AbstractTetrahedralElement.cpp

/*

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/>.

*/

#include "UblasCustomFunctions.hpp"
#include "AbstractTetrahedralElement.hpp"
#include "Exception.hpp"

#include <cassert>

// Implementation

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::RefreshJacobian(c_matrix<double, SPACE_DIM, ELEMENT_DIM>& rJacobian)
{
    if (this->mIsDeleted)
    {
        EXCEPTION("Attempting to Refresh a deleted element");
    }
    for (unsigned i=0; i<SPACE_DIM; i++)
    {
        for (unsigned j=0; j!=ELEMENT_DIM; j++) // Does a j<ELEMENT_DIM without ever having to test j<0U (#186: pointless comparison of unsigned integer with zero)
        {
            rJacobian(i,j) = this->GetNodeLocation(j+1,i) - this->GetNodeLocation(0,i);
        }
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::AbstractTetrahedralElement(unsigned index, const std::vector<Node<SPACE_DIM>*>& rNodes)
    : AbstractElement<ELEMENT_DIM, SPACE_DIM>(index, rNodes)
{
    // Sanity checking
    unsigned num_vectices = ELEMENT_DIM+1;

    double det;

    if (SPACE_DIM == ELEMENT_DIM)
    {
        // This is so we know it's the first time of asking
        // Create Jacobian
        c_matrix<double, SPACE_DIM, ELEMENT_DIM> jacobian;
        try
        {
            CalculateJacobian(jacobian, det);
        }
        catch (Exception)
        {
            // if the Jacobian is negative the orientation of the element is probably
            // wrong, so swap the last two nodes around.

            this->mNodes[num_vectices-1] = rNodes[num_vectices-2];
            this->mNodes[num_vectices-2] = rNodes[num_vectices-1];

            CalculateJacobian(jacobian, det);
            // If determinant < 0 then element nodes are listed clockwise.
            // We want them anticlockwise.
            assert(det > 0.0);
        }
    }
    else
    {
        //This is not a full-dimensional element
        c_vector<double, SPACE_DIM> weighted_direction;
        double det;
        CalculateWeightedDirection(weighted_direction, det);
    }

}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::AbstractTetrahedralElement(unsigned index)
    : AbstractElement<ELEMENT_DIM,SPACE_DIM>(index)
{}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::CalculateJacobian(c_matrix<double, SPACE_DIM, ELEMENT_DIM>& rJacobian, double& rJacobianDeterminant)
{

    assert(ELEMENT_DIM <= SPACE_DIM);
    RefreshJacobian(rJacobian);

    {
        rJacobianDeterminant = Determinant(rJacobian);
        if (rJacobianDeterminant <= DBL_EPSILON)
        {
            EXCEPTION("Jacobian determinant is non-positive: "
                          << "determinant = " << rJacobianDeterminant
                          << " for element " << this->mIndex);
        }
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::CalculateWeightedDirection(c_vector<double, SPACE_DIM>& rWeightedDirection, double& rJacobianDeterminant)
{

    if (ELEMENT_DIM >= SPACE_DIM)
    {
        assert(ELEMENT_DIM == SPACE_DIM);
        EXCEPTION("WeightedDirection undefined for fully dimensional element");
    }

    c_matrix<double, SPACE_DIM, ELEMENT_DIM> jacobian;
    RefreshJacobian(jacobian);

    /*
     * At this point we're only dealing with subspace (ELEMENT_DIM < SPACE_DIM) elem.
     * We assume that the rWeightedDirection vector and rJacobianDeterminant (length
     * of vector) are the values from a previous call.
     */

    // This code is only used when ELEMENT_DIM<SPACE_DIM
    switch (ELEMENT_DIM)
    {
        case 0:
            // See specialised template for ELEMENT_DIM==0
            NEVER_REACHED;
            break;
        case 1:
            // Linear edge in a 2D plane or in 3D
            rWeightedDirection=matrix_column<c_matrix<double,SPACE_DIM,ELEMENT_DIM> >(jacobian, 0);
            break;
        case 2:
            // Surface triangle in a 3d mesh
            assert(SPACE_DIM == 3);
            rWeightedDirection(0) = -SubDeterminant(jacobian, 0, 2);
            rWeightedDirection(1) =  SubDeterminant(jacobian, 1, 2);
            rWeightedDirection(2) = -SubDeterminant(jacobian, 2, 2);
            break;
        default:
           ; // Not going to happen
    }
    rJacobianDeterminant = norm_2(rWeightedDirection);

    if (rJacobianDeterminant < DBL_EPSILON)
    {
        EXCEPTION("Jacobian determinant is zero");
    }
}


template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
c_vector<double, SPACE_DIM> AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::CalculateNormal()
{
    if (ELEMENT_DIM == 1 && SPACE_DIM == 3)
    {
        EXCEPTION("Don't have enough information to calculate a normal vector");
    }
    c_vector<double, SPACE_DIM> normal;
    double determinant;
    CalculateWeightedDirection(normal, determinant);
    normal /= determinant;
    if (ELEMENT_DIM == 1)
    {
        // Need to rotate so tangent becomes normal
        double x = normal[0];
        normal[0] = normal[1];
        normal[1] = -x;
    }
    return normal;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
c_vector<double, SPACE_DIM> AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::CalculateCentroid() const
{
    c_vector<double, SPACE_DIM> centroid = zero_vector<double>(SPACE_DIM);
    for (unsigned i=0; i<=ELEMENT_DIM; i++)
    {
        centroid += this->mNodes[i]->rGetLocation();
    }
    return centroid/((double)(ELEMENT_DIM + 1));
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::CalculateInverseJacobian(c_matrix<double, SPACE_DIM, ELEMENT_DIM>& rJacobian, double& rJacobianDeterminant, c_matrix<double, ELEMENT_DIM, SPACE_DIM>& rInverseJacobian)
{
    assert(ELEMENT_DIM <= SPACE_DIM);
    CalculateJacobian(rJacobian, rJacobianDeterminant);

    // CalculateJacobian should make sure that the determinant is not close to zero (or, in fact, negative)
    assert(rJacobianDeterminant > 0.0);
    rInverseJacobian = Inverse(rJacobian);
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
double AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::GetVolume(double determinant) const
{
    assert(SPACE_DIM == ELEMENT_DIM);

    if (this->mIsDeleted)
    {
        return 0.0;
    }

    double scale_factor = 1.0;

    if (ELEMENT_DIM == 2)
    {
        scale_factor = 2.0; // both the volume of the canonical triangle is 1/2
    }
    else if (ELEMENT_DIM == 3)
    {
        scale_factor = 6.0; // both the volume of the canonical triangle is 1/6
    }
    return determinant/scale_factor;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM>
void AbstractTetrahedralElement<ELEMENT_DIM, SPACE_DIM>::GetStiffnessMatrixGlobalIndices(unsigned problemDim, unsigned* pIndices) const
{
    for (unsigned local_index=0; local_index<ELEMENT_DIM+1; local_index++)
    {
        unsigned node = this->GetNodeGlobalIndex(local_index);

        for (unsigned problem_index=0; problem_index<problemDim; problem_index++)
        {
            //std::cout << local_index*problemDim + problem_index << std::endl;
            pIndices[local_index*problemDim + problem_index] = node*problemDim + problem_index;
        }
    }
}


//                  Specialization for 0d elements                  //

template<unsigned SPACE_DIM>
AbstractTetrahedralElement<0, SPACE_DIM>::AbstractTetrahedralElement(unsigned index, const std::vector<Node<SPACE_DIM>*>& rNodes)
    : AbstractElement<0, SPACE_DIM>(index, rNodes)
{
    // Sanity checking
    //unsigned total_nodes = 1;
    assert(this->mNodes.size() == 1);
    assert(SPACE_DIM > 0);

    // This is so we know it's the first time of asking
    // Create Jacobian
    c_vector<double, SPACE_DIM> weighted_direction;
    double det;

    CalculateWeightedDirection(weighted_direction, det);

    // If determinant < 0 then element nodes are listed clockwise.
    // We want them anticlockwise.
    assert(det > 0.0);
}

template<unsigned SPACE_DIM>
AbstractTetrahedralElement<0, SPACE_DIM>::AbstractTetrahedralElement(unsigned index)
    : AbstractElement<0, SPACE_DIM>(index)
{
}

template<unsigned SPACE_DIM>
void AbstractTetrahedralElement<0, SPACE_DIM>::CalculateWeightedDirection(
        c_vector<double, SPACE_DIM>& rWeightedDirection,
        double& rJacobianDeterminant)
{
    assert(SPACE_DIM > 0);

    // End point of a line
    rWeightedDirection = zero_vector<double>(SPACE_DIM);
    rWeightedDirection(0) = 1.0;

    rJacobianDeterminant = 1.0;
}

template<unsigned SPACE_DIM>
c_vector<double, SPACE_DIM> AbstractTetrahedralElement<0, SPACE_DIM>::CalculateNormal()
{
    assert(SPACE_DIM > 0);

    // End point of a line
    c_vector<double, SPACE_DIM> normal = zero_vector<double>(SPACE_DIM);
    return normal;
}

template<unsigned SPACE_DIM>
c_vector<double, SPACE_DIM> AbstractTetrahedralElement<0, SPACE_DIM>::CalculateCentroid() const
{
    c_vector<double, SPACE_DIM> centroid = this->mNodes[0]->rGetLocation();
    return centroid;
}

template<unsigned SPACE_DIM>
void AbstractTetrahedralElement<0, SPACE_DIM>::GetStiffnessMatrixGlobalIndices(unsigned problemDim, unsigned* pIndices) const
{
    for (unsigned local_index=0; local_index<1; local_index++)
    {
        unsigned node = this->GetNodeGlobalIndex(local_index);

        for (unsigned problem_index=0; problem_index<problemDim; problem_index++)
        {
            //std::cout << local_index*problemDim + problem_index << std::endl;
            pIndices[local_index*problemDim + problem_index] = node*problemDim + problem_index;
        }
    }
}

// Explicit instantiation

template class AbstractTetrahedralElement<0,1>;
template class AbstractTetrahedralElement<1,1>;
template class AbstractTetrahedralElement<0,2>;
template class AbstractTetrahedralElement<1,2>;
template class AbstractTetrahedralElement<2,2>;
template class AbstractTetrahedralElement<0,3>;
template class AbstractTetrahedralElement<1,3>;
template class AbstractTetrahedralElement<2,3>;
template class AbstractTetrahedralElement<3,3>;