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A Methodology for FEA over Tangled Meshes

Danczyk, Josh and Krishnan Suresh

Research Notes, 21st International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 7-10 2012

IMR
PROCEEDINGS

21st International Meshing Roundtable
San Jose, CA
October 7-10, 2012

University of Wisconsin, Madison, WI, U.S.A.
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Summary
A finite element mesh is said to be √ętangled√≠ if two or more its elements overlap. This can occur, for example during mesh optimization and mesh morphing. Modern finite element theory and commercial FEA packages are not designed to handle tangled meshes, i.e., they can lead to erroneous results. In this paper, a new mathematical framework for FEA is proposed for handling tangled simplicial meshes. Specifically, by defining a cell-decomposition of a tangled mesh, and an associated set of cell shape functions as an oriented linear combination of the classic element shape functions, it is shown that one can successfully carry out accurate FEA over tangled meshes. Numerical examples illustrate the correctness of the proposed framework.

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