public override Vector[] Calculate_DerivativesOfShapeFunctions_WRTXi(Vector Xi)
{
Vector[] DNDXi = new Vector[NNPE];
Vector N_1D_L = ParametricInterpolation_1D_L.CalculateShapeFunctions(Xi.Values[0]);
Vector N_1D_M = ParametricInterpolation_1D_M.CalculateShapeFunctions(Xi.Values[1]);
Vector N_1D_N = ParametricInterpolation_1D_N.CalculateShapeFunctions(Xi.Values[2]);
Vector DNDXi_1D_L = ParametricInterpolation_1D_L.CalculateDerivativesOfShapeFunctions_WRTXi(Xi.Values[0]);
Vector DNDXi_1D_M = ParametricInterpolation_1D_M.CalculateDerivativesOfShapeFunctions_WRTXi(Xi.Values[1]);
Vector DNDXi_1D_N = ParametricInterpolation_1D_N.CalculateDerivativesOfShapeFunctions_WRTXi(Xi.Values[2]);
int Index = 0;
for (int k = 0; k < NNPE_n; k++)
{
for (int j = 0; j < NNPE_m; j++)
{
for (int i = 0; i < NNPE_l; i++)
{
DNDXi[Index] = new Vector(3);
DNDXi[Index].Values[0] = N_1D_N.Values[k] * N_1D_M.Values[j] * DNDXi_1D_L.Values[i];
DNDXi[Index].Values[1] = N_1D_N.Values[k] * DNDXi_1D_M.Values[j] * N_1D_L.Values[i];
DNDXi[Index].Values[2] = DNDXi_1D_N.Values[k] * N_1D_M.Values[j] * N_1D_L.Values[i];
Index++;
}
}
}
return(DNDXi);
}
public override Vector Calculate_ShapeFunctions(Vector Xi)
{
Vector N = new Vector(NNPE);
Vector N_1D_M = ParametricInterpolation_1D_M.CalculateShapeFunctions(Xi.Values[0]);
Vector N_1D_N = ParametricInterpolation_1D_N.CalculateShapeFunctions(Xi.Values[1]);
int Index = 0;
for (int j = 0; j < NNPE_n; j++)
{
for (int i = 0; i < NNPE_m; i++)
{
N.Values[Index] = N_1D_M.Values[i] * N_1D_N.Values[j];
Index++;
}
}
return(N);
}
public override Matrix_Jagged Calculate_DerivativesOfShapeFunctions_WRTXi_Matrix_Jagged(Vector Xi)
{
Matrix_Jagged DNDXi = new Matrix_Jagged(NNPE, 2);
Vector N_1D_M = ParametricInterpolation_1D_M.CalculateShapeFunctions(Xi.Values[0]);
Vector N_1D_N = ParametricInterpolation_1D_N.CalculateShapeFunctions(Xi.Values[1]);
Vector DNDXi_1D_M = ParametricInterpolation_1D_M.CalculateDerivativesOfShapeFunctions_WRTXi(Xi.Values[0]);
Vector DNDXi_1D_N = ParametricInterpolation_1D_N.CalculateDerivativesOfShapeFunctions_WRTXi(Xi.Values[1]);
int Index = 0;
for (int j = 0; j < NNPE_n; j++)
{
for (int i = 0; i < NNPE_m; i++)
{
DNDXi.Values[Index][0] = DNDXi_1D_M.Values[i] * N_1D_N.Values[j];
DNDXi.Values[Index][1] = N_1D_M.Values[i] * DNDXi_1D_N.Values[j];
Index++;
}
}
return(DNDXi);
}