AbstractFeVolumeIntegralAssembler.hpp

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#ifndef ABSTRACTFEVOLUMEINTEGRALASSEMBLER_HPP_
#define ABSTRACTFEVOLUMEINTEGRALASSEMBLER_HPP_

#include "AbstractFeAssemblerCommon.hpp"
#include "GaussianQuadratureRule.hpp"
#include "BoundaryConditionsContainer.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 AbstractFeVolumeIntegralAssembler :
     public AbstractFeAssemblerCommon<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM,CAN_ASSEMBLE_VECTOR,CAN_ASSEMBLE_MATRIX,INTERPOLATION_LEVEL>
{
protected:
    AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* mpMesh;

    GaussianQuadratureRule<ELEMENT_DIM>* mpQuadRule;

    typedef LinearBasisFunction<ELEMENT_DIM> BasisFunction;

    void ComputeTransformedBasisFunctionDerivatives(const ChastePoint<ELEMENT_DIM>& rPoint,
                                                    const c_matrix<double, ELEMENT_DIM, SPACE_DIM>& rInverseJacobian,
                                                    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rReturnValue);

    void DoAssemble();

protected:

    virtual 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)
    {
        // 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*(ELEMENT_DIM+1),PROBLEM_DIM*(ELEMENT_DIM+1));
    }

    virtual 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)
    {
        // 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*(ELEMENT_DIM+1));
    }


    virtual void AssembleOnElement(Element<ELEMENT_DIM,SPACE_DIM>& rElement,
                                   c_matrix<double, PROBLEM_DIM*(ELEMENT_DIM+1), PROBLEM_DIM*(ELEMENT_DIM+1) >& rAElem,
                                   c_vector<double, PROBLEM_DIM*(ELEMENT_DIM+1)>& rBElem);

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


public:

    AbstractFeVolumeIntegralAssembler(AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>* pMesh);

    virtual ~AbstractFeVolumeIntegralAssembler()
    {
        delete mpQuadRule;
    }
};

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
AbstractFeVolumeIntegralAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::AbstractFeVolumeIntegralAssembler(
            AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>* pMesh)
    : AbstractFeAssemblerCommon<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>(),
      mpMesh(pMesh)
{
    assert(pMesh);
    // 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.
    mpQuadRule = new GaussianQuadratureRule<ELEMENT_DIM>(2);
}



template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeVolumeIntegralAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::DoAssemble()
{
    assert(this->mAssembleMatrix || this->mAssembleVector);

    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");
    }

    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*(ELEMENT_DIM+1);
    c_matrix<double, STENCIL_SIZE, STENCIL_SIZE> a_elem;
    c_vector<double, STENCIL_SIZE> b_elem;

    // Loop over elements
    for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = mpMesh->GetElementIteratorBegin();
         iter != mpMesh->GetElementIteratorEnd();
         ++iter)
    {
        Element<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 )
        {
            AssembleOnElement(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 - AssembleOnElement and smaller

template <unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM, bool CAN_ASSEMBLE_VECTOR, bool CAN_ASSEMBLE_MATRIX, InterpolationLevel INTERPOLATION_LEVEL>
void AbstractFeVolumeIntegralAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::ComputeTransformedBasisFunctionDerivatives(
        const ChastePoint<ELEMENT_DIM>& rPoint,
        const c_matrix<double, ELEMENT_DIM, SPACE_DIM>& rInverseJacobian,
        c_matrix<double, SPACE_DIM, ELEMENT_DIM+1>& rReturnValue)
{
    assert(ELEMENT_DIM < 4 && ELEMENT_DIM > 0);
    static c_matrix<double, ELEMENT_DIM, ELEMENT_DIM+1> grad_phi;

    LinearBasisFunction<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 AbstractFeVolumeIntegralAssembler<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>::AssembleOnElement(
    Element<ELEMENT_DIM,SPACE_DIM>& rElement,
    c_matrix<double, PROBLEM_DIM*(ELEMENT_DIM+1), PROBLEM_DIM*(ELEMENT_DIM+1) >& rAElem,
    c_vector<double, PROBLEM_DIM*(ELEMENT_DIM+1)>& rBElem)
{
    c_matrix<double, SPACE_DIM, ELEMENT_DIM> jacobian;
    c_matrix<double, ELEMENT_DIM, SPACE_DIM> inverse_jacobian;
    double jacobian_determinant;

    mpMesh->GetInverseJacobianForElement(rElement.GetIndex(), 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, ELEMENT_DIM+1> phi;
    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> grad_phi;

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

        BasisFunction::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 even 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);
            if ( this->mAssembleMatrix || INTERPOLATION_LEVEL==NONLINEAR )
            {
                this->IncrementInterpolatedGradientQuantities(grad_phi, i, p_node);
            }
        }

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

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

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


#endif /*ABSTRACTFEVOLUMEINTEGRALASSEMBLER_HPP_*/