SimpleNonlinearEllipticSolver.cpp

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*/

#include "SimpleNonlinearEllipticSolver.hpp"

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
c_matrix<double,1*(ELEMENT_DIM+1),1*(ELEMENT_DIM+1)> SimpleNonlinearEllipticSolver<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,1>& rU,
        c_matrix<double,1,SPACE_DIM>& rGradU,
        Element<ELEMENT_DIM,SPACE_DIM>* pElement)
{
    c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> ret;

    c_matrix<double, SPACE_DIM, SPACE_DIM> f_of_u = mpNonlinearEllipticPde->ComputeDiffusionTerm(rX, rU(0));
    c_matrix<double, SPACE_DIM, SPACE_DIM> f_of_u_prime = mpNonlinearEllipticPde->ComputeDiffusionTermPrime(rX, rU(0));

    // LinearSourceTerm(x) not needed as it is a constant wrt u
    double forcing_term_prime = mpNonlinearEllipticPde->ComputeNonlinearSourceTermPrime(rX, rU(0));

    // Note rGradU is a 1 by SPACE_DIM matrix, the 1 representing the dimension of
    // u (ie in this problem the unknown is a scalar). r_gradu_0 is rGradU as a vector
    matrix_row< c_matrix<double, 1, SPACE_DIM> > r_gradu_0(rGradU, 0);
    c_vector<double, SPACE_DIM> temp1 = prod(f_of_u_prime, r_gradu_0);
    c_vector<double, ELEMENT_DIM+1> temp1a = prod(temp1, rGradPhi);

    c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> integrand_values1 = outer_prod(temp1a, rPhi);
    c_matrix<double, SPACE_DIM, ELEMENT_DIM+1> temp2 = prod(f_of_u, rGradPhi);
    c_matrix<double, ELEMENT_DIM+1, ELEMENT_DIM+1> integrand_values2 = prod(trans(rGradPhi), temp2);
    c_vector<double, ELEMENT_DIM+1> integrand_values3 = forcing_term_prime * rPhi;

    ret = integrand_values1 + integrand_values2 - outer_prod( scalar_vector<double>(ELEMENT_DIM+1), integrand_values3);

    return ret;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
c_vector<double,1*(ELEMENT_DIM+1)> SimpleNonlinearEllipticSolver<ELEMENT_DIM,SPACE_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,1>& rU,
        c_matrix<double,1,SPACE_DIM>& rGradU,
        Element<ELEMENT_DIM,SPACE_DIM>* pElement)
{
    c_vector<double, 1*(ELEMENT_DIM+1)> ret;

    // For solving an AbstractNonlinearEllipticEquation
    // d/dx [f(U,x) du/dx ] = -g
    // where g(x,U) is the forcing term
    double forcing_term = mpNonlinearEllipticPde->ComputeLinearSourceTerm(rX);
    forcing_term += mpNonlinearEllipticPde->ComputeNonlinearSourceTerm(rX, rU(0));

    c_matrix<double, ELEMENT_DIM, ELEMENT_DIM> FOfU = mpNonlinearEllipticPde->ComputeDiffusionTerm(rX, rU(0));

    // Note rGradU is a 1 by SPACE_DIM matrix, the 1 representing the dimension of
    // u (ie in this problem the unknown is a scalar). rGradU0 is rGradU as a vector.
    matrix_row< c_matrix<double, 1, SPACE_DIM> > rGradU0(rGradU, 0);
    c_vector<double, ELEMENT_DIM+1> integrand_values1 =
        prod(c_vector<double, ELEMENT_DIM>(prod(rGradU0, FOfU)), rGradPhi);

    ret = integrand_values1 - (forcing_term * rPhi);
    return ret;
}


template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
SimpleNonlinearEllipticSolver<ELEMENT_DIM,SPACE_DIM>::SimpleNonlinearEllipticSolver(
                              AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* pMesh,
                              AbstractNonlinearEllipticPde<SPACE_DIM>* pPde,
                              BoundaryConditionsContainer<ELEMENT_DIM, SPACE_DIM, 1>* pBoundaryConditions)
    :  AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM,SPACE_DIM,1>(pMesh,pBoundaryConditions),
       mpNonlinearEllipticPde(pPde)
{
    assert(pPde!=NULL);
}

// Explicit instantiation

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