AbstractBoxDomainPdeModifier.cpp

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#include "AbstractBoxDomainPdeModifier.hpp"
#include "ReplicatableVector.hpp"
#include "LinearBasisFunction.hpp"
 
template<unsigned DIM>
AbstractBoxDomainPdeModifier<DIM>::AbstractBoxDomainPdeModifier(boost::shared_ptr<AbstractLinearPde<DIM,DIM> > pPde,
                                                                boost::shared_ptr<AbstractBoundaryCondition<DIM> > pBoundaryCondition,
                                                                bool isNeumannBoundaryCondition,
                                                                boost::shared_ptr<ChasteCuboid<DIM> > pMeshCuboid,
                                                                double stepSize,
                                                                Vec solution)
    : AbstractPdeModifier<DIM>(pPde,
                               pBoundaryCondition,
                               isNeumannBoundaryCondition,
                               solution),
      mpMeshCuboid(pMeshCuboid),
      mStepSize(stepSize),
      mSetBcsOnBoxBoundary(true),
      mSetBcsOnBoundingSphere(false),
      mUseVoronoiCellsForInterpolation(false),
      mTypicalCellRadius(0.5) // defaults to 0.5
{
    if (pMeshCuboid)
    {
        // We only need to generate mpFeMesh once, as it does not vary with time
        this->GenerateFeMesh(mpMeshCuboid, mStepSize);
        this->mDeleteFeMesh = true;
        // Initialise the boundary nodes
        this->mIsDirichletBoundaryNode = std::vector<double>(this->mpFeMesh->GetNumNodes(), 0.0);
    }
}
 
template<unsigned DIM>
double AbstractBoxDomainPdeModifier<DIM>::GetStepSize() const
{
     return mStepSize;
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::SetBcsOnBoxBoundary(const bool setBcsOnBoxBoundary)
{
    mSetBcsOnBoxBoundary = setBcsOnBoxBoundary;
}
 
template<unsigned DIM>
bool AbstractBoxDomainPdeModifier<DIM>::AreBcsSetOnBoxBoundary() const
{
    return mSetBcsOnBoxBoundary;
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::SetBcsOnBoundingSphere(const bool setBcsOnBoundingSphere)
{
    mSetBcsOnBoundingSphere = setBcsOnBoundingSphere;
}
 
template<unsigned DIM>
bool AbstractBoxDomainPdeModifier<DIM>::AreBcsSetOnBoundingSphere() const
{
    return mSetBcsOnBoundingSphere;
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::SetUseVoronoiCellsForInterpolation(const bool useVoronoiCellsForInterpolation)
{
    mUseVoronoiCellsForInterpolation = useVoronoiCellsForInterpolation;
}
 
template<unsigned DIM>
bool AbstractBoxDomainPdeModifier<DIM>::GetUseVoronoiCellsForInterpolation() const
{
    return mUseVoronoiCellsForInterpolation;
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::SetTypicalCellRadius(const double typicalCellRadius)
{
    assert(mTypicalCellRadius>=0.0);
    mTypicalCellRadius = typicalCellRadius;
}
 
template<unsigned DIM>
double AbstractBoxDomainPdeModifier<DIM>::GetTypicalCellRadius() const
{
    return mTypicalCellRadius;
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::ConstructBoundaryConditionsContainerHelper(AbstractCellPopulation<DIM,DIM>& rCellPopulation,
                                                                                   std::shared_ptr<BoundaryConditionsContainer<DIM,DIM,1> > pBcc)
{
    if (!this->mSetBcsOnBoxBoundary)
    {
        // Here we approximate the cell population by the bounding sphere and apply the boundary conditions outside the sphere.
        if (this->mSetBcsOnBoundingSphere)
        {
            // First find the centre of the tissue by choosing the midpoint of the extrema.
            c_vector<double, DIM> tissue_maxima = zero_vector<double>(DIM);
            c_vector<double, DIM> tissue_minima = zero_vector<double>(DIM);
            for (unsigned i = 0; i < DIM; i++)
            {
                tissue_maxima[i] = -DBL_MAX;
                tissue_minima[i] = DBL_MAX;
            }
            
            
            for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
                cell_iter != rCellPopulation.End();
                ++cell_iter)
            {
                const ChastePoint<DIM>& r_position_of_cell = rCellPopulation.GetLocationOfCellCentre(*cell_iter);
                
                for (unsigned i = 0; i < DIM; i++)
                {
                    if (r_position_of_cell[i] > tissue_maxima[i])
                    {
                        tissue_maxima[i] = r_position_of_cell[i];
                    }
                    if (r_position_of_cell[i] < tissue_minima[i])
                    {
                        tissue_minima[i] = r_position_of_cell[i];
                    }
                }               
            }
 
            c_vector<double, DIM> tissue_centre = 0.5*(tissue_maxima + tissue_minima);
 
 
            double tissue_radius = 0.0;
            for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
                cell_iter != rCellPopulation.End();
                ++cell_iter)
            {
                const ChastePoint<DIM>& r_position_of_cell = rCellPopulation.GetLocationOfCellCentre(*cell_iter);
 
                double radius = norm_2(tissue_centre - r_position_of_cell.rGetLocation());
                
                if (tissue_radius < radius)
                {
                    tissue_radius = radius;
                }                
            }
 
            // Apply boundary condition to the nodes outside the tissue_radius
            if (this->IsNeumannBoundaryCondition())
            {
                NEVER_REACHED;
            }
            else
            {
                // Impose any Dirichlet boundary conditions
                for (unsigned i=0; i<this->mpFeMesh->GetNumNodes(); i++)
                {
                    double radius = norm_2(tissue_centre - this->mpFeMesh->GetNode(i)->rGetLocation());
                    
                    if (radius > tissue_radius)
                    {
                        pBcc->AddDirichletBoundaryCondition(this->mpFeMesh->GetNode(i), this->mpBoundaryCondition.get(), 0, false);
                        this->mIsDirichletBoundaryNode[i] = 1.0;
                    }
                }
            }
        }
        else // Set pde nodes as boundary node if elements don't contain cells or nodes aren't within 0.5CD of a cell centre
        {
            // Get the set of coarse element indices that contain cells
            std::set<unsigned> coarse_element_indices_in_map;
            for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
                cell_iter != rCellPopulation.End();
                ++cell_iter)
            {
                coarse_element_indices_in_map.insert(this->mCellPdeElementMap[*cell_iter]);
            }
 
            // Find the node indices associated with elements whose indices are NOT in the set coarse_element_indices_in_map
            std::set<unsigned> coarse_mesh_boundary_node_indices;
            for (unsigned i=0; i<this->mpFeMesh->GetNumElements(); i++)
            {
                if (coarse_element_indices_in_map.find(i) == coarse_element_indices_in_map.end())
                {
                    Element<DIM,DIM>* p_element = this->mpFeMesh->GetElement(i);
                    for (unsigned j=0; j<DIM+1; j++)
                    {
                        unsigned node_index = p_element->GetNodeGlobalIndex(j);
                        coarse_mesh_boundary_node_indices.insert(node_index);
                    }
                }
            }
 
            // Also remove nodes that are within the typical cell radius from the centre of a cell.
            std::set<unsigned> nearby_node_indices;
            for (unsigned int coarse_mesh_boundary_node_idx : coarse_mesh_boundary_node_indices)
            {
                bool remove_node = false;
 
                c_vector<double,DIM> node_location = this->mpFeMesh->GetNode(coarse_mesh_boundary_node_idx)->rGetLocation();
 
                for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
                cell_iter != rCellPopulation.End();
                ++cell_iter)
                {
                    const ChastePoint<DIM>& r_position_of_cell = rCellPopulation.GetLocationOfCellCentre(*cell_iter);
 
                    double separation = norm_2(node_location - r_position_of_cell.rGetLocation());
 
                    if (separation <= mTypicalCellRadius)
                    {
                        remove_node = true;
                        break;
                    }                
                }
 
                if (remove_node)
                {
                    // Node near cell so set it to be removed from boundary set
                    nearby_node_indices.insert(coarse_mesh_boundary_node_idx);
                }
            }
 
            // Remove nodes that are near cells from boundary set
            for (unsigned int nearby_node_idx : nearby_node_indices)
            {
                coarse_mesh_boundary_node_indices.erase(nearby_node_idx);
            }
 
 
            // Apply boundary condition to the nodes in the set coarse_mesh_boundary_node_indices
            if (this->IsNeumannBoundaryCondition())
            {
                NEVER_REACHED;
            }
            else
            {
                // Impose any Dirichlet boundary conditions
                for (unsigned int coarse_mesh_boundary_node_idx : coarse_mesh_boundary_node_indices)
                {
                    pBcc->AddDirichletBoundaryCondition(this->mpFeMesh->GetNode(coarse_mesh_boundary_node_idx), this->mpBoundaryCondition.get(), 0, false);
                    this->mIsDirichletBoundaryNode[coarse_mesh_boundary_node_idx] = 1.0;
                }
            }
        }
    }
    else // Apply BC at boundary of box domain FE mesh
    {
        if (this->IsNeumannBoundaryCondition())
        {
            // Impose any Neumann boundary conditions
            for (auto elem_iter = this->mpFeMesh->GetBoundaryElementIteratorBegin();
                 elem_iter != this->mpFeMesh->GetBoundaryElementIteratorEnd();
                 ++elem_iter)
            {
                pBcc->AddNeumannBoundaryCondition(*elem_iter, this->mpBoundaryCondition.get());
            }
        }
        else
        {
            // Impose any Dirichlet boundary conditions
            for (auto node_iter = this->mpFeMesh->GetBoundaryNodeIteratorBegin();
                 node_iter != this->mpFeMesh->GetBoundaryNodeIteratorEnd();
                 ++node_iter)
            {
                pBcc->AddDirichletBoundaryCondition(*node_iter, this->mpBoundaryCondition.get());
                this->mIsDirichletBoundaryNode[(*node_iter)->GetIndex()] = 1.0;
            }
        }
    }
}
 
 
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::SetupSolve(AbstractCellPopulation<DIM,DIM>& rCellPopulation, std::string outputDirectory)
{
    AbstractPdeModifier<DIM>::SetupSolve(rCellPopulation, outputDirectory);
 
    InitialiseCellPdeElementMap(rCellPopulation);
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::GenerateFeMesh(boost::shared_ptr<ChasteCuboid<DIM> > pMeshCuboid, double stepSize)
{
    // Create a regular coarse tetrahedral mesh
    this->mpFeMesh = new TetrahedralMesh<DIM,DIM>();
    
    GenerateAndReturnFeMesh(pMeshCuboid, stepSize, this->mpFeMesh);
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::GenerateAndReturnFeMesh(boost::shared_ptr<ChasteCuboid<DIM> > pMeshCuboid, double stepSize, TetrahedralMesh<DIM,DIM>* pMesh)
{
    // Create a regular coarse tetrahedral mesh
    switch (DIM)
    {
        case 1:
            pMesh->ConstructRegularSlabMesh(stepSize, pMeshCuboid->GetWidth(0));
            break;
        case 2:
            pMesh->ConstructRegularSlabMesh(stepSize, pMeshCuboid->GetWidth(0), pMeshCuboid->GetWidth(1));
            break;
        case 3:
            pMesh->ConstructRegularSlabMesh(stepSize, pMeshCuboid->GetWidth(0), pMeshCuboid->GetWidth(1), pMeshCuboid->GetWidth(2));
            break;
        default:
            NEVER_REACHED;
    }
 
    // Get centroid of meshCuboid
    ChastePoint<DIM> upper = pMeshCuboid->rGetUpperCorner();
    ChastePoint<DIM> lower = pMeshCuboid->rGetLowerCorner();
    c_vector<double,DIM> centre_of_cuboid = 0.5*(upper.rGetLocation() + lower.rGetLocation());
 
    // Find the centre of the PDE mesh
    c_vector<double,DIM> centre_of_coarse_mesh = zero_vector<double>(DIM);
    for (unsigned i=0; i<pMesh->GetNumNodes(); i++)
    {
        centre_of_coarse_mesh += pMesh->GetNode(i)->rGetLocation();
    }
    centre_of_coarse_mesh /= pMesh->GetNumNodes();
 
    // Now move the mesh to the correct location
    pMesh->Translate(centre_of_cuboid - centre_of_coarse_mesh);
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::UpdateCellData(AbstractCellPopulation<DIM,DIM>& rCellPopulation)
{
    // Store the PDE solution in an accessible form
    ReplicatableVector solution_repl(this->mSolution);
 
    if (mUseVoronoiCellsForInterpolation) 
    {
        unsigned num_nodes = rCellPopulation.GetNumNodes();
 
        std::vector<double> cell_data(num_nodes, -1);
        std::vector<unsigned> num_cells(num_nodes, -1);
        
        for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
            cell_iter != rCellPopulation.End();
            ++cell_iter)
        {
            unsigned cell_location_index = rCellPopulation.GetLocationIndexUsingCell(*cell_iter);
            cell_data[cell_location_index]=0.0;
            num_cells[cell_location_index]=0;    
        }
 
        // Loop over nodes of the finite element mesh and work out which voronoi region the node is in.
        for (typename TetrahedralMesh<DIM,DIM>::NodeIterator node_iter = this->mpFeMesh->GetNodeIteratorBegin();
                node_iter != this->mpFeMesh->GetNodeIteratorEnd();
                ++node_iter)
        {
            unsigned node_index = node_iter->GetIndex();
 
            c_vector<double,DIM> node_location = node_iter->rGetLocation();
 
            double closest_separation = DBL_MAX;
            unsigned nearest_cell = UNSIGNED_UNSET;
 
            for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
                cell_iter != rCellPopulation.End();
                ++cell_iter)
            {
                c_vector<double, DIM> cell_location = rCellPopulation.GetLocationOfCellCentre(*cell_iter);
 
                double separation = norm_2(node_location - cell_location);
 
                if (separation < closest_separation)
                {
                    closest_separation = separation;
                    nearest_cell = rCellPopulation.GetLocationIndexUsingCell(*cell_iter);
                }                
            }
            assert(closest_separation<DBL_MAX);
 
            cell_data[nearest_cell] = cell_data[nearest_cell] + solution_repl[node_index];
            num_cells[nearest_cell] = num_cells[nearest_cell] + 1;
        }   
        
        // Now calculate the solution in the cell by averaging over all nodes in the voronoi region.
        for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
        cell_iter != rCellPopulation.End();
        ++cell_iter)
        {
            unsigned cell_location_index = rCellPopulation.GetLocationIndexUsingCell(*cell_iter);   
 
            
            if (num_cells[cell_location_index]==0)
            {
                EXCEPTION("One or more of the cells doesnt contain any pde nodes so cant use Voronoi CellData calculation in the ");
            }
 
            double  solution_at_cell = cell_data[cell_location_index]/num_cells[cell_location_index];
            
            cell_iter->GetCellData()->SetItem(this->mDependentVariableName, solution_at_cell);
        }
 
        if (this->mOutputGradient)
        {
            // This is not implemented yet
            NEVER_REACHED;
        }
    }  
    else // Interpolate solutions 
    {
        for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
            cell_iter != rCellPopulation.End();
            ++cell_iter)
        {
            // The cells are not nodes of the mesh, so we must interpolate
            double solution_at_cell = 0.0;
 
            // Find the element in the FE mesh that contains this cell. CellElementMap has been updated so use this.
            unsigned elem_index = mCellPdeElementMap[*cell_iter];
            Element<DIM,DIM>* p_element = this->mpFeMesh->GetElement(elem_index);
 
            const ChastePoint<DIM>& node_location = rCellPopulation.GetLocationOfCellCentre(*cell_iter);
 
            c_vector<double,DIM+1> weights = p_element->CalculateInterpolationWeights(node_location);
 
            for (unsigned i=0; i<DIM+1; i++)
            {
                double nodal_value = solution_repl[p_element->GetNodeGlobalIndex(i)];
                solution_at_cell += nodal_value * weights(i);
            }
 
            cell_iter->GetCellData()->SetItem(this->mDependentVariableName, solution_at_cell);
 
            if (this->mOutputGradient)
            {
                // Now calculate the gradient of the solution and store this in CellVecData
                c_vector<double, DIM> solution_gradient = zero_vector<double>(DIM);
 
                // Calculate the basis functions at any point (e.g. zero) in the element
                c_matrix<double, DIM, DIM> jacobian, inverse_jacobian;
                double jacobian_det;
                this->mpFeMesh->GetInverseJacobianForElement(elem_index, jacobian, jacobian_det, inverse_jacobian);
                const ChastePoint<DIM> zero_point;
                c_matrix<double, DIM, DIM+1> grad_phi;
                LinearBasisFunction<DIM>::ComputeTransformedBasisFunctionDerivatives(zero_point, inverse_jacobian, grad_phi);
 
                for (unsigned node_index=0; node_index<DIM+1; node_index++)
                {
                    double nodal_value = solution_repl[p_element->GetNodeGlobalIndex(node_index)];
 
                    for (unsigned j=0; j<DIM; j++)
                    {
                        solution_gradient(j) += nodal_value* grad_phi(j, node_index);
                    }
                }
 
                switch (DIM)
                {
                    case 1:
                        cell_iter->GetCellData()->SetItem(this->mDependentVariableName+"_grad_x", solution_gradient(0));
                        break;
                    case 2:
                        cell_iter->GetCellData()->SetItem(this->mDependentVariableName+"_grad_x", solution_gradient(0));
                        cell_iter->GetCellData()->SetItem(this->mDependentVariableName+"_grad_y", solution_gradient(1));
                        break;
                    case 3:
                        cell_iter->GetCellData()->SetItem(this->mDependentVariableName+"_grad_x", solution_gradient(0));
                        cell_iter->GetCellData()->SetItem(this->mDependentVariableName+"_grad_y", solution_gradient(1));
                        cell_iter->GetCellData()->SetItem(this->mDependentVariableName+"_grad_z", solution_gradient(2));
                        break;
                    default:
                        NEVER_REACHED;
                }
            }
        }
    }     
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::InitialiseCellPdeElementMap(AbstractCellPopulation<DIM,DIM>& rCellPopulation)
{
    mCellPdeElementMap.clear();
 
    // Find the element of mpFeMesh that contains each cell and populate mCellPdeElementMap
    for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
         cell_iter != rCellPopulation.End();
         ++cell_iter)
    {
        const ChastePoint<DIM>& r_position_of_cell = rCellPopulation.GetLocationOfCellCentre(*cell_iter);
        unsigned elem_index = this->mpFeMesh->GetContainingElementIndex(r_position_of_cell);
        mCellPdeElementMap[*cell_iter] = elem_index;
    }
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::UpdateCellPdeElementMap(AbstractCellPopulation<DIM,DIM>& rCellPopulation)
{
    // Find the element of mpCoarsePdeMesh that contains each cell and populate mCellPdeElementMap
    for (typename AbstractCellPopulation<DIM>::Iterator cell_iter = rCellPopulation.Begin();
         cell_iter != rCellPopulation.End();
         ++cell_iter)
    {
        const ChastePoint<DIM>& r_position_of_cell = rCellPopulation.GetLocationOfCellCentre(*cell_iter);
        unsigned elem_index = this->mpFeMesh->GetContainingElementIndexWithInitialGuess(r_position_of_cell, mCellPdeElementMap[*cell_iter]);
        mCellPdeElementMap[*cell_iter] = elem_index;
    }
}
 
template<unsigned DIM>
void AbstractBoxDomainPdeModifier<DIM>::OutputSimulationModifierParameters(out_stream& rParamsFile)
{
    // No parameters to output, so just call method on direct parent class
    AbstractPdeModifier<DIM>::OutputSimulationModifierParameters(rParamsFile);
}
 
// Explicit instantiation
template class AbstractBoxDomainPdeModifier<1>;
template class AbstractBoxDomainPdeModifier<2>;
template class AbstractBoxDomainPdeModifier<3>;