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Improved Cell Size and Grading In Guaranteed Quality Triangular and Tetrahedral Meshes

Ollivier-Gooch, Carl and Charles Boivin

Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.43-54, October 2000


9th International Meshing Roundtable
October 2-5, 2000, New Orlean Louisiana

Carl Ollivier-Gooch and Charles Boivin
Advanced Numerical Simulation Laboratory
Department of Mechanical Engineering
University of British Columbia


Unstructured mesh quality, as measured geometrically, has long been known to influence solution accuracy and efficiency for finite-element and finite-volume simulations. Recent guaranteed-quality unstructured meshing algorithms are therefore welcome tools. However, these algorithms allow no explicit control over mesh resolution or grading. We present modifications to Rupperts two-dimensional and Shewchukís three-dimensional meshing algorithms that provide such control. We provide proofs of mesh quality, good grading, and size optimality for the two-dimensional case, and speculate about the possibility of proof in three dimensions

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