AbstractFunctionalCalculator.hpp

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*/

#ifndef ABSTRACTFUNCTIONALCALCULATOR_HPP_
#define ABSTRACTFUNCTIONALCALCULATOR_HPP_

#include "LinearBasisFunction.hpp"
#include "GaussianQuadratureRule.hpp"
#include "AbstractTetrahedralMesh.hpp"
#include "ReplicatableVector.hpp"

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
class AbstractFunctionalCalculator
{
private:

    ReplicatableVector mSolutionReplicated;

    virtual double GetIntegrand(ChastePoint<SPACE_DIM>& rX,
                                c_vector<double,PROBLEM_DIM>& rU,
                                c_matrix<double,PROBLEM_DIM,SPACE_DIM>& rGradU)=0;

    virtual bool ShouldSkipThisElement(Element<ELEMENT_DIM,SPACE_DIM>& rElement);

public:

    virtual ~AbstractFunctionalCalculator()
    {
    }

    double Calculate(AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>& rMesh, Vec solution);

    double CalculateOnElement(Element<ELEMENT_DIM,SPACE_DIM>& rElement);
};

// Implementation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
double AbstractFunctionalCalculator<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::CalculateOnElement(Element<ELEMENT_DIM, SPACE_DIM>& rElement)
{
    double result_on_element = 0;

    // Third order quadrature.  Note that the functional may be non-polynomial (see documentation of class).
    GaussianQuadratureRule<ELEMENT_DIM> quad_rule(3);

    double jacobian_determinant;
    c_matrix<double, SPACE_DIM, ELEMENT_DIM> jacobian;
    c_matrix<double, ELEMENT_DIM, SPACE_DIM> inverse_jacobian;
    rElement.CalculateInverseJacobian(jacobian, jacobian_determinant, inverse_jacobian);

    const unsigned num_nodes = rElement.GetNumNodes();

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

        c_vector<double, ELEMENT_DIM+1> phi;
        LinearBasisFunction<ELEMENT_DIM>::ComputeBasisFunctions(quad_point, phi);
        c_matrix<double, ELEMENT_DIM, ELEMENT_DIM+1> grad_phi;
        LinearBasisFunction<ELEMENT_DIM>::ComputeTransformedBasisFunctionDerivatives(quad_point, inverse_jacobian, grad_phi);

        // Location of the Gauss point in the original element will be stored in 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);

        for (unsigned i=0; i<num_nodes; i++)
        {
            const c_vector<double, SPACE_DIM>& r_node_loc = rElement.GetNode(i)->rGetLocation();

            // Interpolate x
            x.rGetLocation() += phi(i)*r_node_loc;

            // Interpolate u and grad u
            unsigned node_global_index = rElement.GetNodeGlobalIndex(i);
            for (unsigned index_of_unknown=0; index_of_unknown<PROBLEM_DIM; index_of_unknown++)
            {
                // NOTE - 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]
                unsigned index_into_vec = PROBLEM_DIM*node_global_index + index_of_unknown;

                double u_at_node = mSolutionReplicated[index_into_vec];
                u(index_of_unknown) += phi(i)*u_at_node;
                // NB. grad_u is PROBLEM_DIM x SPACE_DIM but grad_phi is ELEMENT_DIM x (ELEMENT_DIM+1)
                // Assume here that SPACE_DIM == ELEMENT_DIM and assert it in calling function
                for (unsigned j=0; j<ELEMENT_DIM; j++)
                {
                    grad_u(index_of_unknown,j) += grad_phi(j,i)*u_at_node;
                }
            }
        }

        double wJ = jacobian_determinant * quad_rule.GetWeight(quad_index);
        result_on_element += GetIntegrand(x, u, grad_u) * wJ;
    }

    return result_on_element;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
double AbstractFunctionalCalculator<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::Calculate(AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>& rMesh, Vec solution)
{
    assert(ELEMENT_DIM == SPACE_DIM);    // LCOV_EXCL_LINE
    assert(solution);
    mSolutionReplicated.ReplicatePetscVector(solution);
    if (mSolutionReplicated.GetSize() != rMesh.GetNumNodes() * PROBLEM_DIM)
    {
        EXCEPTION("The solution size does not match the mesh");
    }

    double local_result = 0;

    try
    {
        for (typename AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>::ElementIterator iter = rMesh.GetElementIteratorBegin();
             iter != rMesh.GetElementIteratorEnd();
             ++iter)
        {
            if (rMesh.CalculateDesignatedOwnershipOfElement((*iter).GetIndex()) == true && !ShouldSkipThisElement(*iter))
            {
                local_result += CalculateOnElement(*iter);
            }
        }
    }
    catch (Exception &exception_in_integral)
    {
        PetscTools::ReplicateException(true);
        throw exception_in_integral;
    }
    PetscTools::ReplicateException(false);

    double final_result;
    MPI_Allreduce(&local_result, &final_result, 1, MPI_DOUBLE, MPI_SUM, PETSC_COMM_WORLD);
    return final_result;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
bool AbstractFunctionalCalculator<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::ShouldSkipThisElement(Element<ELEMENT_DIM,SPACE_DIM>& rElement)
{
    return false;
}

#endif /*ABSTRACTFUNCTIONALCALCULATOR_HPP_*/