Numerical inverse isoparametric mapping in 3D FEM

Abstract An extension of numerical inverse isoparametric mapping [Murti and Valliappan, Comput. Struct . 22 , 1011–1021 (1986)] to three dimensional (3D) space is presented. In the 3D finite element method (FEM), the determination of the local coordinate of a point of known Cartesian coordinates is not so straight-forward. A direct iterative technique that may require iterations of order O ( N 3 ) is usually employed instead of solving a system of nonlinear equations. This iteration, however, can be improved to be only of order O ( N 2 ) by defining a line in the 3D Cartesian space and iterating along this line. The details of the method are described and the FORTRAN subroutines for the method proposed are also given.