QuadraticBasisFunction.cpp

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*/

#include "QuadraticBasisFunction.hpp"
#include "Exception.hpp"
#include "UblasIncludes.hpp"

double QuadraticBasisFunction<0>::ComputeBasisFunction(const ChastePoint<0>& rPoint, unsigned basisIndex)
{
    assert(basisIndex == 0);
    return 1.0;
}

void QuadraticBasisFunction<0>::ComputeBasisFunctions(const ChastePoint<0>& rPoint,
                                                      c_vector<double, 1>& rReturnValue)
{
    rReturnValue(0) = ComputeBasisFunction(rPoint, 0);
}

template <unsigned ELEMENT_DIM>
double QuadraticBasisFunction<ELEMENT_DIM>::ComputeBasisFunction(const ChastePoint<ELEMENT_DIM>& rPoint, unsigned basisIndex)
{
    assert(ELEMENT_DIM < 4 && ELEMENT_DIM >= 0);
    double x, y, z;
    switch (ELEMENT_DIM)
    {
    case 0:
        assert(basisIndex == 0);
        return 1.0;
        break;

    case 1:
        x = rPoint[0];
        switch (basisIndex)
        {
            case 0:
                return 2.0*(x-1.0)*(x-0.5);
                break;
            case 1:
                return 2.0*x*(x-0.5);
                break;
            case 2:
                return 4.0*x*(1.0-x);
                break;
            default:
                NEVER_REACHED;
        }
        break;

    case 2:
        x = rPoint[0];
        y = rPoint[1];
        switch (basisIndex)
        {
            case 0: // the node at (0,0)
                return 2.0 * (1.0 - x - y) * (0.5 - x - y);
                break;
            case 1: // the node at (1,0)
                return 2.0*x*(x-0.5);
                break;
            case 2: // the node at (0,1)
                return 2.0*y*(y-0.5);
                break;
            case 3: // the node opposite 0, which is (1/2,1/2)
                return 4.0 * y * x;
                break;
            case 4: // the node opposite 1, which is (0,1/2)
                return 4.0 * (1.0 - x - y) * y;
                break;
            case 5: // the node opposite 2, which is (1/2,0)
                return 4.0 * (1.0 - x - y) * x;
                break;
            default:
                NEVER_REACHED;
        }
        break;

    case 3:
        x = rPoint[0];
        y = rPoint[1];
        z = rPoint[2];
        switch (basisIndex)
        {
            case 0: // the node at (0,0,0)
                return 2.0 * (1.0 - x - y - z) * (0.5 - x - y - z);
                break;
            case 1: // the node at (1,0,0)
                return 2.0*x*(x-0.5);
                break;
            case 2: // the node at (0,1,0)
                return 2.0*y*(y-0.5);
                break;
            case 3: // the node at (0,0,1)
                return 2.0*z*(z-0.5);
                break;
            case 4: // our (tetgen convention), node4 is between nodes 0 and 1, (1/2,0,0)
                return 4.0 * (1.0 - x - y - z) * x;
                break;
            case 5: // our (tetgen convention), node5 is between nodes 1 and 2, (1/2,1/2,0)
                return 4 * x * y;
                break;
            case 6: // our (tetgen convention), node6 is between nodes 0 and 2, (0,1/2,0)
                return 4.0 * (1.0 - x - y - z) * y;
                break;
            case 7: // our (tetgen convention), node7 is between nodes 0 and 3, (0,0,1/2)
                return 4.0 * (1.0 - x - y - z) * z;
                break;
            case 8: // our (tetgen convention), node8 is between nodes 1 and 3, (1/2,0,1/2)
                return 4.0 * x * z;
                break;
            case 9: // our (tetgen convention), node9 is between nodes 2 and 3, (0,1/2,1/2)
                return 4.0 * y * z;
                break;
            default:
                NEVER_REACHED;
        }
        break;
    }
    return 0.0; // Avoid compiler warning
}

template <unsigned ELEMENT_DIM>
c_vector<double, ELEMENT_DIM> QuadraticBasisFunction<ELEMENT_DIM>::ComputeBasisFunctionDerivative(const ChastePoint<ELEMENT_DIM>& rPoint, unsigned basisIndex)
{
    c_vector<double, ELEMENT_DIM> gradN;
    assert(ELEMENT_DIM < 4 && ELEMENT_DIM > 0);

    double x, y, z;
    switch (ELEMENT_DIM)
    {
    case 1:
        x = rPoint[0];
        switch (basisIndex)
        {
            case 0:
                gradN(0) = 4.0*x-3.0;
                break;
            case 1:
                gradN(0) = 4.0*x-1.0;
                break;
            case 2:
                gradN(0) = 4.0-8.0*x;
                break;
            default:
                NEVER_REACHED;
        }
        break;

    case 2:
        x = rPoint[0];
        y = rPoint[1];
        switch (basisIndex)
        {
            case 0:
                gradN(0) = -3.0 + 4.0*x + 4.0*y;
                gradN(1) = -3.0 + 4.0*x + 4.0*y;
                break;
            case 1:
                gradN(0) = 4.0*x - 1.0;
                gradN(1) = 0.0;
                break;
            case 2:
                gradN(0) = 0.0;
                gradN(1) = 4.0*y - 1.0;
                break;
            case 3:
                gradN(0) = 4.0*y;
                gradN(1) = 4.0*x;
                break;
            case 4:
                gradN(0) = -4.0*y;
                gradN(1) = 4.0-4.0*x-8.0*y;
                break;
            case 5:
                gradN(0) = 4.0-8.0*x-4.0*y;
                gradN(1) = -4.0*x;
                break;
            default:
                NEVER_REACHED;
        }
        break;

    case 3:
        x = rPoint[0];
        y = rPoint[1];
        z = rPoint[2];
        switch (basisIndex)
        {
            case 0:
                gradN(0) = -3.0 + 4.0*(x+y+z);
                gradN(1) = -3.0 + 4.0*(x+y+z);
                gradN(2) = -3.0 + 4.0*(x+y+z);
                break;
            case 1:
                gradN(0) =  4.0*x-1.0;
                gradN(1) =  0;
                gradN(2) =  0;
                break;
            case 2:
                gradN(0) =  0;
                gradN(1) =  4.0*y-1.0;
                gradN(2) =  0;
                break;
            case 3:
                gradN(0) =  0;
                gradN(1) =  0;
                gradN(2) =  4.0*z-1.0;
                break;
            case 4:
                gradN(0) =  4.0-8.0*x-4.0*y-4.0*z;
                gradN(1) =  -4.0*x;
                gradN(2) =  -4.0*x;
                break;
            case 5:
                gradN(0) =  4.0*y;
                gradN(1) =  4.0*x;
                gradN(2) =  0.0;
                break;
            case 6:
                gradN(0) =  -4.0*y;
                gradN(1) =  4.0-4.0*x-8.0*y-4.0*z;
                gradN(2) =  -4.0*y;
                break;
            case 7:
                gradN(0) =  -4.0*z;
                gradN(1) =  -4.0*z;
                gradN(2) =  4.0-4.0*x-4.0*y-8.0*z;
                break;
            case 8:
                gradN(0) =  4.0*z;
                gradN(1) =  0;
                gradN(2) =  4.0*x;
                break;
            case 9:
                gradN(0) =  0;
                gradN(1) =  4.0*z;
                gradN(2) =  4.0*y;
                break;
            default:
                NEVER_REACHED;
        }
        break;
    }
    return gradN;
}

template <unsigned ELEMENT_DIM>
void QuadraticBasisFunction<ELEMENT_DIM>::ComputeBasisFunctions(const ChastePoint<ELEMENT_DIM>& rPoint,
                                                             c_vector<double, (ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2>& rReturnValue)
{
    assert(ELEMENT_DIM < 4 && ELEMENT_DIM >= 0);

    for (unsigned i=0; i<(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2; i++)
    {
        rReturnValue(i) = ComputeBasisFunction(rPoint, i);
    }
}

template <unsigned ELEMENT_DIM>
void QuadraticBasisFunction<ELEMENT_DIM>::ComputeBasisFunctionDerivatives(const ChastePoint<ELEMENT_DIM>& rPoint,
                                                                          c_matrix<double, ELEMENT_DIM, (ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2>& rReturnValue)
{
    assert(ELEMENT_DIM < 4 && ELEMENT_DIM > 0);

    for (unsigned j=0; j<(ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2; j++)
    {
        matrix_column<c_matrix<double, ELEMENT_DIM, (ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2> > column(rReturnValue, j);
        column = ComputeBasisFunctionDerivative(rPoint, j);
    }
}

template <unsigned ELEMENT_DIM>
void QuadraticBasisFunction<ELEMENT_DIM>::ComputeTransformedBasisFunctionDerivatives(const ChastePoint<ELEMENT_DIM>& rPoint,
                                                                                     const c_matrix<double, ELEMENT_DIM, ELEMENT_DIM>& rInverseJacobian,
                                                                                     c_matrix<double, ELEMENT_DIM, (ELEMENT_DIM+1)*(ELEMENT_DIM+2)/2>& rReturnValue)
{
    assert(ELEMENT_DIM < 4 && ELEMENT_DIM > 0);

    ComputeBasisFunctionDerivatives(rPoint, rReturnValue);
    rReturnValue = prod(trans(rInverseJacobian), rReturnValue);
}

// Explicit instantiation
template class QuadraticBasisFunction<1>;
template class QuadraticBasisFunction<2>;
template class QuadraticBasisFunction<3>;