Numerical inverse isoparametric mapping in 3D FEM

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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(N3) is usually employed instead of solving a system of nonlinear equations. This iteration, however, can be improved to be only of order O(N2) 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.

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