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

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

MESHING
RESEARCH
CORNER

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

Email: cfog@mech.ubc.ca

Abstract
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 Shewchuk’s 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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