The Meshing Complexity of a Solid: An Introduction

Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp.373-384, October 7-10 2001

MESHING
RESEARCH
CORNER

10th International Meshing Roundtable
Newport Beach, California, U.S.A.
October 7-10, 2001

David R. White, Robert W. Leland, Steven J. Owen
Sandia National Laboratories,
Albuquerque, NM, U.S.A.
Email: drwhite@sandia.gov, leland@sandia.gov, sjowen@sandia.gov

David R. White, Sunil Saigal
Carnegie Mellon University
Pittsburgh, PA, U.S.A.
Email: drwhite@sandia.gov, saigal@andrew.cmu.edu

Abstract
This paper explores potential methods for characterizing the meshing complexity of solid geometry. While numerous metrics exist to measure the quality of the finite element, there are currently no metrics that measure the quality of a solid with respect to its meshing complexity. The meshing complexity of a solid is defined by how difficult it is to generate a valid finite element mesh for a given solid. There are many variables that affect meshing complexity. This paper seeks to discuss methods that are decoupled from more subjective variables such as user expertise and software maturity, and it will focus on methods that describe the topological and geometric aspects of a solid. It will present techniques based on: medial axis transformation, wavelets, curvature, proximity, intersection, heuristic topology search, and the measurement of space (volume/area/length) and will analyze their suitability as meshing complexity metrics.

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