NodeBasedCellPopulation.cpp

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*/
 
#include "NodeBasedCellPopulation.hpp"
#include "MathsCustomFunctions.hpp"
#include "VtkMeshWriter.hpp"
 
template<unsigned DIM>
NodeBasedCellPopulation<DIM>::NodeBasedCellPopulation(NodesOnlyMesh<DIM>& rMesh,
                                      std::vector<CellPtr>& rCells,
                                      const std::vector<unsigned> locationIndices,
                                      bool deleteMesh,
                                      bool validate)
    : AbstractCentreBasedCellPopulation<DIM>(rMesh, rCells, locationIndices),
      mDeleteMesh(deleteMesh),
      mUseVariableRadii(false),
      mLoadBalanceMesh(false),
      mLoadBalanceFrequency(100)
{
    mpNodesOnlyMesh = static_cast<NodesOnlyMesh<DIM>* >(&(this->mrMesh));
 
    if (validate)
    {
        Validate();
    }
}
 
template<unsigned DIM>
NodeBasedCellPopulation<DIM>::NodeBasedCellPopulation(NodesOnlyMesh<DIM>& rMesh)
    : AbstractCentreBasedCellPopulation<DIM>(rMesh),
      mDeleteMesh(true),
      mUseVariableRadii(false), // will be set by serialize() method
      mLoadBalanceMesh(false),
      mLoadBalanceFrequency(100)
{
    mpNodesOnlyMesh = static_cast<NodesOnlyMesh<DIM>* >(&(this->mrMesh));
}
 
template<unsigned DIM>
NodeBasedCellPopulation<DIM>::~NodeBasedCellPopulation()
{
    Clear();
    if (mDeleteMesh)
    {
        delete &this->mrMesh;
    }
}
 
template<unsigned DIM>
NodesOnlyMesh<DIM>& NodeBasedCellPopulation<DIM>::rGetMesh()
{
    return *mpNodesOnlyMesh;
}
 
template<unsigned DIM>
const NodesOnlyMesh<DIM>& NodeBasedCellPopulation<DIM>::rGetMesh() const
{
    return *mpNodesOnlyMesh;
}
 
template<unsigned DIM>
TetrahedralMesh<DIM, DIM>* NodeBasedCellPopulation<DIM>::GetTetrahedralMeshForPdeModifier()
{
    // Note that this code does not yet work in parallel.
    assert(PetscTools::IsSequential());
 
    std::vector<Node<DIM>*> temp_nodes;
 
    // Get the nodes of mpNodesOnlyMesh
    for (typename AbstractMesh<DIM,DIM>::NodeIterator node_iter = mpNodesOnlyMesh->GetNodeIteratorBegin();
         node_iter != mpNodesOnlyMesh->GetNodeIteratorEnd();
         ++node_iter)
    {
        temp_nodes.push_back(new Node<DIM>(node_iter->GetIndex(), node_iter->rGetLocation(), node_iter->IsBoundaryNode()));
    }
 
    return new MutableMesh<DIM,DIM>(temp_nodes);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::Clear()
{
    this->mNodePairs.clear();
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::Validate()
{
    for (typename AbstractMesh<DIM,DIM>::NodeIterator node_iter = this->mrMesh.GetNodeIteratorBegin();
         node_iter != this->mrMesh.GetNodeIteratorEnd();
         ++node_iter)
    {
        try
        {
            this->GetCellUsingLocationIndex(node_iter->GetIndex());
        }
        catch (Exception&)
        {
            EXCEPTION("At time " << SimulationTime::Instance()->GetTime() << ", Node " << node_iter->GetIndex() << " does not appear to have a cell associated with it");
        }
    }
}
 
template<unsigned DIM>
Node<DIM>* NodeBasedCellPopulation<DIM>::GetNode(unsigned index)
{
    return mpNodesOnlyMesh->GetNodeOrHaloNode(index);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::SetNode(unsigned nodeIndex, ChastePoint<DIM>& rNewLocation)
{
    mpNodesOnlyMesh->SetNode(nodeIndex, rNewLocation, false);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::Update(bool hasHadBirthsOrDeaths)
{
    UpdateCellProcessLocation();
 
    mpNodesOnlyMesh->UpdateBoxCollection();
 
    if (mLoadBalanceMesh)
    {
        if ((SimulationTime::Instance()->GetTimeStepsElapsed() % mLoadBalanceFrequency) == 0)
        {
            mpNodesOnlyMesh->LoadBalanceMesh();
 
            UpdateCellProcessLocation();
 
            mpNodesOnlyMesh->UpdateBoxCollection();
        }
    }
 
    RefreshHaloCells();
 
    mpNodesOnlyMesh->CalculateInteriorNodePairs(this->mNodePairs);
 
    AddReceivedHaloCells();
 
    mpNodesOnlyMesh->CalculateBoundaryNodePairs(this->mNodePairs);
 
    /*
     * Update cell radii based on CellData
     */
    if (mUseVariableRadii)
    {
        for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = this->Begin();
             cell_iter != this->End();
             ++cell_iter)
        {
            double cell_radius = cell_iter->GetCellData()->GetItem("Radius");
            unsigned node_index = this->GetLocationIndexUsingCell(*cell_iter);
            this->GetNode(node_index)->SetRadius(cell_radius);
        }
    }
 
    // Make sure that everyone exits update together so that all asynchronous communications are complete.
    PetscTools::Barrier("Update");
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::UpdateMapsAfterRemesh(NodeMap& map)
{
    if (!map.IsIdentityMap())
    {
        UpdateParticlesAfterReMesh(map);
 
        // Update the mappings between cells and location indices
        std::map<Cell*, unsigned> old_map = this->mCellLocationMap;
 
        // Remove any dead pointers from the maps (needed to avoid archiving errors)
        this->mLocationCellMap.clear();
        this->mCellLocationMap.clear();
 
        for (std::list<CellPtr>::iterator it = this->mCells.begin();
             it != this->mCells.end();
             ++it)
        {
            unsigned old_node_index = old_map[(*it).get()];
 
            // This shouldn't ever happen, as the cell vector only contains living cells
            assert(!map.IsDeleted(old_node_index));
 
            unsigned new_node_index = map.GetNewIndex(old_node_index);
            this->SetCellUsingLocationIndex(new_node_index,*it);
        }
 
        this->Validate();
    }
}
 
template<unsigned DIM>
unsigned NodeBasedCellPopulation<DIM>::RemoveDeadCells()
{
    unsigned num_removed = 0;
    for (std::list<CellPtr>::iterator cell_iter = this->mCells.begin();
         cell_iter != this->mCells.end();
         )
    {
        if ((*cell_iter)->IsDead())
        {
            // Remove the node from the mesh
            num_removed++;
            unsigned location_index = mpNodesOnlyMesh->SolveNodeMapping(this->GetLocationIndexUsingCell((*cell_iter)));
            mpNodesOnlyMesh->DeleteNodePriorToReMesh(location_index);
 
            // Update mappings between cells and location indices
            unsigned location_index_of_removed_node = this->GetLocationIndexUsingCell((*cell_iter));
            this->RemoveCellUsingLocationIndex(location_index_of_removed_node, (*cell_iter));
 
            // Update vector of cells
            cell_iter = this->mCells.erase(cell_iter);
        }
        else
        {
            ++cell_iter;
        }
    }
 
    return num_removed;
}
 
template<unsigned DIM>
unsigned NodeBasedCellPopulation<DIM>::AddNode(Node<DIM>* pNewNode)
{
    return mpNodesOnlyMesh->AddNode(pNewNode);
}
 
template<unsigned DIM>
unsigned NodeBasedCellPopulation<DIM>::GetNumNodes()
{
    return mpNodesOnlyMesh->GetNumNodes();
}
 
template<unsigned DIM>
CellPtr NodeBasedCellPopulation<DIM>::GetCellUsingLocationIndex(unsigned index)
{
    std::map<unsigned, CellPtr>::iterator iter = mLocationHaloCellMap.find(index);
    if (iter != mLocationHaloCellMap.end())
    {
        return iter->second;
    }
    else
    {
        return AbstractCellPopulation<DIM, DIM>::GetCellUsingLocationIndex(index);
    }
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::UpdateParticlesAfterReMesh(NodeMap& rMap)
{
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::OutputCellPopulationParameters(out_stream& rParamsFile)
{
    *rParamsFile << "\t\t<MechanicsCutOffLength>" << mpNodesOnlyMesh->GetMaximumInteractionDistance() << "</MechanicsCutOffLength>\n";
    *rParamsFile << "\t\t<UseVariableRadii>" << mUseVariableRadii << "</UseVariableRadii>\n";
 
    // Call method on direct parent class
    AbstractCentreBasedCellPopulation<DIM>::OutputCellPopulationParameters(rParamsFile);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AcceptPopulationWriter(boost::shared_ptr<AbstractCellPopulationWriter<DIM, DIM> > pPopulationWriter)
{
    pPopulationWriter->Visit(this);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AcceptPopulationCountWriter(boost::shared_ptr<AbstractCellPopulationCountWriter<DIM, DIM> > pPopulationCountWriter)
{
    pPopulationCountWriter->Visit(this);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AcceptPopulationEventWriter(boost::shared_ptr<AbstractCellPopulationEventWriter<DIM, DIM> > pPopulationEventWriter)
{
    pPopulationEventWriter->Visit(this);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AcceptCellWriter(boost::shared_ptr<AbstractCellWriter<DIM, DIM> > pCellWriter, CellPtr pCell)
{
    pCellWriter->VisitCell(pCell, this);
}
 
template<unsigned DIM>
double NodeBasedCellPopulation<DIM>::GetMechanicsCutOffLength()
{
    return mpNodesOnlyMesh->GetMaximumInteractionDistance();
}
 
template<unsigned DIM>
bool NodeBasedCellPopulation<DIM>::GetUseVariableRadii()
{
    return mUseVariableRadii;
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::SetUseVariableRadii(bool useVariableRadii)
{
    mUseVariableRadii = useVariableRadii;
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::SetLoadBalanceMesh(bool loadBalanceMesh)
{
    mLoadBalanceMesh = loadBalanceMesh;
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::SetLoadBalanceFrequency(unsigned loadBalanceFrequency)
{
    mLoadBalanceFrequency = loadBalanceFrequency;
}
 
template<unsigned DIM>
double NodeBasedCellPopulation<DIM>::GetWidth(const unsigned& rDimension)
{
    return mpNodesOnlyMesh->GetWidth(rDimension);
}
 
template<unsigned DIM>
c_vector<double, DIM> NodeBasedCellPopulation<DIM>::GetSizeOfCellPopulation()
{
    c_vector<double, DIM> local_size = AbstractCellPopulation<DIM, DIM>::GetSizeOfCellPopulation();
    c_vector<double, DIM> global_size;
 
    for (unsigned i=0; i<DIM; i++)
    {
        MPI_Allreduce(&local_size[i], &global_size[i], 1, MPI_DOUBLE, MPI_MAX, PetscTools::GetWorld());
    }
 
    return global_size;
}
 
template<unsigned DIM>
std::set<unsigned> NodeBasedCellPopulation<DIM>::GetNodesWithinNeighbourhoodRadius(unsigned index, double neighbourhoodRadius)
{
    // Check neighbourhoodRadius is less than the interaction radius. If not you wont return all the correct nodes
    if (neighbourhoodRadius > mpNodesOnlyMesh->GetMaximumInteractionDistance())
    {
        EXCEPTION("neighbourhoodRadius should be less than or equal to the  the maximum interaction radius defined on the NodesOnlyMesh");
    }
 
    std::set<unsigned> neighbouring_node_indices;
 
    // Get location
    Node<DIM>* p_node_i = this->GetNode(index);
    const c_vector<double, DIM>& r_node_i_location = p_node_i->rGetLocation();
 
    // Check the mNodeNeighbours has been set up correctly
    if (!(p_node_i->GetNeighboursSetUp()))
    {
        EXCEPTION("mNodeNeighbours not set up. Call Update() before GetNodesWithinNeighbourhoodRadius()");
    }
 
    // Get set of 'candidate' neighbours.
    std::vector<unsigned>& near_nodes = p_node_i->rGetNeighbours();
 
    // Find which ones are actually close
    for (std::vector<unsigned>::iterator iter = near_nodes.begin();
         iter != near_nodes.end();
         ++iter)
    {
        // Be sure not to return the index itself.
        if ((*iter) != index)
        {
            Node<DIM>* p_node_j = this->GetNode((*iter));
 
            // Get the location of this node
            const c_vector<double, DIM>& r_node_j_location = p_node_j->rGetLocation();
 
            // Get the vector the two nodes (using GetVectorFromAtoB to catch periodicities etc.)
            c_vector<double, DIM> node_to_node_vector = mpNodesOnlyMesh->GetVectorFromAtoB(r_node_j_location, r_node_i_location);
 
            // Calculate the distance between the two nodes
            double distance_between_nodes = norm_2(node_to_node_vector);
 
            // If the cell j is within the neighbourhood of radius neighbourhoodRadius
            // of cell i
            if (distance_between_nodes <= neighbourhoodRadius)// + DBL_EPSILSON)
            {
                // ...then add this node index to the set of neighbouring node indices
                neighbouring_node_indices.insert((*iter));
            }
        }
    }
 
    return neighbouring_node_indices;
}
 
template<unsigned DIM>
std::set<unsigned> NodeBasedCellPopulation<DIM>::GetNeighbouringNodeIndices(unsigned index)
{
    std::set<unsigned> neighbouring_node_indices;
 
    // Get location and radius of node
    Node<DIM>* p_node_i = this->GetNode(index);
    const c_vector<double, DIM>& r_node_i_location = p_node_i->rGetLocation();
    double radius_of_cell_i = p_node_i->GetRadius();
 
    // Check the mNodeNeighbours has been set up correctly
    if (!(p_node_i->GetNeighboursSetUp()))
    {
        EXCEPTION("mNodeNeighbours not set up. Call Update() before GetNeighbouringNodeIndices()");
    }
 
    // Make sure that the max_interaction distance is smaller than or equal to the box collection size
    if (!(radius_of_cell_i * 2.0 <= mpNodesOnlyMesh->GetMaximumInteractionDistance()))
    {
        EXCEPTION("mpNodesOnlyMesh::mMaxInteractionDistance is smaller than twice the radius of cell " << index << " (" << radius_of_cell_i << ") so interactions may be missed. Make the cut-off larger to avoid errors.");
    }
 
    // Get set of 'candidate' neighbours
    std::vector<unsigned>& near_nodes = p_node_i->rGetNeighbours();
 
    // Find which ones are actually close
    for (std::vector<unsigned>::iterator iter = near_nodes.begin();
         iter != near_nodes.end();
         ++iter)
    {
        // Be sure not to return the index itself
        if ((*iter) != index)
        {
            Node<DIM>* p_node_j = this->GetNode((*iter));
 
            // Get the location of this node
            const c_vector<double, DIM>& r_node_j_location = p_node_j->rGetLocation();
 
            // Get the vector the two nodes (using GetVectorFromAtoB to catch periodicities etc.)
            c_vector<double, DIM> node_to_node_vector = mpNodesOnlyMesh->GetVectorFromAtoB(r_node_j_location, r_node_i_location);
 
            // Calculate the distance between the two nodes
            double distance_between_nodes = norm_2(node_to_node_vector);
 
            // Get the radius of the cell corresponding to this node
            double radius_of_cell_j = p_node_j->GetRadius();
 
            // If the cells are close enough to exert a force on each other...
            double max_interaction_distance = radius_of_cell_i + radius_of_cell_j;
 
            // Make sure that the max_interaction distance is smaller than or equal to the box collection size
            if (!(max_interaction_distance <= mpNodesOnlyMesh->GetMaximumInteractionDistance()))
            {
                EXCEPTION("mpNodesOnlyMesh::mMaxInteractionDistance is smaller than the sum of radius of cell " << index << " (" << radius_of_cell_i << ") and cell " << (*iter) << " (" << radius_of_cell_j <<"). Make the cut-off larger to avoid errors.");
            }
            if (distance_between_nodes <= max_interaction_distance)// + DBL_EPSILSON) //Assumes that max_interaction_distance is of order 1
            {
                // ...then add this node index to the set of neighbouring node indices
                neighbouring_node_indices.insert((*iter));
            }
        }
    }
 
    return neighbouring_node_indices;
}
 
template <unsigned DIM>
double NodeBasedCellPopulation<DIM>::GetVolumeOfCell([[maybe_unused]] CellPtr pCell)
{
    // Not implemented or tested in 1D
    if constexpr ((DIM == 2) || (DIM == 3))
    {
        // Get node index corresponding to this cell
        unsigned node_index = this->GetLocationIndexUsingCell(pCell);
        Node<DIM>* p_node = this->GetNode(node_index);
 
        // Get cell radius
        double cell_radius = p_node->GetRadius();
 
        // Begin code to approximate cell volume
        double averaged_cell_radius = 0.0;
        unsigned num_cells = 0;
 
        // Get the location of this node
        const c_vector<double, DIM>& r_node_i_location = GetNode(node_index)->rGetLocation();
 
        // Get the set of node indices corresponding to this cell's neighbours
        std::set<unsigned> neighbouring_node_indices = GetNeighbouringNodeIndices(node_index);
 
        // THe number of neighbours in equilibrium configuration, from sphere packing problem
        unsigned num_neighbours_equil;
        if (DIM == 2)
        {
            num_neighbours_equil = 6;
        }
        else // DIM == 3
        {
            num_neighbours_equil = 12;
        }
 
        // Loop over this set
        for (std::set<unsigned>::iterator iter = neighbouring_node_indices.begin();
            iter != neighbouring_node_indices.end();
            ++iter)
        {
            Node<DIM>* p_node_j = this->GetNode(*iter);
 
            // Get the location of the neighbouring node
            const c_vector<double, DIM>& r_node_j_location = p_node_j->rGetLocation();
 
            double neighbouring_cell_radius = p_node_j->GetRadius();
 
            // If this throws then you may not be considering all cell interactions use a larger cut off length
            assert(cell_radius+neighbouring_cell_radius<mpNodesOnlyMesh->GetMaximumInteractionDistance());
 
            // Calculate the distance between the two nodes and add to cell radius
            double separation = norm_2(mpNodesOnlyMesh->GetVectorFromAtoB(r_node_j_location, r_node_i_location));
 
            if (separation < cell_radius+neighbouring_cell_radius)
            {
                // The effective radius is the mid point of the overlap
                averaged_cell_radius = averaged_cell_radius + cell_radius - (cell_radius+neighbouring_cell_radius-separation)/2.0;
                num_cells++;
            }
        }
        if (num_cells < num_neighbours_equil)
        {
            averaged_cell_radius += (num_neighbours_equil-num_cells)*cell_radius;
 
            averaged_cell_radius /= num_neighbours_equil;
        }
        else
        {
            averaged_cell_radius /= num_cells;
        }
        assert(averaged_cell_radius < mpNodesOnlyMesh->GetMaximumInteractionDistance()/2.0);
 
        cell_radius = averaged_cell_radius;
 
        // End code to approximate cell volume
 
        // Calculate cell volume from radius of cell
        double cell_volume = 0.0;
        if (DIM == 2)
        {
            cell_volume = M_PI*cell_radius*cell_radius;
        }
        else // DIM == 3
        {
            cell_volume = (4.0/3.0)*M_PI*cell_radius*cell_radius*cell_radius;
        }
 
        return cell_volume;
    }
    else
    {
        NEVER_REACHED;
    }
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::WriteVtkResultsToFile(const std::string& rDirectory)
{
    // Store the present time as a string
    std::stringstream time;
    time << SimulationTime::Instance()->GetTimeStepsElapsed();
 
    // Make sure the nodes are ordered contiguously in memory
    NodeMap map(1 + this->mpNodesOnlyMesh->GetMaximumNodeIndex());
    this->mpNodesOnlyMesh->ReMesh(map);
 
    // Create mesh writer for VTK output
    VtkMeshWriter<DIM, DIM> mesh_writer(rDirectory, "results_"+time.str(), false);
    mesh_writer.SetParallelFiles(*mpNodesOnlyMesh);
 
    auto num_nodes = GetNumNodes();
 
    // For each cell that this process owns, find the corresponding node index, which we only want to calculate once
    std::vector<unsigned> node_indices_in_cell_order;
    for (auto cell_iter = this->Begin(); cell_iter != this->End(); ++cell_iter)
    {
        // Get the node index corresponding to this cell
        unsigned global_index = this->GetLocationIndexUsingCell(*cell_iter);
        unsigned node_index = this->rGetMesh().SolveNodeMapping(global_index);
 
        node_indices_in_cell_order.emplace_back(node_index);
    }
 
    // Iterate over any cell writers that are present.  This is in a separate loop to below, because the writer loop
    // needs to the the outer loop.
    for (auto&& p_cell_writer : this->mCellWriters)
    {
        // Add any scalar data
        if (p_cell_writer->GetOutputScalarData())
        {
            std::vector<double> vtk_cell_data(num_nodes);
 
            unsigned loop_it = 0;
            for (auto cell_iter = this->Begin(); cell_iter != this->End(); ++cell_iter, ++loop_it)
            {
                unsigned node_idx = node_indices_in_cell_order[loop_it];
                vtk_cell_data[node_idx] = p_cell_writer->GetCellDataForVtkOutput(*cell_iter, this);
            }
 
            mesh_writer.AddPointData(p_cell_writer->GetVtkCellDataName(), vtk_cell_data);
        }
 
        // Add any vector data
        if (p_cell_writer->GetOutputVectorData())
        {
            std::vector<c_vector<double, DIM>> vtk_cell_data(num_nodes);
 
            unsigned loop_it = 0;
            for (auto cell_iter = this->Begin(); cell_iter != this->End(); ++cell_iter, ++loop_it)
            {
                unsigned node_idx = node_indices_in_cell_order[loop_it];
                vtk_cell_data[node_idx] = p_cell_writer->GetVectorCellDataForVtkOutput(*cell_iter, this);
            }
 
            mesh_writer.AddPointData(p_cell_writer->GetVtkVectorCellDataName(), vtk_cell_data);
        }
    }
 
    // Process rank and cell data can be collected on a cell-by-cell basis, and both occur in the following loop
    // We assume the first cell is representative of all cells
    if (this->Begin() != this->End())  // some processes may own no cells, so can't do this->Begin()->GetCellData()
    {
        auto num_cell_data_items = this->Begin()->GetCellData()->GetNumItems();
        std::vector<std::string> cell_data_names = this->Begin()->GetCellData()->GetKeys();
        std::vector<std::vector<double>> cell_data(num_cell_data_items, std::vector<double>(num_nodes));
 
        std::vector<double> rank(num_nodes);
 
        unsigned loop_it = 0;
        for (auto cell_iter = this->Begin(); cell_iter != this->End(); ++cell_iter, ++loop_it)
        {
            unsigned node_idx = node_indices_in_cell_order[loop_it];
 
            for (unsigned cell_data_idx = 0; cell_data_idx < num_cell_data_items; ++cell_data_idx)
            {
                cell_data[cell_data_idx][node_idx] = cell_iter->GetCellData()->GetItem(cell_data_names[cell_data_idx]);
            }
 
            rank[node_idx] = (PetscTools::GetMyRank());
        }
 
        // Add point data to writers
        mesh_writer.AddPointData("Process rank", rank);
        for (unsigned cell_data_idx = 0; cell_data_idx < num_cell_data_items; ++cell_data_idx)
        {
            mesh_writer.AddPointData(cell_data_names[cell_data_idx], cell_data[cell_data_idx]);
        }
    }
 
    mesh_writer.WriteFilesUsingMesh(*mpNodesOnlyMesh);
 
    *(this->mpVtkMetaFile) << "        <DataSet timestep=\"";
    *(this->mpVtkMetaFile) << SimulationTime::Instance()->GetTimeStepsElapsed();
    *(this->mpVtkMetaFile) << R"(" group="" part="0" file="results_)";
    *(this->mpVtkMetaFile) << SimulationTime::Instance()->GetTimeStepsElapsed();
    if (PetscTools::IsSequential())
    {
        *(this->mpVtkMetaFile) << ".vtu\"/>\n";
    }
    else
    {
        // Parallel vtu files  .vtu -> .pvtu
        *(this->mpVtkMetaFile) << ".pvtu\"/>\n";
    }
}
 
template<unsigned DIM>
CellPtr NodeBasedCellPopulation<DIM>::AddCell(CellPtr pNewCell, CellPtr pParentCell)
{
    assert(pNewCell);
 
    // Add new cell to population
    CellPtr p_created_cell = AbstractCentreBasedCellPopulation<DIM>::AddCell(pNewCell, pParentCell);
    assert(p_created_cell == pNewCell);
 
    // Then set the new cell radius in the NodesOnlyMesh
    unsigned parent_node_index = this->GetLocationIndexUsingCell(pParentCell);
    Node<DIM>* p_parent_node = this->GetNode(parent_node_index);
 
    unsigned new_node_index = this->GetLocationIndexUsingCell(p_created_cell);
    Node<DIM>* p_new_node = this->GetNode(new_node_index);
 
    p_new_node->SetRadius(p_parent_node->GetRadius());
 
    // Return pointer to new cell
    return p_created_cell;
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AddMovedCell(CellPtr pCell, boost::shared_ptr<Node<DIM> > pNode)
{
    // Create a new node
    mpNodesOnlyMesh->AddMovedNode(pNode);
 
    // Update cells vector
    this->mCells.push_back(pCell);
 
    // Update mappings between cells and location indices
    this->AddCellUsingLocationIndex(pNode->GetIndex(), pCell);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::DeleteMovedCell(unsigned index)
{
    mpNodesOnlyMesh->DeleteMovedNode(index);
 
    // Update vector of cells
    for (std::list<CellPtr>::iterator cell_iter = this->mCells.begin();
         cell_iter != this->mCells.end();
         ++cell_iter)
    {
        if (this->GetLocationIndexUsingCell(*cell_iter) == index)
        {
            // Update mappings between cells and location indices
            this->RemoveCellUsingLocationIndex(index, (*cell_iter));
            cell_iter = this->mCells.erase(cell_iter);
 
            break;
        }
    }
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::SendCellsToNeighbourProcesses()
{
    MPI_Status status;
 
    if (!PetscTools::AmTopMost())
    {
        boost::shared_ptr<std::vector<std::pair<CellPtr, Node<DIM>* > > > p_cells_right(&mCellsToSendRight, null_deleter());
        mpCellsRecvRight = mRightCommunicator.SendRecvObject(p_cells_right, PetscTools::GetMyRank() + 1, mCellCommunicationTag, PetscTools::GetMyRank() + 1, mCellCommunicationTag, status);
    }
    if (!PetscTools::AmMaster())
    {
        boost::shared_ptr<std::vector<std::pair<CellPtr, Node<DIM>* > > > p_cells_left(&mCellsToSendLeft, null_deleter());
        mpCellsRecvLeft = mLeftCommunicator.SendRecvObject(p_cells_left, PetscTools::GetMyRank() - 1, mCellCommunicationTag, PetscTools::GetMyRank() - 1, mCellCommunicationTag, status);
    }
    else if ( mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection()  )
    {
        boost::shared_ptr<std::vector<std::pair<CellPtr, Node<DIM>* > > > p_cells_left(&mCellsToSendLeft, null_deleter());
        mpCellsRecvLeft = mLeftCommunicator.SendRecvObject(p_cells_left, PetscTools::GetNumProcs() - 1, mCellCommunicationTag, PetscTools::GetNumProcs() - 1, mCellCommunicationTag, status);
}
 
    // We need to leave this to the end (rather than as an else if for AmTopMost())
    // otherwise there will be a cyclic send-receive and it will stall
    if ( PetscTools::AmTopMost() && mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection() )
    {
        boost::shared_ptr<std::vector<std::pair<CellPtr, Node<DIM>* > > > p_cells_right(&mCellsToSendRight, null_deleter());
        mpCellsRecvRight = mRightCommunicator.SendRecvObject(p_cells_right, 0, mCellCommunicationTag, 0, mCellCommunicationTag, status);
    }
}
 
// helper function for NonBlockingSendCellsToNeighbourProcess() to calculate the tag
template<unsigned DIM>
unsigned NodeBasedCellPopulation<DIM>::CalculateMessageTag(unsigned senderI, unsigned receiverJ)
{
    /* Old function was overloading integer type for nProcs > 12
     unsigned tag = SmallPow(2u, 1+ PetscTools::GetMyRank() ) * SmallPow (3u, 1 + PetscTools::GetMyRank() + 1);
     Instead we use a Cantor pairing function which produces lower paired values
     See: https://en.wikipedia.org/wiki/Pairing_function */
    unsigned tag = 0.5*((senderI+receiverJ)*(senderI+receiverJ+1) + 2*receiverJ);
    assert(tag < UINT_MAX); //Just make sure doesnt hit UINT_MAX as old method did.
    return tag;
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::NonBlockingSendCellsToNeighbourProcesses()
{
    if (!PetscTools::AmTopMost())
    {
        boost::shared_ptr<std::vector<std::pair<CellPtr, Node<DIM>* > > > p_cells_right(&mCellsToSendRight, null_deleter());
        unsigned tag = CalculateMessageTag( PetscTools::GetMyRank(), PetscTools::GetMyRank()+1 );
        mRightCommunicator.ISendObject(p_cells_right, PetscTools::GetMyRank() + 1, tag);
    }
    if (!PetscTools::AmMaster())
    {
        unsigned tag = CalculateMessageTag( PetscTools::GetMyRank(), PetscTools::GetMyRank()-1 );
        boost::shared_ptr<std::vector<std::pair<CellPtr, Node<DIM>* > > > p_cells_left(&mCellsToSendLeft, null_deleter());
        mLeftCommunicator.ISendObject(p_cells_left, PetscTools::GetMyRank() - 1, tag);
    }
    else if ( mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection() )
    {
        unsigned tag = CalculateMessageTag( PetscTools::GetMyRank(), PetscTools::GetNumProcs()-1 );
        boost::shared_ptr<std::vector<std::pair<CellPtr, Node<DIM>* > > > p_cells_left(&mCellsToSendLeft, null_deleter());
        mLeftCommunicator.ISendObject(p_cells_left, PetscTools::GetNumProcs()-1, tag);
    }
    if ( PetscTools::AmTopMost() && mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection() )
    {
        unsigned tag = CalculateMessageTag( PetscTools::GetMyRank(), 0 );
        boost::shared_ptr<std::vector<std::pair<CellPtr, Node<DIM>* > > > p_cells_right(&mCellsToSendRight, null_deleter());
        mRightCommunicator.ISendObject(p_cells_right, 0, tag);
    }
 
    // Now post receives to start receiving data before returning.
    if (!PetscTools::AmTopMost())
    {
        unsigned tag = CalculateMessageTag( PetscTools::GetMyRank()+1, PetscTools::GetMyRank() );
        mRightCommunicator.IRecvObject(PetscTools::GetMyRank() + 1, tag);
    }
    if (!PetscTools::AmMaster())
    {
        unsigned tag = CalculateMessageTag( PetscTools::GetMyRank()-1, PetscTools::GetMyRank() );
        mLeftCommunicator.IRecvObject(PetscTools::GetMyRank() - 1, tag);
    }
    else if ( mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection() )
    {
        unsigned tag = CalculateMessageTag( PetscTools::GetNumProcs()-1, PetscTools::GetMyRank() );
        mLeftCommunicator.IRecvObject(PetscTools::GetNumProcs() - 1, tag);
}
    if ( PetscTools::AmTopMost() && mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection() )
    {
        unsigned tag = CalculateMessageTag( 0, PetscTools::GetMyRank() );
        mRightCommunicator.IRecvObject(0, tag);
}
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::GetReceivedCells()
{
    if (!PetscTools::AmTopMost())
    {
        mpCellsRecvRight = mRightCommunicator.GetRecvObject();
    }
    if (!PetscTools::AmMaster() || mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection() )
    {
        mpCellsRecvLeft = mLeftCommunicator.GetRecvObject();
    }
    // Periodicity across processors has to be in this set order
    if ( PetscTools::AmTopMost() && mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection() )
    {
        mpCellsRecvRight = mRightCommunicator.GetRecvObject();
}
}
 
template<unsigned DIM>
std::pair<CellPtr, Node<DIM>* > NodeBasedCellPopulation<DIM>::GetCellNodePair(unsigned nodeIndex)
{
    Node<DIM>* p_node = this->GetNode(nodeIndex);
 
    CellPtr p_cell = this->GetCellUsingLocationIndex(nodeIndex);
 
    std::pair<CellPtr, Node<DIM>* > new_pair(p_cell, p_node);
 
    return new_pair;
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AddNodeAndCellToSendRight(unsigned nodeIndex)
{
    std::pair<CellPtr, Node<DIM>* > pair = GetCellNodePair(nodeIndex);
 
    mCellsToSendRight.push_back(pair);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AddNodeAndCellToSendLeft(unsigned nodeIndex)
{
    std::pair<CellPtr, Node<DIM>* > pair = GetCellNodePair(nodeIndex);
 
    mCellsToSendLeft.push_back(pair);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AddReceivedCells()
{
    if (!PetscTools::AmMaster() || mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection() )
    {
        for (typename std::vector<std::pair<CellPtr, Node<DIM>* > >::iterator iter = mpCellsRecvLeft->begin();
             iter != mpCellsRecvLeft->end();
             ++iter)
        {
            // Make a shared pointer to the node to make sure it is correctly deleted.
            boost::shared_ptr<Node<DIM> > p_node(iter->second);
            AddMovedCell(iter->first, p_node);
        }
    }
    if (!PetscTools::AmTopMost() || mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection())
    {
        for (typename std::vector<std::pair<CellPtr, Node<DIM>* > >::iterator iter = mpCellsRecvRight->begin();
             iter != mpCellsRecvRight->end();
             ++iter)
        {
            boost::shared_ptr<Node<DIM> > p_node(iter->second);
            AddMovedCell(iter->first, p_node);
        }
    }
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::UpdateCellProcessLocation()
{
    mpNodesOnlyMesh->ResizeBoxCollection();
 
    mpNodesOnlyMesh->CalculateNodesOutsideLocalDomain();
 
    std::vector<unsigned> nodes_to_send_right = mpNodesOnlyMesh->rGetNodesToSendRight();
    AddCellsToSendRight(nodes_to_send_right);
 
    std::vector<unsigned> nodes_to_send_left = mpNodesOnlyMesh->rGetNodesToSendLeft();
    AddCellsToSendLeft(nodes_to_send_left);
 
    // Post non-blocking send / receives so communication on both sides can start.
    SendCellsToNeighbourProcesses();
 
    // Post blocking receive calls that wait until communication complete.
    //GetReceivedCells();
 
    for (std::vector<unsigned>::iterator iter = nodes_to_send_right.begin();
         iter != nodes_to_send_right.end();
         ++iter)
    {
        DeleteMovedCell(*iter);
    }
 
    for (std::vector<unsigned>::iterator iter = nodes_to_send_left.begin();
         iter != nodes_to_send_left.end();
         ++iter)
    {
        DeleteMovedCell(*iter);
    }
 
    AddReceivedCells();
 
    NodeMap map(1 + mpNodesOnlyMesh->GetMaximumNodeIndex());
    mpNodesOnlyMesh->ReMesh(map);
    UpdateMapsAfterRemesh(map);
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::RefreshHaloCells()
{
    mpNodesOnlyMesh->ClearHaloNodes();
 
    mHaloCells.clear();
    mHaloCellLocationMap.clear();
    mLocationHaloCellMap.clear();
 
    std::vector<unsigned> halos_to_send_right = mpNodesOnlyMesh->rGetHaloNodesToSendRight();
    AddCellsToSendRight(halos_to_send_right);
 
    std::vector<unsigned> halos_to_send_left = mpNodesOnlyMesh->rGetHaloNodesToSendLeft();
    AddCellsToSendLeft(halos_to_send_left);
 
    NonBlockingSendCellsToNeighbourProcesses();
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AddCellsToSendRight(std::vector<unsigned>& cellLocationIndices)
{
    mCellsToSendRight.clear();
 
    for (unsigned i=0; i < cellLocationIndices.size(); i++)
    {
        AddNodeAndCellToSendRight(cellLocationIndices[i]);
    }
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AddCellsToSendLeft(std::vector<unsigned>& cellLocationIndices)
{
    mCellsToSendLeft.clear();
 
    for (unsigned i=0; i < cellLocationIndices.size(); i++)
    {
        AddNodeAndCellToSendLeft(cellLocationIndices[i]);
    }
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AddReceivedHaloCells()
{
    GetReceivedCells();
 
    if (!PetscTools::AmMaster() || mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection())
    {
        for (typename std::vector<std::pair<CellPtr, Node<DIM>* > >::iterator iter = mpCellsRecvLeft->begin();
                iter != mpCellsRecvLeft->end();
                ++iter)
        {
            boost::shared_ptr<Node<DIM> > p_node(iter->second);
            AddHaloCell(iter->first, p_node);
 
        }
    }
    if (!PetscTools::AmTopMost() || mpNodesOnlyMesh->GetIsPeriodicAcrossProcsFromBoxCollection())
    {
        for (typename std::vector<std::pair<CellPtr, Node<DIM>* > >::iterator iter = mpCellsRecvRight->begin();
                iter != mpCellsRecvRight->end();
                ++iter)
        {
            boost::shared_ptr<Node<DIM> > p_node(iter->second);
            AddHaloCell(iter->first, p_node);
        }
    }
 
    mpNodesOnlyMesh->AddHaloNodesToBoxes();
}
 
template<unsigned DIM>
void NodeBasedCellPopulation<DIM>::AddHaloCell(CellPtr pCell, boost::shared_ptr<Node<DIM> > pNode)
{
    mHaloCells.push_back(pCell);
 
    mpNodesOnlyMesh->AddHaloNode(pNode);
 
    mHaloCellLocationMap[pCell] = pNode->GetIndex();
 
    mLocationHaloCellMap[pNode->GetIndex()] = pCell;
}
 
// Explicit instantiation
template class NodeBasedCellPopulation<1>;
template class NodeBasedCellPopulation<2>;
template class NodeBasedCellPopulation<3>;
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
EXPORT_TEMPLATE_CLASS_SAME_DIMS(NodeBasedCellPopulation)