form a set for the boundary element node indices
        std::set<unsigned> boundary_element_node_indices;
        for (unsigned i=0; i<ELEMENT_DIM; i++)
        {
            boundary_element_node_indices.insert( (*face_iter)->GetNodeGlobalIndex(i) );
        }
 
        Node<SPACE_DIM>* p_opposite_node = nullptr;
        Node<SPACE_DIM>* p_representative_node = (*face_iter)->GetNode(0);
          for (typename Node<SPACE_DIM>::ContainingElementIterator element_iter = p_representative_node->ContainingElementsBegin();
             element_iter != p_representative_node->ContainingElementsEnd();
             ++element_iter)
        {
            Element<ELEMENT_DIM, SPACE_DIM>* p_element = this->GetElement(*element_iter);
            //Form a set for the element node indices
            std::set<unsigned> element_node_indices;
            for (unsigned i=0; i<=ELEMENT_DIM; i++)
            {
                element_node_indices.insert( p_element->GetNodeGlobalIndex(i) );
            }
 
            std::vector<unsigned> difference(ELEMENT_DIM);
 
            std::vector<unsigned>::iterator set_iter = std::set_difference(
                    element_node_indices.begin(),element_node_indices.end(),
                    boundary_element_node_indices.begin(), boundary_element_node_indices.end(),
                    difference.begin());
            if (set_iter - difference.begin() == 1)
            {
                p_opposite_node = this -> GetNodeOrHaloNode(difference[0]);
                break;
            }
        }
        assert(p_opposite_node != nullptr);
 
        // Vector from centroid of face to opposite node
        c_vector<double, SPACE_DIM> into_mesh = p_opposite_node->rGetLocation() - (*face_iter)->CalculateCentroid();
        c_vector<double, SPACE_DIM> normal = (*face_iter)->CalculateNormal();
 
        if (inner_prod(into_mesh, normal) > 0.0)
        {
            EXCEPTION("Inward facing normal in boundary element index "<<(*face_iter)->GetIndex());
        }
    }
}
 
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructLinearMesh(unsigned width)
{
    assert(ELEMENT_DIM == 1);     // LCOV_EXCL_LINE
 
    for (unsigned node_index=0; node_index<=width; node_index++)
    {
        Node<SPACE_DIM>* p_node = new Node<SPACE_DIM>(node_index, node_index==0 || node_index==width, node_index);
        this->mNodes.push_back(p_node); // create node
        if (node_index==0) // create left boundary node and boundary element
        {
            this->mBoundaryNodes.push_back(p_node);
            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);
            this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(1, p_node) );
        }
        if (node_index > 0) // create element
        {
            std::vector<Node<SPACE_DIM>*> nodes;
            nodes.push_back(this->mNodes[node_index-1]);
            nodes.push_back(this->mNodes[node_index]);
            this->mElements.push_back(new Element<ELEMENT_DIM,SPACE_DIM>(node_index-1, nodes) );
        }
    }
 
    this->RefreshMesh();
}
 
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructRectangularMesh(unsigned width, unsigned height, bool stagger)
{
    assert(SPACE_DIM == 2);     // LCOV_EXCL_LINE
    assert(ELEMENT_DIM == 2);     // LCOV_EXCL_LINE
 
    //Construct the nodes
    unsigned node_index=0;
    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 || i==width || j==height)
            {
                is_boundary=true;
            }
            //Check in place for parallel
            assert(node_index==(width+1)*(j) + i);
            Node<SPACE_DIM>* p_node = new Node<SPACE_DIM>(node_index++, is_boundary, i, j);
            this->mNodes.push_back(p_node);
            if (is_boundary)
            {
                this->mBoundaryNodes.push_back(p_node);
            }
        }
    }
 
    //Construct the boundary elements
    unsigned belem_index=0;
    //Top
    for (unsigned i=0; i<width; i++)
    {
        std::vector<Node<SPACE_DIM>*> nodes;
        nodes.push_back(this->mNodes[height*(width+1)+i+1]);
        nodes.push_back(this->mNodes[height*(width+1)+i]);
        assert(belem_index==i);
        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,nodes));
    }
    //Right
    for (unsigned j=1; j<=height; j++)
    {
        std::vector<Node<SPACE_DIM>*> nodes;
        nodes.push_back(this->mNodes[(width+1)*j-1]);
        nodes.push_back(this->mNodes[(width+1)*(j+1)-1]);
        assert(belem_index==width+j-1);
        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,nodes));
    }
    //Bottom
    for (unsigned i=0; i<width; i++)
    {
        std::vector<Node<SPACE_DIM>*> nodes;
        nodes.push_back(this->mNodes[i]);
        nodes.push_back(this->mNodes[i+1]);
        assert(belem_index==width+height+i);
        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,nodes));
    }
    //Left
    for (unsigned j=0; j<height; j++)
    {
        std::vector<Node<SPACE_DIM>*> nodes;
        nodes.push_back(this->mNodes[(width+1)*(j+1)]);
        nodes.push_back(this->mNodes[(width+1)*(j)]);
        assert(belem_index==2*width+height+j);
        this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,nodes));
    }
 
    //Construct the elements
    unsigned elem_index = 0;
    for (unsigned j=0; j<height; 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(this->mNodes[nw]);
            upper_nodes.push_back(this->mNodes[nw+1]);
            if (stagger==false  || parity == 1)
            {
                upper_nodes.push_back(this->mNodes[sw+1]);
            }
            else
            {
                upper_nodes.push_back(this->mNodes[sw]);
            }
            assert(elem_index==2*(j*width+i));
            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(this->mNodes[sw+1]);
            lower_nodes.push_back(this->mNodes[sw]);
            if (stagger==false  ||parity == 1)
            {
                lower_nodes.push_back(this->mNodes[nw]);
            }
            else
            {
                lower_nodes.push_back(this->mNodes[nw+1]);
            }
            this->mElements.push_back(new Element<ELEMENT_DIM,SPACE_DIM>(elem_index++,lower_nodes));
        }
    }
 
    this->RefreshMesh();
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructCuboid(unsigned width,
        unsigned height,
        unsigned depth)
{
    assert(SPACE_DIM == 3);     // LCOV_EXCL_LINE
    assert(ELEMENT_DIM == 3);     // LCOV_EXCL_LINE
    //Construct the nodes
 
    unsigned node_index = 0;
    for (unsigned k=0; k<depth+1; 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;
                }
                assert(node_index == (k*(height+1)+j)*(width+1)+i);
                Node<SPACE_DIM>* p_node = new Node<SPACE_DIM>(node_index++, is_boundary, i, j, k);
 
                this->mNodes.push_back(p_node);
                if (is_boundary)
                {
                    this->mBoundaryNodes.push_back(p_node);
                }
            }
        }
    }
 
    // Construct the elements
 
    unsigned elem_index = 0;
    unsigned belem_index = 0;
    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}};
/* Alternative tessellation - (gerardus)
 * Note that our method (above) has a bias that all tetrahedra share a
 * common edge (the diagonal 0 - 7).  In the following method the cube is
 * split along the "face diagonal" 1-2-5-6 into two prisms.  This also has a bias.
 *
    unsigned element_nodes[6][4] = {{ 0, 6, 5, 4},
                                    { 0, 2, 6, 1},
                                    { 0, 1, 6, 5},
                                    { 1, 2, 3, 7},
                                    { 1, 2, 6, 7},
                                    { 1, 6, 7, 5 }};
*/
    std::vector<Node<SPACE_DIM>*> tetrahedra_nodes;
 
    for (unsigned k=0; k<depth; k++)
    {
        if (k!=0)
        {
            // height*width squares on upper face, k layers of 2*height+2*width square aroun
            assert(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(this->mNodes[global_node_indices[element_nodes[m][n]]]);
                    }
 
                    assert(elem_index == 6 * ((k*height+j)*width+i)+m );
                    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(this->mNodes[global_node_indices[0]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[2]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[6]]);
                    this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    triangle_nodes.clear();
                    triangle_nodes.push_back(this->mNodes[global_node_indices[0]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[6]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[4]]);
                    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(this->mNodes[global_node_indices[1]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[5]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[7]]);
                    this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    triangle_nodes.clear();
                    triangle_nodes.push_back(this->mNodes[global_node_indices[1]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[7]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[3]]);
                    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(this->mNodes[global_node_indices[0]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[5]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[1]]);
                    this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    triangle_nodes.clear();
                    triangle_nodes.push_back(this->mNodes[global_node_indices[0]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[4]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[5]]);
                    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(this->mNodes[global_node_indices[2]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[3]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[7]]);
                    this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    triangle_nodes.clear();
                    triangle_nodes.push_back(this->mNodes[global_node_indices[2]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[7]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[6]]);
                    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(this->mNodes[global_node_indices[0]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[3]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[2]]);
                    this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    triangle_nodes.clear();
                    triangle_nodes.push_back(this->mNodes[global_node_indices[0]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[1]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[3]]);
                    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(this->mNodes[global_node_indices[4]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[7]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[5]]);
                    this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                    triangle_nodes.clear();
                    triangle_nodes.push_back(this->mNodes[global_node_indices[4]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[6]]);
                    triangle_nodes.push_back(this->mNodes[global_node_indices[7]]);
                    this->mBoundaryElements.push_back(new BoundaryElement<ELEMENT_DIM-1,SPACE_DIM>(belem_index++,triangle_nodes));
                }
            }//i
        }//j
    }//k
 
    this->RefreshMesh();
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructRegularSlabMesh(double spaceStep, double width, double height, double depth)
{
    assert(spaceStep>0.0);
    assert(width>0.0);
    if (ELEMENT_DIM > 1)
    {
        assert(height>0.0);
    }
    if (ELEMENT_DIM > 2)
    {
        assert(depth>0.0);
    }
    unsigned num_elem_x=(unsigned)((width+0.5*spaceStep)/spaceStep); //0.5*spaceStep is to ensure that rounding down snaps to correct number
    unsigned num_elem_y=(unsigned)((height+0.5*spaceStep)/spaceStep);
    unsigned num_elem_z=(unsigned)((depth+0.5*spaceStep)/spaceStep);
 
    //Make it obvious that actual_width_x etc. are temporaries used in spotting for exception
    {
        double actual_width_x=num_elem_x*spaceStep;
        double actual_width_y=num_elem_y*spaceStep;
        double actual_width_z=num_elem_z*spaceStep;
 
        //Note here that in ELEMENT_DIM > 1 cases there may be a zero height or depth - in which case we don't need to use relative comparisons
        // Doing relative comparisons with zero is okay - if we avoid division by zero.
        // However, it's best not to test whether " fabs( 0.0 - 0.0) > DBL_EPSILON*0.0 "
        if (fabs (actual_width_x - width) > DBL_EPSILON*width
            ||( height!= 0.0 &&  fabs (actual_width_y - height) > DBL_EPSILON*height)
            ||( depth != 0.0 &&  fabs (actual_width_z - depth) > DBL_EPSILON*depth ))
        {
            EXCEPTION("Space step does not divide the size of the mesh");
        }
    }
    switch (ELEMENT_DIM)
    {
        case 1:
            this->ConstructLinearMesh(num_elem_x);
            break;
        case 2:
            this->ConstructRectangularMesh(num_elem_x, num_elem_y); // Stagger=default value
            break;
        default:
        case 3:
            this->ConstructCuboid(num_elem_x, num_elem_y, num_elem_z);
    }
    this->Scale(spaceStep, spaceStep, spaceStep);
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructRegularSlabMeshWithDimensionSplit(
        unsigned dimension, double spaceStep,
        double width, double height, double depth)
{
    assert(ELEMENT_DIM == SPACE_DIM);     // LCOV_EXCL_LINE
    if (dimension >= SPACE_DIM)
    {
        EXCEPTION("Cannot split on non-existent dimension");
    }
    // Rotate the width -> height -> depth around (if dimension is non-default)
    if (SPACE_DIM == 2 && dimension == 0)
    {
        double temp = height ;
        height = width;
        width = temp;
    }
    else if (SPACE_DIM == 3)
    {
        unsigned rotate_perm = SPACE_DIM - 1u - dimension; // How many shuffles to get the user's axis to the top
        for (unsigned i=0; i<rotate_perm; i++)
        {
            double temp = depth;
            depth = height;
            height = width;
            width = temp;
        }
    }
    this->ConstructRegularSlabMesh(spaceStep, width, height, depth);
    if (SPACE_DIM == 2 && dimension == 0)
    {
        // Rotate the positions back again x -> y -> x
        // this->Rotate(M_PI_2);
        c_matrix<double, 2, 2> axis_rotation = zero_matrix<double>(2, 2);
        axis_rotation(0,1)=1.0;
        axis_rotation(1,0)=-1.0;
        this->Rotate(axis_rotation);
        this->Translate(0.0, width); // Formerly known as height, but we rotated it
    }
    else if (SPACE_DIM == 3 && dimension == 0)
    {
        //        this->RotateZ(M_PI_2);
        //        this->RotateY(M_PI_2);
        // RotY * RotZ = [0 0 1; 1 0 0; 0 1 0] x->y->z->x
        //this->Translate(depth /*old width*/, width /*old height*/, 0.0);
        c_matrix<double, 3, 3> axis_permutation = zero_matrix<double>(3, 3);
        axis_permutation(0, 2)=1.0;
        axis_permutation(1, 0)=1.0;
        axis_permutation(2, 1)=1.0;
        this->Rotate(axis_permutation);
    }
    else if (SPACE_DIM == 3 && dimension == 1)
    {
        //        this->RotateY(-M_PI_2);
        //        this->RotateZ(-M_PI_2);
        //        // RotZ' after RotY' = RotZ' * RotY' = [0 1 0; 0 0 1; 1 0 0] x->z->y->x
        //        this->Translate(height /*old width*/, 0.0, width /*old depth*/);
        c_matrix<double, 3, 3> axis_permutation = zero_matrix<double>(3, 3);
        axis_permutation(0, 1)=1.0;
        axis_permutation(1, 2)=1.0;
        axis_permutation(2, 0)=1.0;
        this->Rotate(axis_permutation);
    }
 
}
 
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
bool AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateDesignatedOwnershipOfBoundaryElement( unsigned faceIndex )
{
    // This may throw in the distributed parallel case
    unsigned tie_break_index = this->GetBoundaryElement(faceIndex)->GetNodeGlobalIndex(0);
 
    // if it is in my range
    if (this->GetDistributedVectorFactory()->IsGlobalIndexLocal(tie_break_index))
    {
        return true;
    }
    else
    {
        return false;
    }
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
bool AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateDesignatedOwnershipOfElement( unsigned elementIndex )
{
    // This may throw in the distributed parallel case
    unsigned tie_break_index = this->GetElement(elementIndex)->GetNodeGlobalIndex(0);
 
    // if it is in my range
    if (this->GetDistributedVectorFactory()->IsGlobalIndexLocal(tie_break_index))
    {
        return true;
    }
    else
    {
        return false;
    }
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateMaximumNodeConnectivityPerProcess() const
{
 
    if (this->mNodes.size() == 0u)
    {
// LCOV_EXCL_START
        /*
         * Coverage of this block requires a mesh regular slab mesh with the number of
         * elements in the primary dimension less than (num_procs - 1), e.g. a 1D mesh
         * one element wide with num_procs >=3.
         * Note that if a process owns no nodes, then it will still need to enter the
         * collective call to MatMPIAIJSetPreallocation. In PetscTools::SetupMat, the
         * rowPreallocation parameter uses the special value zero to indicate no preallocation.
         */
 
        // This process owns no nodes and thus owns none of the mesh
        return (1u);
// LCOV_EXCL_STOP
    }
 
    unsigned nodes_per_element = this->mElements[0]->GetNumNodes(); //Usually ELEMENT_DIM+1, except in Quadratic case
    if (ELEMENT_DIM <= 2u)
    {
        /*
         *  Note that we start assuming that each internal node is connected to 1 element.
         *  This is to avoid the trivial situation in which there are no internal nodes (a
         *  single line or a single triangle.  We need the minimum connectivity to be 2 (in 1D) or
         *  3 (in 2D) even if there is only one element.
         */
        unsigned max_num = 1u; // See note above.
        unsigned boundary_max_num = 0u;
        for (unsigned local_node_index=0; local_node_index<this->mNodes.size(); local_node_index++)
        {
            unsigned num = this->mNodes[local_node_index]->GetNumContainingElements();
            if (this->mNodes[local_node_index]->IsBoundaryNode()==false && num>max_num)
            {
                max_num = num;
            }
            if (this->mNodes[local_node_index]->IsBoundaryNode() && num>boundary_max_num)
            {
                boundary_max_num = num;
            }
        }
        bool linear = (nodes_per_element == ELEMENT_DIM + 1);
        /*
         * In 1d each containing element is connected to one node (or 2 if quadratic), add to this the node itself
         * and the connectivity is GetNumContainingElements() + 1 or 2*GetNumContainingElements() + 1
         */
        if (ELEMENT_DIM == 1)
        {
            if (linear)
            {
                return max_num+1;
            }
            else
            {
                return 2*max_num+1;
            }
        }
        // Not returned ...else if  (ELEMENT_DIM == 2)
        /*
         * In 2d each containing element adds one connected node (since one node will be shared by a previous element)
         * this leads to a connectivity of GetNumContainingElements() + 1 (or 3*GetNumContainingElements() + 1) in the quadratic case
         *
         * If the node is on a boundary then the one elements will have an unpaired node and the connectivity is
         * GetNumContainingElements() + 1 (or 3*(GetNumContainingElements() + 3 for quadratic)
         */
        if (linear)
        {
            return std::max(max_num+1, boundary_max_num+2);
        }
        else
        {
            return std::max(3*max_num+1, 3*boundary_max_num+3);
        }
    }
 
    /*
     * In 3d there are many more cases.  In general a non-boundary node has fewer connecting nodes than it has elements.
     * A node on the boundary may have even fewer, unless it is on a corner and has more faces than it has elements.
     * We can, in the linear case estimate an upper bound as max(elements, faces)+2.
     * However for the sake of accuracy we are going for a brute force solution.
     *
     * This may prove to be a bottle-neck...
     */
 
    std::set<unsigned> forward_star_nodes; // Used to collect each node's neighbours
    unsigned max_connectivity = 0u;
    for (unsigned local_node_index=0; local_node_index<this->mNodes.size(); local_node_index++)
    {
        forward_star_nodes.clear();
 
        for (typename Node<SPACE_DIM>::ContainingElementIterator it = this->mNodes[local_node_index]->ContainingElementsBegin();
                it != this->mNodes[local_node_index]->ContainingElementsEnd();
                ++it)
        {
            Element<ELEMENT_DIM, SPACE_DIM>* p_elem = this->GetElement(*it);
            for (unsigned i=0; i<nodes_per_element; i++)
            {
                forward_star_nodes.insert(p_elem->GetNodeGlobalIndex(i));
            }
        }
        if (forward_star_nodes.size() > max_connectivity)
        {
            max_connectivity = forward_star_nodes.size();
        }
    }
    return max_connectivity;
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetHaloNodeIndices(std::vector<unsigned>& rHaloIndices) const
{
    // Make sure the output vector is empty
    rHaloIndices.clear();
}
 
template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ConstructFromMesh(AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>& rOtherMesh)
{
    for (unsigned i=0; i<rOtherMesh.GetNumNodes(); i++)
    {
        Node<SPACE_DIM>* p_node =  rOtherMesh.GetNode(i);
        assert(!p_node->IsDeleted());
        const c_vector<double, SPACE_DIM>& location=p_node->rGetLocation();
        bool is_boundary=p_node->IsBoundaryNode();
 
        Node<SPACE_DIM>* p_node_copy = new Node<SPACE_DIM>(i, location, is_boundary);
        this->mNodes.push_back( p_node_copy );
        if (is_boundary)
        {
            this->mBoundaryNodes.push_back( p_node_copy );
        }
    }
 
    for (unsigned i=0; i<rOtherMesh.GetNumElements(); i++)
    {
        Element<ELEMENT_DIM, SPACE_DIM>* p_elem = rOtherMesh.GetElement(i);
        assert(!p_elem->IsDeleted());
        std::vector<Node<SPACE_DIM>*> nodes_for_element;
        for (unsigned j=0; j<p_elem->GetNumNodes(); j++)
        {
            nodes_for_element.push_back(this->mNodes[ p_elem->GetNodeGlobalIndex(j) ]);
        }
        Element<ELEMENT_DIM, SPACE_DIM>* p_elem_copy = new Element<ELEMENT_DIM, SPACE_DIM>(i, nodes_for_element);
        p_elem_copy->RegisterWithNodes();
        this->mElements.push_back(p_elem_copy);
    }
 
    for (unsigned i=0; i<rOtherMesh.GetNumBoundaryElements(); i++)
    {
        BoundaryElement<ELEMENT_DIM-1, SPACE_DIM>* p_b_elem =  rOtherMesh.GetBoundaryElement(i);
        assert(!p_b_elem->IsDeleted());
        std::vector<Node<SPACE_DIM>*> nodes_for_element;
        for (unsigned j=0; j<p_b_elem->GetNumNodes(); j++)
        {
            nodes_for_element.push_back(this->mNodes[ p_b_elem->GetNodeGlobalIndex(j) ]);
        }
        BoundaryElement<ELEMENT_DIM-1, SPACE_DIM>* p_b_elem_copy = new BoundaryElement<ELEMENT_DIM-1, SPACE_DIM>(i, nodes_for_element);
        p_b_elem_copy->RegisterWithNodes();
        this->mBoundaryElements.push_back(p_b_elem_copy);
    }
    this->RefreshMesh();
 
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateNodeExchange(
                                     std::vector<std::vector<unsigned> >& rNodesToSendPerProcess,
                                     std::vector<std::vector<unsigned> >& rNodesToReceivePerProcess)
{
    assert( rNodesToSendPerProcess.empty() );
    assert( rNodesToReceivePerProcess.empty() );
 
    //Initialise vectors of sets for the exchange data
    std::vector<std::set<unsigned> > node_sets_to_send_per_process;
    std::vector<std::set<unsigned> > node_sets_to_receive_per_process;
 
    node_sets_to_send_per_process.resize(PetscTools::GetNumProcs());
    node_sets_to_receive_per_process.resize(PetscTools::GetNumProcs());
    std::vector<unsigned> global_lows = this->GetDistributedVectorFactory()->rGetGlobalLows();
 
    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = this->GetElementIteratorBegin();
         iter != this->GetElementIteratorEnd();
         ++iter)
    {
        std::vector <unsigned> nodes_on_this_process;
        std::vector <unsigned> nodes_not_on_this_process;
        //Calculate local and non-local node indices
        for (unsigned i=0; i<ELEMENT_DIM+1; i++)
        {
            unsigned node_index=iter->GetNodeGlobalIndex(i);
            if (this->GetDistributedVectorFactory()->IsGlobalIndexLocal(node_index))
            {
                nodes_on_this_process.push_back(node_index);
            }
            else
            {
                nodes_not_on_this_process.push_back(node_index);
            }
        }
        /*
         * If this is a TetrahedralMesh (not distributed) then it's possible that we own none
         * of the nodes in this element.  In that case we must skip the element.
         */
        if (nodes_on_this_process.empty())
        {
            continue; //Move on to the next element.
        }
        // If there are any non-local nodes on this element then we need to add to the data exchange
        if (!nodes_not_on_this_process.empty())
        {
            for (unsigned i=0; i<nodes_not_on_this_process.size(); i++)
            {
                // Calculate who owns this remote node
                unsigned remote_process=global_lows.size()-1;
                for (; global_lows[remote_process] > nodes_not_on_this_process[i]; remote_process--)
                {
                }
 
                // Add this node to the correct receive set
                node_sets_to_receive_per_process[remote_process].insert(nodes_not_on_this_process[i]);
 
                // Add all local nodes to the send set
                for (unsigned j=0; j<nodes_on_this_process.size(); j++)
                {
                    node_sets_to_send_per_process[remote_process].insert(nodes_on_this_process[j]);
                }
            }
        }
    }
 
    for (unsigned process_number = 0; process_number < PetscTools::GetNumProcs(); process_number++)
    {
        std::vector<unsigned> process_send_vector( node_sets_to_send_per_process[process_number].begin(),
                                                   node_sets_to_send_per_process[process_number].end()    );
        std::sort(process_send_vector.begin(), process_send_vector.end());
 
        rNodesToSendPerProcess.push_back(process_send_vector);
 
        std::vector<unsigned> process_receive_vector( node_sets_to_receive_per_process[process_number].begin(),
                                                      node_sets_to_receive_per_process[process_number].end()    );
        std::sort(process_receive_vector.begin(), process_receive_vector.end());
 
        rNodesToReceivePerProcess.push_back(process_receive_vector);
    }
 
}
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
c_vector<double, 2> AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::CalculateMinMaxEdgeLengths()
{
    c_vector<double, 2> min_max;
    min_max[0] = DBL_MAX;
    min_max[1] = 0.0;
    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator ele_iter = GetElementIteratorBegin();
            ele_iter != GetElementIteratorEnd();
            ++ele_iter)
    {
        c_vector<double, 2> ele_min_max = ele_iter->CalculateMinMaxEdgeLengths();
        if (ele_min_max[0] < min_max[0])
        {
            min_max[0] = ele_min_max[0];
        }
        if (ele_min_max[1] > min_max[1])
        {
            min_max[1] = ele_min_max[1];
        }
    }
    return min_max;
}
 
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetContainingElementIndex(const ChastePoint<SPACE_DIM>& rTestPoint,
                                                                            bool strict,
                                                                            std::set<unsigned> testElements,
                                                                            bool onlyTryWithTestElements)
{
    for (std::set<unsigned>::iterator iter=testElements.begin(); iter!=testElements.end(); iter++)
    {
        assert(*iter<this->GetNumElements());
        if (this->mElements[*iter]->IncludesPoint(rTestPoint, strict))
        {
            assert(!this->mElements[*iter]->IsDeleted());
            return *iter;
        }
    }
 
    if (!onlyTryWithTestElements)
    {
        for (unsigned i=0; i<this->mElements.size(); i++)
        {
            if (this->mElements[i]->IncludesPoint(rTestPoint, strict))
            {
                assert(!this->mElements[i]->IsDeleted());
                return i;
            }
        }
    }
 
    // If it's in none of the elements, then throw
    std::stringstream ss;
    ss << "Point [";
    for (unsigned j=0; (int)j<(int)SPACE_DIM-1; j++)
    {
        ss << rTestPoint[j] << ",";
    }
    ss << rTestPoint[SPACE_DIM-1] << "] is not in ";
    if (!onlyTryWithTestElements)
    {
        ss << "mesh - all elements tested";
    }
    else
    {
        ss << "set of elements given";
    }
    EXCEPTION(ss.str());
}
 
template <unsigned ELEMENT_DIM, unsigned SPACE_DIM>
unsigned AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::GetNearestElementIndexFromTestElements(const ChastePoint<SPACE_DIM>& rTestPoint,
                                                                                                 std::set<unsigned> testElements)
{
    assert(testElements.size() > 0);
    EXCEPT_IF_NOT(ELEMENT_DIM == SPACE_DIM); // LCOV_EXCL_LINE // CalculateInterpolationWeights hits an assertion otherwise
 
    double max_min_weight = -std::numeric_limits<double>::infinity();
    unsigned closest_index = 0;
    for (std::set<unsigned>::iterator iter = testElements.begin();
        iter != testElements.end();
        iter++)
    {
        c_vector<double, ELEMENT_DIM+1> weight = this->mElements[*iter]->CalculateInterpolationWeights(rTestPoint);
        double neg_weight_sum = 0.0;
        for (unsigned j=0; j<=ELEMENT_DIM; j++)
        {
            if (weight[j] < 0.0)
            {
                neg_weight_sum += weight[j];
            }
        }
        if (neg_weight_sum > max_min_weight)
        {
            max_min_weight = neg_weight_sum;
            closest_index = *iter;
        }
    }
    assert(!this->mElements[closest_index]->IsDeleted());
    return closest_index;
}
 
// Explicit instantiation
template class AbstractTetrahedralMesh<1,1>;
template class AbstractTetrahedralMesh<1,2>;
template class AbstractTetrahedralMesh<1,3>;
template class AbstractTetrahedralMesh<2,2>;
template class AbstractTetrahedralMesh<2,3>;
template class AbstractTetrahedralMesh<3,3>;