17th GAMM-Seminar Leipzig on
Construction of Grid Generation Algorithms

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  17th GAMM-Seminar
February, 1st-3rd, 2001
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  Conditions for the Invertibility of the Isoparametric Mapping for 3D Multi-Linear Finite Elements
G. Summ (Uni Erlangen)

We consider the isoparametric transformation, which maps a given reference element onto a global element given by its vertices, for multi-linear finite elements on pyramids, prisms and hexahedrons.

In the cases of pyramids and prisms we derive easily computable conditions on the position of the vertices, which ensure that the isoparametric transformation is invertible. We give a geometric interpretation of these conditions and illustrate their application with some examples.

In the case of hexahedrons we present an algorithm, which checks arbitrarily sharp sufficient conditions for the positivity of the jacobian determinant and therefore ensures the local invertibility of the isoparametric transformation. Again, we give some examples for illustration.

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Last updated:
30.11.2004 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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