ShapeHex20-impl.h

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namespace
{
inline double ShapeFunctionHexHQ_Corner(const double r, const double s,
                                        const double t)
{
    return 0.125 * (r - 1) * (s - 1) * (t - 1) * (r + s + t + 2.0);
}
 
inline double ShapeFunctionHexHQ_Middle(const double r, const double s,
                                        const double t)
{
    return 0.25 * (1 - r * r) * (s - 1) * (t - 1);
}
 
inline double dShapeFunctionHexHQ_Corner(const double r, const double s,
                                         const double t, const int ty)
{
    switch (ty)
    {
        case 0:
            return 0.125 * (s - 1) * (t - 1) * (2.0 * r + s + t + 1.0);
        case 1:
            return 0.125 * (t - 1) * (r - 1) * (2.0 * s + r + t + 1.0);
        case 2:
            return 0.125 * (r - 1) * (s - 1) * (2.0 * t + s + r + 1.0);
    }
    return 0.0;
}
 
inline double dShapeFunctionHexHQ_Middle(const double r, const double s,
                                         const double t, const int ty)
{
    switch (ty)
    {
        case 0:
            return -0.5 * r * (s - 1) * (t - 1);
        case 1:
            return 0.25 * (1 - r * r) * (t - 1);
        case 2:
            return 0.25 * (1 - r * r) * (s - 1);
    }
    return 0.0;
}
 
}  // namespace
 
namespace NumLib
{
template <class T_X, class T_N>
void ShapeHex20::computeShapeFunction(const T_X& rst, T_N& N)
{
    const double r = rst[0];
    const double s = rst[1];
    const double t = rst[2];
 
    N[0] = ShapeFunctionHexHQ_Corner(r, s, t);
    N[1] = ShapeFunctionHexHQ_Corner(-r, s, t);
    N[2] = ShapeFunctionHexHQ_Corner(-r, -s, t);
    N[3] = ShapeFunctionHexHQ_Corner(r, -s, t);
    N[4] = ShapeFunctionHexHQ_Corner(r, s, -t);
    N[5] = ShapeFunctionHexHQ_Corner(-r, s, -t);
    N[6] = ShapeFunctionHexHQ_Corner(-r, -s, -t);
    N[7] = ShapeFunctionHexHQ_Corner(r, -s, -t);
 
    N[8] = ShapeFunctionHexHQ_Middle(r, s, t);
    N[10] = ShapeFunctionHexHQ_Middle(r, -s, t);
    N[14] = ShapeFunctionHexHQ_Middle(r, -s, -t);
    N[12] = ShapeFunctionHexHQ_Middle(r, s, -t);
 
    N[11] = ShapeFunctionHexHQ_Middle(s, t, r);
    N[15] = ShapeFunctionHexHQ_Middle(s, -t, r);
    N[13] = ShapeFunctionHexHQ_Middle(s, -t, -r);
    N[9] = ShapeFunctionHexHQ_Middle(s, t, -r);
 
    N[16] = ShapeFunctionHexHQ_Middle(t, r, s);
    N[17] = ShapeFunctionHexHQ_Middle(t, -r, s);
    N[18] = ShapeFunctionHexHQ_Middle(t, -r, -s);
    N[19] = ShapeFunctionHexHQ_Middle(t, r, -s);
}
 
template <class T_X, class T_N>
void ShapeHex20::computeGradShapeFunction(const T_X& rst, T_N& dNdr)
{
    const double r = rst[0];
    const double s = rst[1];
    const double t = rst[2];
    const static double sign1[] = {-1.0, 1.0, 1.0};
    const static double sign2[] = {1.0, -1.0, 1.0};
    const static double sign3[] = {1.0, 1.0, -1.0};
    for (int i = 0; i < 3; i++)
    {
        dNdr[20 * i + 0] = dShapeFunctionHexHQ_Corner(r, s, t, i);
        dNdr[20 * i + 1] = sign1[i] * dShapeFunctionHexHQ_Corner(-r, s, t, i);
        dNdr[20 * i + 2] =
            sign1[i] * sign2[i] * dShapeFunctionHexHQ_Corner(-r, -s, t, i);
        dNdr[20 * i + 3] = sign2[i] * dShapeFunctionHexHQ_Corner(r, -s, t, i);
        dNdr[20 * i + 4] = sign3[i] * dShapeFunctionHexHQ_Corner(r, s, -t, i);
        dNdr[20 * i + 5] =
            sign1[i] * sign3[i] * dShapeFunctionHexHQ_Corner(-r, s, -t, i);
        dNdr[20 * i + 6] = sign1[i] * sign2[i] * sign3[i] *
                           dShapeFunctionHexHQ_Corner(-r, -s, -t, i);
        dNdr[20 * i + 7] =
            sign2[i] * sign3[i] * dShapeFunctionHexHQ_Corner(r, -s, -t, i);
 
        dNdr[20 * i + 8] = dShapeFunctionHexHQ_Middle(r, s, t, i);
        dNdr[20 * i + 10] = sign2[i] * dShapeFunctionHexHQ_Middle(r, -s, t, i);
        dNdr[20 * i + 14] =
            sign2[i] * sign3[i] * dShapeFunctionHexHQ_Middle(r, -s, -t, i);
        dNdr[20 * i + 12] = sign3[i] * dShapeFunctionHexHQ_Middle(r, s, -t, i);
 
        {
            int const co = (i + 2) % 3;
            dNdr[20 * i + 11] = dShapeFunctionHexHQ_Middle(s, t, r, co);
            dNdr[20 * i + 15] =
                sign3[i] * dShapeFunctionHexHQ_Middle(s, -t, r, co);
            dNdr[20 * i + 13] =
                sign1[i] * sign3[i] * dShapeFunctionHexHQ_Middle(s, -t, -r, co);
            dNdr[20 * i + 9] =
                sign1[i] * dShapeFunctionHexHQ_Middle(s, t, -r, co);
        }
 
        {
            int const co = (i + 1) % 3;
            dNdr[20 * i + 16] = dShapeFunctionHexHQ_Middle(t, r, s, co);
            dNdr[20 * i + 17] =
                sign1[i] * dShapeFunctionHexHQ_Middle(t, -r, s, co);
            dNdr[20 * i + 18] =
                sign1[i] * sign2[i] * dShapeFunctionHexHQ_Middle(t, -r, -s, co);
            dNdr[20 * i + 19] =
                sign2[i] * dShapeFunctionHexHQ_Middle(t, r, -s, co);
        }
    }
}
 
}  // namespace NumLib