AbstractFunctionalCalculator.hpp

/*

Copyright (C) University of Oxford, 2005-2011

University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details. The offer of Chaste under the terms of the
License is subject to the License being interpreted in accordance with
English Law and subject to any action against the University of Oxford
being under the jurisdiction of the English Courts.

You should have received a copy of the GNU Lesser General Public License
along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/

#ifndef ABSTRACTFUNCTIONALCALCULATOR_HPP_
#define ABSTRACTFUNCTIONALCALCULATOR_HPP_

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

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;

    GaussianQuadratureRule<ELEMENT_DIM> quad_rule(2);

    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;
                for (unsigned j=0; j<SPACE_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(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)
            {
                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;
}

#endif /*ABSTRACTFUNCTIONALCALCULATOR_HPP_*/