LinearParabolicPdeSystemWithCoupledOdeSystemSolver.hpp

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*/
#ifndef LINEARPARABOLICPDESYSTEMWITHCOUPLEDODESYSTEMSOLVER_HPP_
#define LINEARPARABOLICPDESYSTEMWITHCOUPLEDODESYSTEMSOLVER_HPP_

#include "AbstractAssemblerSolverHybrid.hpp"
#include "AbstractDynamicLinearPdeSolver.hpp"
#include "AbstractLinearParabolicPdeSystemForCoupledOdeSystem.hpp"
#include "TetrahedralMesh.hpp"
#include "BoundaryConditionsContainer.hpp"
#include "AbstractOdeSystemForCoupledPdeSystem.hpp"
#include "CvodeAdaptor.hpp"
#include "BackwardEulerIvpOdeSolver.hpp"
#include "Warnings.hpp"
#include "VtkMeshWriter.hpp"

#include <boost/shared_ptr.hpp>

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM=ELEMENT_DIM, unsigned PROBLEM_DIM=1>
class LinearParabolicPdeSystemWithCoupledOdeSystemSolver
    : public AbstractAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, NORMAL>,
      public AbstractDynamicLinearPdeSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>
{
private:

    AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* mpMesh;

    AbstractLinearParabolicPdeSystemForCoupledOdeSystem<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* mpPdeSystem;

    std::vector<AbstractOdeSystemForCoupledPdeSystem*> mOdeSystemsAtNodes;

    std::vector<double> mInterpolatedOdeStateVariables;

    boost::shared_ptr<AbstractIvpOdeSolver> mpOdeSolver;

    double mSamplingTimeStep;

    bool mOdeSystemsPresent;

    out_stream mpVtkMetaFile;

    bool mClearOutputDirectory;

    void WriteVtkResultsToFile();

    c_matrix<double, PROBLEM_DIM*(ELEMENT_DIM+1), PROBLEM_DIM*(ELEMENT_DIM+1)> ComputeMatrixTerm(
        c_vector<double, ELEMENT_DIM+1>& rPhi,
        c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
        ChastePoint<SPACE_DIM>& rX,
        c_vector<double,PROBLEM_DIM>& rU,
        c_matrix<double, PROBLEM_DIM, SPACE_DIM>& rGradU,
        Element<ELEMENT_DIM, SPACE_DIM>* pElement);

    c_vector<double, PROBLEM_DIM*(ELEMENT_DIM+1)> ComputeVectorTerm(
        c_vector<double, ELEMENT_DIM+1>& rPhi,
        c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
        ChastePoint<SPACE_DIM>& rX,
        c_vector<double,PROBLEM_DIM>& rU,
        c_matrix<double,PROBLEM_DIM,SPACE_DIM>& rGradU,
        Element<ELEMENT_DIM, SPACE_DIM>* pElement);

    void ResetInterpolatedQuantities();

    void IncrementInterpolatedQuantities(double phiI, const Node<SPACE_DIM>* pNode);

    void InitialiseForSolve(Vec initialSolution=NULL);

    void SetupLinearSystem(Vec currentSolution, bool computeMatrix);

public:

    LinearParabolicPdeSystemWithCoupledOdeSystemSolver(TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* pMesh,
                                                       AbstractLinearParabolicPdeSystemForCoupledOdeSystem<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* pPdeSystem,
                                                       BoundaryConditionsContainer<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* pBoundaryConditions,
                                                       std::vector<AbstractOdeSystemForCoupledPdeSystem*> odeSystemsAtNodes=std::vector<AbstractOdeSystemForCoupledPdeSystem*>(),
                                                       boost::shared_ptr<AbstractIvpOdeSolver> pOdeSolver=boost::shared_ptr<AbstractIvpOdeSolver>());

    ~LinearParabolicPdeSystemWithCoupledOdeSystemSolver();

    void PrepareForSetupLinearSystem(Vec currentPdeSolution);

    void SetOutputDirectory(std::string outputDirectory, bool clearDirectory=false);

    void SetSamplingTimeStep(double samplingTimeStep);

    void SolveAndWriteResultsToFile();

    void WriteVtkResultsToFile(Vec solution, unsigned numTimeStepsElapsed);

    AbstractOdeSystemForCoupledPdeSystem* GetOdeSystemAtNode(unsigned index);
};

// Implementation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
c_matrix<double, PROBLEM_DIM*(ELEMENT_DIM+1), PROBLEM_DIM*(ELEMENT_DIM+1)> LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::ComputeMatrixTerm(
    c_vector<double, ELEMENT_DIM+1>& rPhi,
    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
    ChastePoint<SPACE_DIM>& rX,
    c_vector<double,PROBLEM_DIM>& rU,
    c_matrix<double, PROBLEM_DIM, SPACE_DIM>& rGradU,
    Element<ELEMENT_DIM, SPACE_DIM>* pElement)
{
    double timestep_inverse = PdeSimulationTime::GetPdeTimeStepInverse();
    c_matrix<double, PROBLEM_DIM*(ELEMENT_DIM+1), PROBLEM_DIM*(ELEMENT_DIM+1)> matrix_term = zero_matrix<double>(PROBLEM_DIM*(ELEMENT_DIM+1), PROBLEM_DIM*(ELEMENT_DIM+1));

    // Loop over PDEs and populate matrix_term
    for (unsigned pde_index=0; pde_index<PROBLEM_DIM; pde_index++)
    {
        double this_dudt_coefficient = mpPdeSystem->ComputeDuDtCoefficientFunction(rX, pde_index);
        c_matrix<double, SPACE_DIM, SPACE_DIM> this_pde_diffusion_term = mpPdeSystem->ComputeDiffusionTerm(rX, pde_index, pElement);
        c_matrix<double, 1*(ELEMENT_DIM+1), 1*(ELEMENT_DIM+1)> this_stiffness_matrix =
            prod(trans(rGradPhi), c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>(prod(this_pde_diffusion_term, rGradPhi)) )
                + timestep_inverse * this_dudt_coefficient * outer_prod(rPhi, rPhi);

        for (unsigned i=0; i<ELEMENT_DIM+1; i++)
        {
            for (unsigned j=0; j<ELEMENT_DIM+1; j++)
            {
                matrix_term(i*PROBLEM_DIM + pde_index, j*PROBLEM_DIM + pde_index) = this_stiffness_matrix(i,j);
            }
        }
    }
    return matrix_term;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
c_vector<double, PROBLEM_DIM*(ELEMENT_DIM+1)> LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::ComputeVectorTerm(
    c_vector<double, ELEMENT_DIM+1>& rPhi,
    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rGradPhi,
    ChastePoint<SPACE_DIM>& rX,
    c_vector<double,PROBLEM_DIM>& rU,
    c_matrix<double,PROBLEM_DIM,SPACE_DIM>& rGradU,
    Element<ELEMENT_DIM, SPACE_DIM>* pElement)
{
    double timestep_inverse = PdeSimulationTime::GetPdeTimeStepInverse();
    c_vector<double, PROBLEM_DIM*(ELEMENT_DIM+1)> vector_term = zero_vector<double>(PROBLEM_DIM*(ELEMENT_DIM+1));

    // Loop over PDEs and populate vector_term
    for (unsigned pde_index=0; pde_index<PROBLEM_DIM; pde_index++)
    {
        double this_dudt_coefficient = mpPdeSystem->ComputeDuDtCoefficientFunction(rX, pde_index);
        double this_source_term = mpPdeSystem->ComputeSourceTerm(rX, rU, mInterpolatedOdeStateVariables, pde_index);
        c_vector<double, ELEMENT_DIM+1> this_vector_term = (this_source_term + timestep_inverse*this_dudt_coefficient*rU(pde_index))* rPhi;

        for (unsigned i=0; i<ELEMENT_DIM+1; i++)
        {
            vector_term(i*PROBLEM_DIM + pde_index) = this_vector_term(i);
        }
    }

    return vector_term;
}


template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::ResetInterpolatedQuantities()
{
    mInterpolatedOdeStateVariables.clear();

    if (mOdeSystemsPresent)
    {
        unsigned num_state_variables = mOdeSystemsAtNodes[0]->GetNumberOfStateVariables();
        mInterpolatedOdeStateVariables.resize(num_state_variables, 0.0);
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::IncrementInterpolatedQuantities(double phiI, const Node<SPACE_DIM>* pNode)
{
    if (mOdeSystemsPresent)
    {
        unsigned num_state_variables = mOdeSystemsAtNodes[0]->GetNumberOfStateVariables();

        for (unsigned i=0; i<num_state_variables; i++)
        {
            mInterpolatedOdeStateVariables[i] += phiI * mOdeSystemsAtNodes[pNode->GetIndex()]->rGetStateVariables()[i];
        }
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::InitialiseForSolve(Vec initialSolution)
{
    if (this->mpLinearSystem == NULL)
    {
        unsigned preallocation = mpMesh->CalculateMaximumContainingElementsPerProcess() + ELEMENT_DIM;
        if (ELEMENT_DIM > 1)
        {
            // Highest connectivity is closed
            preallocation--;
        }
        preallocation *= PROBLEM_DIM;

        /*
         * Use the current solution (ie the initial solution) as the
         * template in the alternative constructor of LinearSystem.
         * This is to avoid problems with VecScatter.
         */
        this->mpLinearSystem = new LinearSystem(initialSolution, preallocation);
    }

    assert(this->mpLinearSystem);
    this->mpLinearSystem->SetMatrixIsSymmetric(true);
    this->mpLinearSystem->SetKspType("cg");
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::SetupLinearSystem(Vec currentSolution, bool computeMatrix)
{
    this->SetupGivenLinearSystem(currentSolution, computeMatrix, this->mpLinearSystem);
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::LinearParabolicPdeSystemWithCoupledOdeSystemSolver(
        TetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* pMesh,
        AbstractLinearParabolicPdeSystemForCoupledOdeSystem<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* pPdeSystem,
        BoundaryConditionsContainer<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* pBoundaryConditions,
        std::vector<AbstractOdeSystemForCoupledPdeSystem*> odeSystemsAtNodes,
        boost::shared_ptr<AbstractIvpOdeSolver> pOdeSolver)
    : AbstractAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, NORMAL>(pMesh, pBoundaryConditions),
      AbstractDynamicLinearPdeSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>(pMesh),
      mpMesh(pMesh),
      mpPdeSystem(pPdeSystem),
      mOdeSystemsAtNodes(odeSystemsAtNodes),
      mpOdeSolver(pOdeSolver),
      mSamplingTimeStep(DOUBLE_UNSET),
      mOdeSystemsPresent(false),
      mClearOutputDirectory(false)
{
    this->mpBoundaryConditions = pBoundaryConditions;

    /*
     * If any ODE systems are passed in to the constructor, then we aren't just
     * solving a coupled PDE system, in which case the number of ODE system objects
     * must match the number of nodes in the finite element mesh.
     */
    if (!mOdeSystemsAtNodes.empty())
    {
        mOdeSystemsPresent = true;
        assert(mOdeSystemsAtNodes.size() == mpMesh->GetNumNodes());

        /*
         * In this case, if an ODE solver is not explicitly passed into the
         * constructor, then we create a default solver.
         */
        if (!mpOdeSolver)
        {
#ifdef CHASTE_CVODE
            mpOdeSolver.reset(new CvodeAdaptor);
#else
            mpOdeSolver.reset(new BackwardEulerIvpOdeSolver(mOdeSystemsAtNodes[0]->GetNumberOfStateVariables()));
#endif //CHASTE_CVODE
        }
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::~LinearParabolicPdeSystemWithCoupledOdeSystemSolver()
{
    if (mOdeSystemsPresent)
    {
        for (unsigned i=0; i<mOdeSystemsAtNodes.size(); i++)
        {
            delete mOdeSystemsAtNodes[i];
        }
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::PrepareForSetupLinearSystem(Vec currentPdeSolution)
{
    if (mOdeSystemsPresent)
    {
        double time = PdeSimulationTime::GetTime();
        double next_time = PdeSimulationTime::GetNextTime();
        double dt = PdeSimulationTime::GetPdeTimeStep();

        ReplicatableVector soln_repl(currentPdeSolution);
        std::vector<double> current_soln_this_node(PROBLEM_DIM);

        // Loop over nodes
        for (unsigned node_index=0; node_index<mpMesh->GetNumNodes(); node_index++)
        {
            // Store the current solution to the PDE system at this node
            for (unsigned pde_index=0; pde_index<PROBLEM_DIM; pde_index++)
            {
                double current_soln_this_pde_this_node = soln_repl[PROBLEM_DIM*node_index + pde_index];
                current_soln_this_node[pde_index] = current_soln_this_pde_this_node;
            }

            // Pass it into the ODE system at this node
            mOdeSystemsAtNodes[node_index]->SetPdeSolution(current_soln_this_node);

            // Solve ODE system at this node
            mpOdeSolver->SolveAndUpdateStateVariable(mOdeSystemsAtNodes[node_index], time, next_time, dt);
        }
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::SetOutputDirectory(std::string outputDirectory, bool clearDirectory)
{
    mClearOutputDirectory = clearDirectory;
    this->mOutputDirectory = outputDirectory;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::SetSamplingTimeStep(double samplingTimeStep)
{
    assert(samplingTimeStep >= this->mIdealTimeStep);
    mSamplingTimeStep = samplingTimeStep;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::SolveAndWriteResultsToFile()
{
    // A number of methods must have been called prior to this method
    if (this->mOutputDirectory == "")
    {
        EXCEPTION("SetOutputDirectory() must be called prior to SolveAndWriteResultsToFile()");
    }
    if (this->mTimesSet == false)
    {
        EXCEPTION("SetTimes() must be called prior to SolveAndWriteResultsToFile()");
    }
    if (this->mIdealTimeStep <= 0.0)
    {
        EXCEPTION("SetTimeStep() must be called prior to SolveAndWriteResultsToFile()");
    }
    if (mSamplingTimeStep == DOUBLE_UNSET)
    {
        EXCEPTION("SetSamplingTimeStep() must be called prior to SolveAndWriteResultsToFile()");
    }
    if (!this->mInitialCondition)
    {
        EXCEPTION("SetInitialCondition() must be called prior to SolveAndWriteResultsToFile()");
    }

#ifdef CHASTE_VTK
    // Create a .pvd output file
    OutputFileHandler output_file_handler(this->mOutputDirectory, mClearOutputDirectory);
    mpVtkMetaFile = output_file_handler.OpenOutputFile("results.pvd");
    *mpVtkMetaFile << "<?xml version=\"1.0\"?>\n";
    *mpVtkMetaFile << "<VTKFile type=\"Collection\" version=\"0.1\" byte_order=\"LittleEndian\" compressor=\"vtkZLibDataCompressor\">\n";
    *mpVtkMetaFile << "    <Collection>\n";

    // Write initial condition to VTK
    Vec initial_condition = this->mInitialCondition;
    WriteVtkResultsToFile(initial_condition, 0);

    // The helper class TimeStepper deals with issues such as small final timesteps so we don't have to
    TimeStepper stepper(this->mTstart, this->mTend, mSamplingTimeStep);

    // Main time loop
    while (!stepper.IsTimeAtEnd())
    {
        // Reset start and end times
        this->SetTimes(stepper.GetTime(), stepper.GetNextTime());

        // Solve the system up to the new end time
        Vec soln = this->Solve();

        // Reset the initial condition for the next timestep
        if (this->mInitialCondition != initial_condition)
        {
            PetscTools::Destroy(this->mInitialCondition);
        }
        this->mInitialCondition = soln;

        // Move forward in time
        stepper.AdvanceOneTimeStep();

        // Write solution to VTK
        WriteVtkResultsToFile(soln, stepper.GetTotalTimeStepsTaken());
    }

    // Restore saved initial condition to avoid user confusion!
    if (this->mInitialCondition != initial_condition)
    {
        PetscTools::Destroy(this->mInitialCondition);
    }
    this->mInitialCondition = initial_condition;

    // Close .pvd output file
    *mpVtkMetaFile << "    </Collection>\n";
    *mpVtkMetaFile << "</VTKFile>\n";
    mpVtkMetaFile->close();
#else //CHASTE_VTK
#define COVERAGE_IGNORE // We only test this in weekly builds
    WARNING("VTK is not installed and is required for this functionality");
#undef COVERAGE_IGNORE
#endif //CHASTE_VTK
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::WriteVtkResultsToFile(Vec solution, unsigned numTimeStepsElapsed)
{
#ifdef CHASTE_VTK

    // Create a new VTK file for this time step
    std::stringstream time;
    time << numTimeStepsElapsed;
    VtkMeshWriter<ELEMENT_DIM, SPACE_DIM> mesh_writer(this->mOutputDirectory, "results_"+time.str(), false);

    /*
     * We first loop over PDEs. For each PDE we store the solution
     * at each node in a vector, then pass this vector to the mesh
     * writer.
     */
    ReplicatableVector solution_repl(solution);
    unsigned num_nodes = mpMesh->GetNumNodes();
    for (unsigned pde_index=0; pde_index<PROBLEM_DIM; pde_index++)
    {
        // Store the solution of this PDE at each node
        std::vector<double> pde_index_data;
        pde_index_data.resize(num_nodes, 0.0);
        for (unsigned node_index=0; node_index<num_nodes; node_index++)
        {
            pde_index_data[node_index] = solution_repl[PROBLEM_DIM*node_index + pde_index];
        }

        // Add this data to the mesh writer
        std::stringstream data_name;
        data_name << "PDE variable " << pde_index;
        mesh_writer.AddPointData(data_name.str(), pde_index_data);
    }

    if (mOdeSystemsPresent)
    {
        /*
         * We cannot loop over ODEs like PDEs, since the solutions are not
         * stored in one place. Therefore we build up a large 'vector of
         * vectors', then pass each component of this vector to the mesh
         * writer.
         */
        std::vector<std::vector<double> > ode_data;
        unsigned num_odes = mOdeSystemsAtNodes[0]->rGetStateVariables().size();
        ode_data.resize(num_odes);
        for (unsigned ode_index=0; ode_index<num_odes; ode_index++)
        {
            ode_data[ode_index].resize(num_nodes, 0.0);
        }

        for (unsigned node_index=0; node_index<num_nodes; node_index++)
        {
            std::vector<double> all_odes_this_node = mOdeSystemsAtNodes[node_index]->rGetStateVariables();
            for (unsigned i=0; i<num_odes; i++)
            {
                ode_data[i][node_index] = all_odes_this_node[i];
            }
        }

        for (unsigned ode_index=0; ode_index<num_odes; ode_index++)
        {
            std::vector<double> ode_index_data = ode_data[ode_index];

            // Add this data to the mesh writer
            std::stringstream data_name;
            data_name << "ODE variable " << ode_index;
            mesh_writer.AddPointData(data_name.str(), ode_index_data);
        }
    }

    mesh_writer.WriteFilesUsingMesh(*mpMesh);
    *mpVtkMetaFile << "        <DataSet timestep=\"";
    *mpVtkMetaFile << numTimeStepsElapsed;
    *mpVtkMetaFile << "\" group=\"\" part=\"0\" file=\"results_";
    *mpVtkMetaFile << numTimeStepsElapsed;
    *mpVtkMetaFile << ".vtu\"/>\n";
#endif // CHASTE_VTK
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
AbstractOdeSystemForCoupledPdeSystem* LinearParabolicPdeSystemWithCoupledOdeSystemSolver<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::GetOdeSystemAtNode(unsigned index)
{
    return mOdeSystemsAtNodes[index];
}

#endif /*LINEARPARABOLICPDESYSTEMWITHCOUPLEDODESYSTEMSOLVER_HPP_*/