AbstractFeVolumeIntegralAssembler.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 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, unsigned numQuadPoints=2);

    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, unsigned numQuadPoints)
    : AbstractFeAssemblerCommon<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>(),
      mpMesh(pMesh)
{
    assert(pMesh);
    assert(numQuadPoints > 0);

    mpQuadRule = new GaussianQuadratureRule<ELEMENT_DIM>(numQuadPoints);
}



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);
        }

        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_*/