FineCoarseMeshPair.cpp

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*/
 
#include "FineCoarseMeshPair.hpp"
 
template<unsigned DIM>
FineCoarseMeshPair<DIM>::FineCoarseMeshPair(AbstractTetrahedralMesh<DIM,DIM>& rFineMesh, AbstractTetrahedralMesh<DIM,DIM>& rCoarseMesh)
    : mrFineMesh(rFineMesh),
      mrCoarseMesh(rCoarseMesh),
      mpFineMeshBoxCollection(nullptr),
      mpCoarseMeshBoxCollection(nullptr)
{
    ResetStatisticsVariables();
}
 
template<unsigned DIM>
const AbstractTetrahedralMesh<DIM,DIM>& FineCoarseMeshPair<DIM>::GetFineMesh() const
{
    return  mrFineMesh;
}
 
template<unsigned DIM>
const AbstractTetrahedralMesh<DIM,DIM>& FineCoarseMeshPair<DIM>::GetCoarseMesh() const
{
    return  mrCoarseMesh;
}
 
template<unsigned DIM>
FineCoarseMeshPair<DIM>::~FineCoarseMeshPair()
{
    DeleteFineBoxCollection();
    DeleteCoarseBoxCollection();
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::DeleteFineBoxCollection()
{
    if (mpFineMeshBoxCollection != nullptr)
    {
        delete mpFineMeshBoxCollection;
        mpFineMeshBoxCollection = nullptr;
    }
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::DeleteCoarseBoxCollection()
{
    if (mpCoarseMeshBoxCollection != nullptr)
    {
        delete mpCoarseMeshBoxCollection;
        mpCoarseMeshBoxCollection = nullptr;
    }
}
 
//   Setting up boxes methods
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::SetUpBoxesOnFineMesh(double boxWidth)
{
    SetUpBoxes(mrFineMesh, boxWidth, mpFineMeshBoxCollection);
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::SetUpBoxesOnCoarseMesh(double boxWidth)
{
    SetUpBoxes(mrCoarseMesh, boxWidth, mpCoarseMeshBoxCollection);
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::SetUpBoxes(AbstractTetrahedralMesh<DIM, DIM>& rMesh,
                                         double boxWidth,
                                         DistributedBoxCollection<DIM>*& rpBoxCollection)
{
    if (rpBoxCollection)
    {
        delete rpBoxCollection;
        rpBoxCollection = nullptr;
    }
 
    // Compute min and max values for the fine mesh nodes
    ChasteCuboid<DIM> bounding_box = rMesh.CalculateBoundingBox();
 
    // Set up the boxes using a domain that is slightly larger than the fine mesh
    c_vector<double,2*DIM> extended_min_and_max;
    for (unsigned i=0; i<DIM; i++)
    {
        double width = bounding_box.GetWidth(i);
 
        // Subtract from the minima
        extended_min_and_max(2*i) = bounding_box.rGetLowerCorner()[i] - 0.05*width;
 
        // Add to the maxima
        extended_min_and_max(2*i+1) = bounding_box.rGetUpperCorner()[i] + 0.05*width;
    }
 
    if (boxWidth < 0)
    {
        /*
         * Use default value = max(max_edge_length, w20),  where w20 is the width
         * corresponding to 20 boxes in the x-direction.
         *
         * BoxCollection creates an extra box so divide by 19 not 20. Add a little
         * bit on to ensure minor numerical fluctuations don't change the answer.
         */
        boxWidth = (extended_min_and_max(1) - extended_min_and_max(0))/19.000000001;
 
        // Determine the maximum edge length
        c_vector<double, 2> min_max_edge_length = rMesh.CalculateMinMaxEdgeLengths();
 
        if (boxWidth < min_max_edge_length[1])
        {
            boxWidth = 1.1*min_max_edge_length[1];
        }
    }
 
    rpBoxCollection = new DistributedBoxCollection<DIM>(boxWidth, extended_min_and_max);
    rpBoxCollection->SetupAllLocalBoxes();
 
    // For each element, if ANY of its nodes are physically in a box, put that element in that box
    for (unsigned i=0; i<rMesh.GetNumElements(); i++)
    {
        Element<DIM,DIM>* p_element = rMesh.GetElement(i);
 
        std::set<unsigned> box_indices_each_node_this_elem;
        for (unsigned j=0; j<DIM+1; j++) // num vertices per element
        {
            Node<DIM>* p_node = p_element->GetNode(j);
            // Only take note of box inclusions which are in our domain
            if (rpBoxCollection->IsOwned(p_node))
            {
                unsigned box_index = rpBoxCollection->CalculateContainingBox(p_node);
                box_indices_each_node_this_elem.insert(box_index);
            }
        }
        for (std::set<unsigned>::iterator iter = box_indices_each_node_this_elem.begin();
            iter != box_indices_each_node_this_elem.end();
            ++iter)
        {
            assert(rpBoxCollection->IsBoxOwned( *iter ));
            rpBoxCollection->rGetBox( *iter ).AddElement(p_element);
        }
    }
}
 
// ComputeFineElementsAndWeightsForCoarseQuadPoints()
// and
// ComputeFineElementsAndWeightsForCoarseNodes()
// and
// common method
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::ComputeFineElementsAndWeightsForCoarseQuadPoints(GaussianQuadratureRule<DIM>& rQuadRule,
                                                                               bool safeMode)
{
    if (mpFineMeshBoxCollection == nullptr)
    {
        EXCEPTION("Call SetUpBoxesOnFineMesh() before ComputeFineElementsAndWeightsForCoarseQuadPoints()");
    }
 
    // Get the quad point (physical) positions
    QuadraturePointsGroup<DIM> quad_point_posns(mrCoarseMesh, rQuadRule);
 
    // Resize the elements and weights vector.
    mFineMeshElementsAndWeights.resize(quad_point_posns.Size());
    // Make sure that, in parallel, silent processes have their structs initialised to zero values
    for (unsigned i=0; i<mFineMeshElementsAndWeights.size(); i++)
    {
        mFineMeshElementsAndWeights[i].ElementNum = 0u;
        mFineMeshElementsAndWeights[i].Weights = zero_vector<double>(DIM+1);
    }
 
 
    // LCOV_EXCL_START
    if (CommandLineArguments::Instance()->OptionExists("-mesh_pair_verbose"))
    {
        std::cout << "\nComputing fine elements and weights for coarse quad points\n";
    }
    // LCOV_EXCL_STOP
 
 
    ResetStatisticsVariables();
    for (unsigned i=0; i<quad_point_posns.Size(); i++)
    {
        // LCOV_EXCL_START
        if (CommandLineArguments::Instance()->OptionExists("-mesh_pair_verbose"))
        {
            std::cout << "\t" << i << " of " << quad_point_posns.Size() << std::flush;
        }
        // LCOV_EXCL_STOP
 
        // Get the box this point is in
        unsigned box_for_this_point = mpFineMeshBoxCollection->CalculateContainingBox( quad_point_posns.rGet(i) );
        if (mpFineMeshBoxCollection->IsBoxOwned(box_for_this_point))
        {
            // A chaste point version of the c-vector is needed for the GetContainingElement call.
            ChastePoint<DIM> point(quad_point_posns.rGet(i));
 
            ComputeFineElementAndWeightForGivenPoint(point, safeMode, box_for_this_point, i);
        }
        else
        {
            assert(mFineMeshElementsAndWeights[i].ElementNum == 0u);
            assert(norm_2(mFineMeshElementsAndWeights[i].Weights) == 0.0 );
        }
    }
    ShareFineElementData();
    if (mStatisticsCounters[1] > 0)
    {
        WARNING(mStatisticsCounters[1] << " of " << quad_point_posns.Size() << " coarse-mesh quadrature points were outside the fine mesh");
    }
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::ComputeFineElementsAndWeightsForCoarseNodes(bool safeMode)
{
    if (mpFineMeshBoxCollection==nullptr)
    {
        EXCEPTION("Call SetUpBoxesOnFineMesh() before ComputeFineElementsAndWeightsForCoarseNodes()");
    }
 
    // Resize the elements and weights vector.
    mFineMeshElementsAndWeights.resize(mrCoarseMesh.GetNumNodes());
    // Make sure that, in parallel, silent processes have their structs initialised to zero values
    for (unsigned i=0; i<mFineMeshElementsAndWeights.size(); i++)
    {
        mFineMeshElementsAndWeights[i].ElementNum = 0u;
        mFineMeshElementsAndWeights[i].Weights = zero_vector<double>(DIM+1);
    }
 
    // LCOV_EXCL_START
    if (CommandLineArguments::Instance()->OptionExists("-mesh_pair_verbose"))
    {
        std::cout << "\nComputing fine elements and weights for coarse nodes\n";
    }
    // LCOV_EXCL_STOP
 
 
    ResetStatisticsVariables();
    for (unsigned i=0; i<mrCoarseMesh.GetNumNodes(); i++)
    {
        // LCOV_EXCL_START
        if (CommandLineArguments::Instance()->OptionExists("-mesh_pair_verbose"))
        {
            std::cout << "\t" << i << " of " << mrCoarseMesh.GetNumNodes() << std::flush;
        }
        // LCOV_EXCL_STOP
 
        Node<DIM>* p_node = mrCoarseMesh.GetNode(i);
 
        // Get the box this point is in
        unsigned box_for_this_point = mpFineMeshBoxCollection->CalculateContainingBox( p_node->rGetModifiableLocation() );
        if (mpFineMeshBoxCollection->IsBoxOwned(box_for_this_point))
        {
            // A chaste point version of the c-vector is needed for the GetContainingElement call
            ChastePoint<DIM> point(p_node->rGetLocation());
 
            ComputeFineElementAndWeightForGivenPoint(point, safeMode, box_for_this_point, i);
        }
    }
    ShareFineElementData();
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::ComputeFineElementAndWeightForGivenPoint(ChastePoint<DIM>& rPoint,
                                                                       bool safeMode,
                                                                       unsigned boxForThisPoint,
                                                                       unsigned index)
{
    std::set<unsigned> test_element_indices;
 
    /*
     * The elements to try (initially) are those contained in the box the point is in.
     *
     * Note: it is possible the point to be in an element not 'in' this box, as it is
     * possible for all element nodes to be in different boxes.
     */
    CollectElementsInContainingBox(mpFineMeshBoxCollection, boxForThisPoint, test_element_indices);
 
    unsigned elem_index;
    c_vector<double,DIM+1> weight;
 
    try
    {
        //std::cout << "\n" << "# test elements initially " << test_element_indices.size() << "\n";
        // Try these elements only, initially
        elem_index = mrFineMesh.GetContainingElementIndex(rPoint,
                                                          false,
                                                          test_element_indices,
                                                          true /* quit if not in test_elements */);
        weight = mrFineMesh.GetElement(elem_index)->CalculateInterpolationWeights(rPoint);
 
        mStatisticsCounters[0]++;
    }
    catch(Exception&) //not_in_box
    {
        // Now try all elements, trying the elements contained in the boxes local to this element first
        test_element_indices.clear();
 
        CollectElementsInLocalBoxes(mpFineMeshBoxCollection, boxForThisPoint, test_element_indices);
 
        try
        {
            elem_index = mrFineMesh.GetContainingElementIndex(rPoint, false, test_element_indices, true);
            weight = mrFineMesh.GetElement(elem_index)->CalculateInterpolationWeights(rPoint);
            mStatisticsCounters[0]++;
        }
        catch(Exception&) //not_in_local_boxes
        {
            if (safeMode)
            {
                // Try the remaining elements
                try
                {
                    elem_index = mrFineMesh.GetContainingElementIndex(rPoint, false);
                    weight = mrFineMesh.GetElement(elem_index)->CalculateInterpolationWeights(rPoint);
                    mStatisticsCounters[0]++;
 
                }
                catch (Exception&) // not_in_mesh
                {
                    // The point is not in ANY element, so store the nearest element and corresponding weights
                    elem_index = mrFineMesh.GetNearestElementIndexFromTestElements(rPoint,test_element_indices);
                    weight = mrFineMesh.GetElement(elem_index)->CalculateInterpolationWeights(rPoint);
 
                    mNotInMesh.push_back(index);
                    mNotInMeshNearestElementWeights.push_back(weight);
                    mStatisticsCounters[1]++;
                }
            }
            else
            {
                assert(test_element_indices.size() > 0); // boxes probably too small if this fails
 
                /*
                 * Immediately assume it isn't in the rest of the mesh - this should be the
                 * case assuming the box width was chosen suitably. Store the nearest element
                 * and corresponding weights.
                 */
                elem_index = mrFineMesh.GetNearestElementIndexFromTestElements(rPoint,test_element_indices);
                weight = mrFineMesh.GetElement(elem_index)->CalculateInterpolationWeights(rPoint);
 
                mNotInMesh.push_back(index);
                mNotInMeshNearestElementWeights.push_back(weight);
                mStatisticsCounters[1]++;
            }
        }
    }
 
    mFineMeshElementsAndWeights[index].ElementNum = elem_index;
    mFineMeshElementsAndWeights[index].Weights = weight;
}
 
// ComputeCoarseElementsForFineNodes
// and
// ComputeCoarseElementsForFineElementCentroids
// and
// common method
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::ComputeCoarseElementsForFineNodes(bool safeMode)
{
    if (mpCoarseMeshBoxCollection==nullptr)
    {
        EXCEPTION("Call SetUpBoxesOnCoarseMesh() before ComputeCoarseElementsForFineNodes()");
    }
 
    // LCOV_EXCL_START
    if (CommandLineArguments::Instance()->OptionExists("-mesh_pair_verbose"))
    {
        std::cout << "\nComputing coarse elements for fine nodes\n";
    }
    // LCOV_EXCL_STOP
    mCoarseElementsForFineNodes.clear();
    mCoarseElementsForFineNodes.resize(mrFineMesh.GetNumNodes(), 0.0);
 
    ResetStatisticsVariables();
    for (unsigned i=0; i<mCoarseElementsForFineNodes.size(); i++)
    {
        // LCOV_EXCL_START
        if (CommandLineArguments::Instance()->OptionExists("-mesh_pair_verbose"))
        {
            std::cout << "\t" << i << " of " << mCoarseElementsForFineNodes.size() << std::flush;
        }
        // LCOV_EXCL_STOP
 
        ChastePoint<DIM> point = mrFineMesh.GetNode(i)->GetPoint();
 
        // Get the box this point is in
        unsigned box_for_this_point = mpCoarseMeshBoxCollection->CalculateContainingBox(mrFineMesh.GetNode(i)->rGetModifiableLocation());
        if (mpCoarseMeshBoxCollection->IsBoxOwned(box_for_this_point))
        {
            mCoarseElementsForFineNodes[i] = ComputeCoarseElementForGivenPoint(point, safeMode, box_for_this_point);
        }
    }
    ShareCoarseElementData();
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::ComputeCoarseElementsForFineElementCentroids(bool safeMode)
{
    if (mpCoarseMeshBoxCollection==nullptr)
    {
        EXCEPTION("Call SetUpBoxesOnCoarseMesh() before ComputeCoarseElementsForFineElementCentroids()");
    }
 
    // LCOV_EXCL_START
    if (CommandLineArguments::Instance()->OptionExists("-mesh_pair_verbose"))
    {
        std::cout << "\nComputing coarse elements for fine element centroids\n";
    }
    // LCOV_EXCL_STOP
 
    mCoarseElementsForFineElementCentroids.clear();
    mCoarseElementsForFineElementCentroids.resize(mrFineMesh.GetNumElements(), 0.0);
 
    ResetStatisticsVariables();
    for (unsigned i=0; i<mrFineMesh.GetNumElements(); i++)
    {
        // LCOV_EXCL_START
        if (CommandLineArguments::Instance()->OptionExists("-mesh_pair_verbose"))
        {
            std::cout << "\t" << i << " of " << mrFineMesh.GetNumElements() << std::flush;
        }
        // LCOV_EXCL_STOP
 
        c_vector<double,DIM> point_cvec = mrFineMesh.GetElement(i)->CalculateCentroid();
        ChastePoint<DIM> point(point_cvec);
 
        // Get the box this point is in
        unsigned box_for_this_point = mpCoarseMeshBoxCollection->CalculateContainingBox( point_cvec );
 
        if (mpCoarseMeshBoxCollection->IsBoxOwned(box_for_this_point))
        {
            mCoarseElementsForFineElementCentroids[i] = ComputeCoarseElementForGivenPoint(point, safeMode, box_for_this_point);
        }
    }
    ShareCoarseElementData();
}
 
template<unsigned DIM>
unsigned FineCoarseMeshPair<DIM>::ComputeCoarseElementForGivenPoint(ChastePoint<DIM>& rPoint,
                                                                    bool safeMode,
                                                                    unsigned boxForThisPoint)
{
    std::set<unsigned> test_element_indices;
    CollectElementsInContainingBox(mpCoarseMeshBoxCollection, boxForThisPoint, test_element_indices);
 
    unsigned elem_index;
 
    try
    {
        elem_index = mrCoarseMesh.GetContainingElementIndex(rPoint,
                                                            false,
                                                            test_element_indices,
                                                            true /* quit if not in test_elements */);
 
        mStatisticsCounters[0]++;
    }
    catch(Exception&) // not_in_box
    {
        // Now try all elements, trying the elements contained in the boxes local to this element first
        test_element_indices.clear();
        CollectElementsInLocalBoxes(mpCoarseMeshBoxCollection, boxForThisPoint, test_element_indices);
 
        try
        {
            elem_index = mrCoarseMesh.GetContainingElementIndex(rPoint, false, test_element_indices, true);
            mStatisticsCounters[0]++;
        }
        catch(Exception&) // not_in_local_boxes
        {
            if (safeMode)
            {
                // Try the remaining elements
                try
                {
                    elem_index = mrCoarseMesh.GetContainingElementIndex(rPoint, false);
 
                    mStatisticsCounters[0]++;
                }
                catch (Exception&) // not_in_mesh
                {
                    // The point is not in ANY element, so store the nearest element and corresponding weights
                    elem_index = mrCoarseMesh.GetNearestElementIndexFromTestElements(rPoint,test_element_indices);
                    mStatisticsCounters[1]++;
                }
            }
            else
            {
                assert(test_element_indices.size() > 0); // boxes probably too small if this fails
 
                /*
                 * Immediately assume it isn't in the rest of the mesh - this should be the
                 * case assuming the box width was chosen suitably. Store the nearest element
                 * and corresponding weights.
                 */
                elem_index = mrCoarseMesh.GetNearestElementIndexFromTestElements(rPoint,test_element_indices);
                mStatisticsCounters[1]++;
            }
        }
    }
 
    return elem_index;
}
 
// Helper methods for code
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::CollectElementsInContainingBox(DistributedBoxCollection<DIM>*& rpBoxCollection,
                                                             unsigned boxIndex,
                                                             std::set<unsigned>& rElementIndices)
{
    for (typename std::set<Element<DIM,DIM>*>::iterator elem_iter = rpBoxCollection->rGetBox(boxIndex).rGetElementsContained().begin();
         elem_iter != rpBoxCollection->rGetBox(boxIndex).rGetElementsContained().end();
         ++elem_iter)
    {
        rElementIndices.insert((*elem_iter)->GetIndex());
    }
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::CollectElementsInLocalBoxes(DistributedBoxCollection<DIM>*& rpBoxCollection,
                                                          unsigned boxIndex,
                                                          std::set<unsigned>& rElementIndices)
{
    std::set<unsigned> local_boxes = rpBoxCollection->rGetLocalBoxes(boxIndex);
    for (std::set<unsigned>::iterator local_box_iter = local_boxes.begin();
         local_box_iter != local_boxes.end();
         ++local_box_iter)
    {
        for (typename std::set<Element<DIM,DIM>*>::iterator elem_iter = rpBoxCollection->rGetBox(*local_box_iter).rGetElementsContained().begin();
             elem_iter != rpBoxCollection->rGetBox(*local_box_iter).rGetElementsContained().end();
             ++elem_iter)
        {
            rElementIndices.insert((*elem_iter)->GetIndex());
        }
    }
}
 
// Statistics related methods
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::ResetStatisticsVariables()
{
    mNotInMesh.clear();
    mNotInMeshNearestElementWeights.clear();
    mStatisticsCounters.resize(2, 0u);
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::ShareFineElementData()
{
    if (PetscTools::IsSequential())
    {
        return;
    }
 
    // This sums the results so it isn't idempotent: you get a different result if you call this method twice
    // Should not matter: the methods which call this helper method have reset everything which is about to be shared
    std::vector<unsigned> local_counters = mStatisticsCounters;
    MPI_Allreduce(&local_counters[0], &mStatisticsCounters[0], 2u, MPI_UNSIGNED, MPI_SUM, PETSC_COMM_WORLD);
 
 
    // Get all the element number and weights into a contiguous format
    unsigned elements_size = mFineMeshElementsAndWeights.size();
    std::vector<unsigned> all_element_indices(elements_size);
    unsigned weights_size = elements_size*(DIM+1);
    std::vector<double> all_weights(weights_size);
    for (unsigned index=0; index<mFineMeshElementsAndWeights.size(); index++)
    {
        all_element_indices[index] = mFineMeshElementsAndWeights[index].ElementNum;
        for (unsigned j=0; j<DIM+1; j++)
        {
            all_weights[index*(DIM+1)+j] = mFineMeshElementsAndWeights[index].Weights[j];
        }
    }
 
    // Copy and share
    std::vector<unsigned> local_all_element_indices = all_element_indices;
    std::vector<double> local_all_weights = all_weights;
    MPI_Allreduce(&local_all_element_indices[0], &all_element_indices[0], elements_size, MPI_UNSIGNED, MPI_SUM, PETSC_COMM_WORLD);
    MPI_Allreduce( &local_all_weights[0], &all_weights[0], weights_size, MPI_DOUBLE, MPI_SUM, PETSC_COMM_WORLD);
 
    // Put back into the regular data structure
    for (unsigned index=0; index<mFineMeshElementsAndWeights.size(); index++)
    {
        mFineMeshElementsAndWeights[index].ElementNum = all_element_indices[index];
        for (unsigned j=0; j<DIM+1; j++)
        {
            mFineMeshElementsAndWeights[index].Weights[j] = all_weights[index*(DIM+1)+j] ;
        }
    }
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::ShareCoarseElementData()
{
    if (PetscTools::IsSequential())
    {
        return;
    }
 
    // This sums the results so it isn't idempotent: you get a different result if you call this method twice
    // Should not matter: the methods which call this helper method have reset #mStatisticsCounters
    std::vector<unsigned> local_counters = mStatisticsCounters;
    MPI_Allreduce(&local_counters[0], &mStatisticsCounters[0], 2u, MPI_UNSIGNED, MPI_SUM, PETSC_COMM_WORLD);
 
    // The rest uses "max" so it is idempotent.  You can safely re-share results between processes without them changing.
    if (mCoarseElementsForFineNodes.empty() == false)
    {
        std::vector<unsigned> temp_coarse_elements = mCoarseElementsForFineNodes;
        MPI_Allreduce( &temp_coarse_elements[0], &mCoarseElementsForFineNodes[0], mCoarseElementsForFineNodes.size(), MPI_UNSIGNED, MPI_MAX, PETSC_COMM_WORLD);
    }
    if (mCoarseElementsForFineElementCentroids.empty() == false)
    {
        std::vector<unsigned> temp_coarse_elements = mCoarseElementsForFineElementCentroids;
        MPI_Allreduce( &temp_coarse_elements[0], &mCoarseElementsForFineElementCentroids[0], mCoarseElementsForFineElementCentroids.size(), MPI_UNSIGNED, MPI_MAX, PETSC_COMM_WORLD);
    }
}
 
template<unsigned DIM>
void FineCoarseMeshPair<DIM>::PrintStatistics()
{
    std::cout << "\nFineCoarseMeshPair statistics for the last-called method:\n";
 
//    std::cout << "\tNum points for which containing element was found, using box containing that point = " << mStatisticsCounters[0] << "\n";
//    std::cout << "\tNum points for which containing element was in local box = " << mStatisticsCounters[1] << "\n";
//    std::cout << "\tNum points for which containing element was in an element in a non-local box = " << mStatisticsCounters[2] << "\n";
//    std::cout << "\tNum points for which no containing element was found = " << mStatisticsCounters[3] << "\n";
 
    std::cout << "\tNum points for which containing element was found: " << mStatisticsCounters[0] << "\n";
    std::cout << "\tNum points for which no containing element was found = " << mStatisticsCounters[1] << "\n";
 
    if (mNotInMesh.size() > 0)
    {
        std::cout << "\tIndices and weights for points (nodes/quad points) for which no containing element was found:\n";
        for (unsigned i=0; i<mNotInMesh.size(); i++)
        {
            std::cout << "\t\t" << mNotInMesh[i] << ", " << mNotInMeshNearestElementWeights[i] << "\n";
        }
    }
}
 
 
template class FineCoarseMeshPair<1>;
template class FineCoarseMeshPair<2>;
template class FineCoarseMeshPair<3>;