public void Calculate_X_DNDX_DetJacobian(Vector Xi, Node_ND[] ElementNodes, out Vector X, out Matrix_Jagged DNDX, out double Det_Jac)
{
Vector[] Xp = Get_ElementNodal_X(ElementNodes);
Vector N;
Vector[] dNdXi = Calculate_DerivativesOfShapeFunctions_WRTXi(Xi, out N);
X = Interpolate_Variable(Xp, N);
Matrix_Jagged DNDXi = new Matrix_Jagged(dNdXi).Transpose();
Matrix_Jagged DXDXi = Interpolate_DerivativeOfVariable_WRTXi(Xp, dNdXi);
Matrix_Jagged DXiDX = DXDXi.Invert(out Det_Jac);
DNDX = DNDXi * DXiDX;
}
public virtual Matrix_Jagged Calculate_InverseJacobian_DXiDX(Vector Xi, Node_ND[] ElementNodes)
{
Matrix_Jagged DXDXi = Calculate_Jacobian_DXDXi(Xi, ElementNodes);
return(DXDXi.Invert());
}
public virtual Matrix_Jagged Calculate_InverseJacobian_DXiDX(Vector Xi, Node_ND[] ElementNodes, out Matrix_Jagged DXDXi, out double Det_Jacobian)
{
DXDXi = Calculate_Jacobian_DXDXi(Xi, ElementNodes);
return(DXDXi.Invert(out Det_Jacobian));
}
public virtual void Calculate_dNdXi_DXDXi_DXiDX_DetJac(Vector Xi, Node_ND[] ElementNodes, out Vector[] dNdXi, out Matrix_Jagged DXDXi, out Matrix_Jagged DXiDX, out double DetJac)
{
Calculate_dNdXi_DXDXi(Xi, ElementNodes, out dNdXi, out DXDXi);
DXiDX = DXDXi.Invert(out DetJac);
}