AbstractFeVolumeIntegralAssembler.hpp

/*

Copyright (c) 2005-2015, University of Oxford.
All rights reserved.

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.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
 * Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.
 * Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.
 * Neither the name of the University of Oxford nor the names of its
   contributors may be used to endorse or promote products derived from this
   software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

*/

#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);

    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)
    : AbstractFeAssemblerCommon<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM, CAN_ASSEMBLE_VECTOR, CAN_ASSEMBLE_MATRIX, INTERPOLATION_LEVEL>(),
      mpMesh(pMesh)
{
    assert(pMesh);
    // Default to 2nd order quadrature.  Our default basis functions are piecewise linear
    // which means that we are integrating functions which in the worst case (mass matrix)
    // are quadratic.
    mpQuadRule = new GaussianQuadratureRule<ELEMENT_DIM>(2);
}



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);
            if ( this->mAssembleMatrix || INTERPOLATION_LEVEL==NONLINEAR )
            {
                this->IncrementInterpolatedGradientQuantities(grad_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_*/