AbstractFeCableIntegralAssembler.hpp

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#ifndef ABSTRACTFECABLEINTEGRALASSEMBLER_HPP_
#define ABSTRACTFECABLEINTEGRALASSEMBLER_HPP_

#include "AbstractFeAssemblerCommon.hpp"
#include "GaussianQuadratureRule.hpp"
#include "PetscVecTools.hpp"
#include "PetscMatTools.hpp"

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
class AbstractFeCableIntegralAssembler : public AbstractFeAssemblerCommon<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM,CAN_ASSEMBLE_VECTOR,CAN_ASSEMBLE_MATRIX,INTERPOLATION_LEVEL>
{
protected:
    static const unsigned CABLE_ELEMENT_DIM = 1;

    static const unsigned NUM_CABLE_ELEMENT_NODES = 2;

    MixedDimensionMesh<ELEMENT_DIM, SPACE_DIM>* mpMesh;

    GaussianQuadratureRule<1>* mpCableQuadRule;

    typedef LinearBasisFunction<1> CableBasisFunction;

    void ComputeTransformedBasisFunctionDerivatives(const ChastePoint<CABLE_ELEMENT_DIM>& rPoint,
                                                    const c_matrix<double, CABLE_ELEMENT_DIM, SPACE_DIM>& rInverseJacobian,
                                                    c_matrix<double, SPACE_DIM, NUM_CABLE_ELEMENT_NODES>& rReturnValue);

    void DoAssemble();

    virtual c_matrix<double,PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES,PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES> ComputeCableMatrixTerm(
        c_vector<double, NUM_CABLE_ELEMENT_NODES>& rPhi,
        c_matrix<double, SPACE_DIM, NUM_CABLE_ELEMENT_NODES>& rGradPhi,
        ChastePoint<SPACE_DIM>& rX,
        c_vector<double,PROBLEM_DIM>& rU,
        c_matrix<double, PROBLEM_DIM, SPACE_DIM>& rGradU,
        Element<CABLE_ELEMENT_DIM,SPACE_DIM>* pElement)
    {
        // If this line is reached this means this method probably hasn't been over-ridden correctly in
        // the concrete class
        NEVER_REACHED;
        return zero_matrix<double>(PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES,PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES);
    }

    virtual c_vector<double,PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES> ComputeCableVectorTerm(
        c_vector<double, NUM_CABLE_ELEMENT_NODES>& rPhi,
        c_matrix<double, SPACE_DIM, NUM_CABLE_ELEMENT_NODES>& rGradPhi,
        ChastePoint<SPACE_DIM>& rX,
        c_vector<double,PROBLEM_DIM>& rU,
        c_matrix<double, PROBLEM_DIM, SPACE_DIM>& rGradU,
        Element<CABLE_ELEMENT_DIM,SPACE_DIM>* pElement)
    {
        // If this line is reached this means this method probably hasn't been over-ridden correctly in
        // the concrete class
        NEVER_REACHED;
        return zero_vector<double>(PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES);
    }

    virtual void AssembleOnCableElement(Element<CABLE_ELEMENT_DIM,SPACE_DIM>& rElement,
                                        c_matrix<double, PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES, PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES >& rAElem,
                                        c_vector<double, PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES>& rBElem);


    virtual bool ElementAssemblyCriterion(Element<CABLE_ELEMENT_DIM,SPACE_DIM>& rElement)
    {
        return true;
    }

public:

    AbstractFeCableIntegralAssembler(MixedDimensionMesh<ELEMENT_DIM,SPACE_DIM>* pMesh);

    virtual ~AbstractFeCableIntegralAssembler()
    {
        delete mpCableQuadRule;
    }
};



template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
AbstractFeCableIntegralAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::AbstractFeCableIntegralAssembler(
            MixedDimensionMesh<ELEMENT_DIM,SPACE_DIM>* pMesh)
    : AbstractFeAssemblerCommon<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>(),
      mpMesh(pMesh)
{
    assert(pMesh);
    assert(CAN_ASSEMBLE_VECTOR || CAN_ASSEMBLE_MATRIX);
    // Default to 2nd order quadrature.  Our default basis functions are piecewise linear
    // which means that we are integrating functions which in the worst case (mass matrix)
    // are quadratic.
    mpCableQuadRule = new GaussianQuadratureRule<CABLE_ELEMENT_DIM>(2);

    // Not supporting this yet - if a nonlinear assembler on cable elements is required, uncomment code
    // in AssembleOnCableElement below (search for NONLINEAR)
    assert(INTERPOLATION_LEVEL!=NONLINEAR);
}


template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeCableIntegralAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::DoAssemble()
{
    HeartEventHandler::EventType assemble_event;
    if (this->mAssembleMatrix)
    {
        assemble_event = HeartEventHandler::ASSEMBLE_SYSTEM;
    }
    else
    {
        assemble_event = HeartEventHandler::ASSEMBLE_RHS;
    }

    if (this->mAssembleMatrix && this->mMatrixToAssemble==NULL)
    {
        EXCEPTION("Matrix to be assembled has not been set");
    }
    if (this->mAssembleVector && this->mVectorToAssemble==NULL)
    {
        EXCEPTION("Vector to be assembled has not been set");
    }

    // This has to be below PrepareForAssembleSystem as in that method the ODEs are solved in cardiac problems
    HeartEventHandler::BeginEvent(assemble_event);

    // Zero the matrix/vector if it is to be assembled
    if (this->mAssembleVector && this->mZeroVectorBeforeAssembly)
    {
        PetscVecTools::Zero(this->mVectorToAssemble);
    }
    if (this->mAssembleMatrix && this->mZeroMatrixBeforeAssembly)
    {
        PetscMatTools::Zero(this->mMatrixToAssemble);
    }

    const size_t STENCIL_SIZE=PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES;
    c_matrix<double, STENCIL_SIZE, STENCIL_SIZE> a_elem;
    c_vector<double, STENCIL_SIZE> b_elem;

    // Loop over elements
    if (this->mAssembleMatrix || this->mAssembleVector)
    {
        for (typename MixedDimensionMesh<CABLE_ELEMENT_DIM, SPACE_DIM>::CableElementIterator iter = mpMesh->GetCableElementIteratorBegin();
             iter != mpMesh->GetCableElementIteratorEnd();
             ++iter)
        {
            Element<CABLE_ELEMENT_DIM, SPACE_DIM>& r_element = *(*iter);

            // Test for ownership first, since it's pointless to test the criterion on something which we might know nothing about.
            if ( r_element.GetOwnership() == true && ElementAssemblyCriterion(r_element)==true )
            {
                AssembleOnCableElement(r_element, a_elem, b_elem);

                unsigned p_indices[STENCIL_SIZE];
                r_element.GetStiffnessMatrixGlobalIndices(PROBLEM_DIM, p_indices);

                if (this->mAssembleMatrix)
                {
                    PetscMatTools::AddMultipleValues<STENCIL_SIZE>(this->mMatrixToAssemble, p_indices, a_elem);
                }

                if (this->mAssembleVector)
                {
                    PetscVecTools::AddMultipleValues<STENCIL_SIZE>(this->mVectorToAssemble, p_indices, b_elem);
                }
            }
        }
    }

    HeartEventHandler::EndEvent(assemble_event);
}

// Implementation - AssembleOnCableElement and smaller

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeCableIntegralAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::ComputeTransformedBasisFunctionDerivatives(
        const ChastePoint<CABLE_ELEMENT_DIM>& rPoint,
        const c_matrix<double, CABLE_ELEMENT_DIM, SPACE_DIM>& rInverseJacobian,
        c_matrix<double, SPACE_DIM, NUM_CABLE_ELEMENT_NODES>& rReturnValue)
{
    static c_matrix<double, CABLE_ELEMENT_DIM, NUM_CABLE_ELEMENT_NODES> grad_phi;

    LinearBasisFunction<CABLE_ELEMENT_DIM>::ComputeBasisFunctionDerivatives(rPoint, grad_phi);
    rReturnValue = prod(trans(rInverseJacobian), grad_phi);
}

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeCableIntegralAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::AssembleOnCableElement(
    Element<CABLE_ELEMENT_DIM,SPACE_DIM>& rElement,
    c_matrix<double, PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES, PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES >& rAElem,
    c_vector<double, PROBLEM_DIM*NUM_CABLE_ELEMENT_NODES>& rBElem)
{
    c_matrix<double, SPACE_DIM, CABLE_ELEMENT_DIM> jacobian;
    c_matrix<double, CABLE_ELEMENT_DIM, SPACE_DIM> inverse_jacobian;
    double jacobian_determinant;

    // mpMesh->GetInverseJacobianForElement(rElement.GetIndex(), jacobian, jacobian_determinant, inverse_jacobian);
    rElement.CalculateInverseJacobian(jacobian, jacobian_determinant, inverse_jacobian);

    if (this->mAssembleMatrix)
    {
        rAElem.clear();
    }

    if (this->mAssembleVector)
    {
        rBElem.clear();
    }

    const unsigned num_nodes = rElement.GetNumNodes();

    // Allocate memory for the basis functions values and derivative values
    c_vector<double, NUM_CABLE_ELEMENT_NODES> phi;
    c_matrix<double, SPACE_DIM, NUM_CABLE_ELEMENT_NODES> grad_phi;

    // Loop over Gauss points
    for (unsigned quad_index=0; quad_index < mpCableQuadRule->GetNumQuadPoints(); quad_index++)
    {
        const ChastePoint<CABLE_ELEMENT_DIM>& quad_point = mpCableQuadRule->rGetQuadPoint(quad_index);

        CableBasisFunction::ComputeBasisFunctions(quad_point, phi);

        if ( this->mAssembleMatrix || INTERPOLATION_LEVEL==NONLINEAR )
        {
            ComputeTransformedBasisFunctionDerivatives(quad_point, inverse_jacobian, grad_phi);
        }

        // Location of the Gauss point in the original element will be stored in x
        // Where applicable, u will be set to the value of the current solution at x
        ChastePoint<SPACE_DIM> x(0,0,0);

        c_vector<double,PROBLEM_DIM> u = zero_vector<double>(PROBLEM_DIM);
        c_matrix<double,PROBLEM_DIM,SPACE_DIM> grad_u = zero_matrix<double>(PROBLEM_DIM,SPACE_DIM);

        // Allow the concrete version of the assembler to interpolate any desired quantities
        this->ResetInterpolatedQuantities();

        // Interpolation
        for (unsigned i=0; i<num_nodes; i++)
        {
            const Node<SPACE_DIM>* p_node = rElement.GetNode(i);

            if (INTERPOLATION_LEVEL != CARDIAC) // don't interpolate X if cardiac problem
            {
                const c_vector<double, SPACE_DIM>& r_node_loc = p_node->rGetLocation();
                // interpolate x
                x.rGetLocation() += phi(i)*r_node_loc;
            }

            // Interpolate u and grad u if a current solution or guess exists
            unsigned node_global_index = rElement.GetNodeGlobalIndex(i);
            if (this->mCurrentSolutionOrGuessReplicated.GetSize() > 0)
            {
                for (unsigned index_of_unknown=0; index_of_unknown<(INTERPOLATION_LEVEL!=CARDIAC ? PROBLEM_DIM : 1); index_of_unknown++)
                {
                    /*
                     * If we have a solution (e.g. this is a dynamic problem) then
                     * interpolate the value at this quadrature point.
                     *
                     * NOTE: the following assumes that if, say, there are two unknowns
                     * u and v, they are stored in the current solution vector as
                     * [U1 V1 U2 V2 ... U_n V_n].
                     */
                    double u_at_node = this->GetCurrentSolutionOrGuessValue(node_global_index, index_of_unknown);
                    u(index_of_unknown) += phi(i)*u_at_node;

//                    if (INTERPOLATION_LEVEL==NONLINEAR) // don't need to construct grad_phi or grad_u in other cases
//                    {
//                        for (unsigned j=0; j<SPACE_DIM; j++)
//                        {
//                            grad_u(index_of_unknown,j) += grad_phi(j,i)*u_at_node;
//                        }
//                    }
                }
            }

            // Allow the concrete version of the assembler to interpolate any desired quantities
            this->IncrementInterpolatedQuantities(phi(i), p_node);
        }

        double wJ = jacobian_determinant * mpCableQuadRule->GetWeight(quad_index);

        // Create rAElem and rBElem
        if (this->mAssembleMatrix)
        {
            noalias(rAElem) += ComputeCableMatrixTerm(phi, grad_phi, x, u, grad_u, &rElement) * wJ;
        }

        if (this->mAssembleVector)
        {
            noalias(rBElem) += ComputeCableVectorTerm(phi, grad_phi, x, u, grad_u, &rElement) * wJ;
        }
    }
}

#endif /*ABSTRACTFECABLEINTEGRALASSEMBLER_HPP_*/