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Numerical inverse isoparametric mapping in 3D FEM. (English) Zbl 0638.73037
An extension of numerical inverse isoparametric mapping [see the first and the last author, ibid. 22, 1011-1021 (1986; Zbl 0578.73067)] to three dimensional (3D) space is presented. In the three-dimensional 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 three-dimensional 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.

74S05 Finite element methods applied to problems in solid mechanics
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
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