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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.

##### MSC:
 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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