ExtendedBidomainAssembler.cpp

/*

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*/

#include "ExtendedBidomainAssembler.hpp"
#include <boost/numeric/ublas/vector_proxy.hpp>

#include "Exception.hpp"
#include "DistributedVector.hpp"
#include "PdeSimulationTime.hpp"
#include "ConstBoundaryCondition.hpp"

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
c_matrix<double,3*(ELEMENT_DIM+1),3*(ELEMENT_DIM+1)>
    ExtendedBidomainAssembler<ELEMENT_DIM,SPACE_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,3> &rU,
            c_matrix<double, 3, SPACE_DIM> &rGradU /* not used */,
            Element<ELEMENT_DIM,SPACE_DIM>* pElement)
{
    // get bidomain parameters
    double Am1 = mpExtendedBidomainTissue->GetAmFirstCell();
    double Am2 = mpExtendedBidomainTissue->GetAmSecondCell();
    double Cm1 = mpExtendedBidomainTissue->GetCmFirstCell();
    double Cm2 = mpExtendedBidomainTissue->GetCmSecondCell();

    const c_matrix<double, SPACE_DIM, SPACE_DIM>& sigma_i_first_cell = mpExtendedBidomainTissue->rGetIntracellularConductivityTensor(pElement->GetIndex());
    const c_matrix<double, SPACE_DIM, SPACE_DIM>& sigma_i_second_cell = mpExtendedBidomainTissue->rGetIntracellularConductivityTensorSecondCell(pElement->GetIndex());
    const c_matrix<double, SPACE_DIM, SPACE_DIM>& sigma_e = mpExtendedBidomainTissue->rGetExtracellularConductivityTensor(pElement->GetIndex());

    double delta_t = PdeSimulationTime::GetPdeTimeStep();

    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> temp_1 = prod(sigma_i_first_cell, rGradPhi);
    c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> grad_phi_sigma_i_first_cell_grad_phi =
        prod(trans(rGradPhi), temp_1);

    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> temp_2 = prod(sigma_i_second_cell, rGradPhi);
    c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> grad_phi_sigma_i_second_cell_grad_phi =
        prod(trans(rGradPhi), temp_2);

    c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> basis_outer_prod =
        outer_prod(rPhi, rPhi);

    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> temp_ext = prod(sigma_e, rGradPhi);
    c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> grad_phi_sigma_e_grad_phi =
        prod(trans(rGradPhi), temp_ext);


    c_matrix<double,3*(ELEMENT_DIM+1),3*(ELEMENT_DIM+1)> ret;

    // first equation, first unknown
    matrix_slice<c_matrix<double, 3*ELEMENT_DIM+3, 3*ELEMENT_DIM+3> >
    slice100(ret, slice (0, 3, ELEMENT_DIM+1), slice (0, 3, ELEMENT_DIM+1));
    slice100 = (Am1*Cm1/delta_t)*basis_outer_prod + grad_phi_sigma_i_first_cell_grad_phi;

    // first equation, second unknown
    matrix_slice<c_matrix<double, 3*ELEMENT_DIM+3, 3*ELEMENT_DIM+3> >
    slice200(ret, slice (0, 3, ELEMENT_DIM+1), slice (1, 3, ELEMENT_DIM+1));
    slice200 = zero_matrix<double>(ELEMENT_DIM+1, ELEMENT_DIM+1);

    // first equation, third unknown
    matrix_slice<c_matrix<double, 3*ELEMENT_DIM+3, 3*ELEMENT_DIM+3> >
    slice300(ret, slice (0, 3, ELEMENT_DIM+1), slice (2, 3, ELEMENT_DIM+1));
    slice300 = - (Am1*Cm1/delta_t)*basis_outer_prod;

    // second equation, first unknown
    matrix_slice<c_matrix<double, 3*ELEMENT_DIM+3, 3*ELEMENT_DIM+3> >
    slice010(ret, slice (1, 3, ELEMENT_DIM+1), slice (0, 3, ELEMENT_DIM+1));
    slice010 = zero_matrix<double>(ELEMENT_DIM+1, ELEMENT_DIM+1);

    // second equation, second unknown
    matrix_slice<c_matrix<double, 3*ELEMENT_DIM+3, 3*ELEMENT_DIM+3> >
    slice020(ret, slice (1, 3, ELEMENT_DIM+1), slice (1, 3, ELEMENT_DIM+1));
    slice020 = (Am2*Cm2/delta_t)*basis_outer_prod + grad_phi_sigma_i_second_cell_grad_phi;

    // second equation, third unknown
    matrix_slice<c_matrix<double, 3*ELEMENT_DIM+3, 3*ELEMENT_DIM+3> >
    slice030(ret, slice (1, 3, ELEMENT_DIM+1), slice (2, 3, ELEMENT_DIM+1));
    slice030 = - (Am2*Cm2/delta_t)*basis_outer_prod;

    // third equation, first unknown
    matrix_slice<c_matrix<double, 3*ELEMENT_DIM+3, 3*ELEMENT_DIM+3> >
    slice001(ret, slice (2, 3, ELEMENT_DIM+1), slice (0, 3, ELEMENT_DIM+1));
    slice001 =   - grad_phi_sigma_i_first_cell_grad_phi;

    // third equation, second unknown
    matrix_slice<c_matrix<double, 3*ELEMENT_DIM+3, 3*ELEMENT_DIM+3> >
    slice002(ret, slice (2, 3, ELEMENT_DIM+1), slice (1, 3, ELEMENT_DIM+1));
    slice002 =  - grad_phi_sigma_i_second_cell_grad_phi;

    // third equation, third unknown
    matrix_slice<c_matrix<double, 3*ELEMENT_DIM+3, 3*ELEMENT_DIM+3> >
    slice003(ret, slice (2, 3, ELEMENT_DIM+1), slice (2, 3, ELEMENT_DIM+1));
    slice003 =  - grad_phi_sigma_e_grad_phi;

    return ret;
}


template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
ExtendedBidomainAssembler<ELEMENT_DIM,SPACE_DIM>::ExtendedBidomainAssembler(
                                AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>* pMesh,
                                ExtendedBidomainTissue<SPACE_DIM>* pTissue,
                                unsigned numQuadPoints)
    : AbstractCardiacFeVolumeIntegralAssembler<ELEMENT_DIM,SPACE_DIM,3,true,true,NORMAL>(pMesh,pTissue,numQuadPoints),
              mpExtendedBidomainTissue(pTissue)
{
    assert(pTissue != NULL);
    mpConfig = HeartConfig::Instance();
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
ExtendedBidomainAssembler<ELEMENT_DIM,SPACE_DIM>::~ExtendedBidomainAssembler()
{
}

// Explicit instantiation

template class ExtendedBidomainAssembler<1,1>;
template class ExtendedBidomainAssembler<2,2>;
template class ExtendedBidomainAssembler<3,3>;