Generation of Tetrahedral Finite Element Meshes: Variational Delaunay Approach

Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.273-284, October 1998

MESHING
RESEARCH
CORNER

7th International Meshing Roundtable
October 26-28, 1998
Dearborn, Michigan, USA

Petr Krysl
Staff scientist,
California Institute of Technology,
Email: pkrysl@atlantis.caltech.edu

Michael Ortiz
Professor of Aeronautics and Applied Mechanics,
California Institute of Technology,
Email: ortiz@atlantis.caltech.edu

Abstract
The goal is to generate tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets. The principle idea is that a vertex set in general positions guarantees existence of a unique triangulation which satisfies the Delaunay empty-sphere property. (Algorithms for robust, parallel construction of such triangulations are available.) However, all of the input surface facets do not necessarily appear in such a triangulation. In order to represent the boundary of the solid, we iterate two operations, edge flip and edge split with the insertion of additional vertex, until all of the boundary facets are present in the tetrahedral mesh. The outcome of the vertex insertion is another triangulation of the input surfaces, but one which is represented as a subset of the tetrahedral faces.

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