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
21st International Meshing Roundtable
San Jose, CA
October 7-10, 2012
University of Wisconsin, Madison, WI, U.S.A.
A finite element mesh is said to be ëtangledí 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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