AbstractTetrahedralElement.cpp

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*/
 
#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 (const 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;
        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)
        {
            std::stringstream message;
            message << "Jacobian determinant is non-positive: "
                    << "determinant = " << rJacobianDeterminant
                    << " for element " << this->mIndex << " (" << ELEMENT_DIM
                    << "D element in " << SPACE_DIM << "D space). Nodes are at:" << std::endl;
 
            for (unsigned local_node_index=0u; local_node_index != ELEMENT_DIM+1; local_node_index++)
            {
                c_vector<double, SPACE_DIM> location = this->GetNodeLocation(local_node_index);
                message << "Node " << this->GetNodeGlobalIndex(local_node_index) << ":\t";
 
                for (unsigned i=0; i<SPACE_DIM; i++)
                {
                    message << location[i];
                    if (i==SPACE_DIM - 1u)
                    {
                        message << std::endl;
                    }
                    else
                    {
                        message << "\t";
                    }
                }
            }
            EXCEPTION(message.str());
        }
    }
}
 
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);     // LCOV_EXCL_LINE
    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
{
 
    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);     // LCOV_EXCL_LINE
 
    // 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);     // LCOV_EXCL_LINE
 
    // 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);     // LCOV_EXCL_LINE
 
    // 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>;