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A Measure of the Conformity of a Mesh to an Anisotropic Metric

Labbe, Paul, Julien Dompierre, Marie-Gabrielle Vallet, Francois Guibault and Jean-Yves Trepanier

Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp.319-326, October 7-10 2001

IMR
PROCEEDINGS

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

Centre de recherche en calcul applique (CERCA)
5160, boul. Decarie, bureau 400,
Montreal, QC, H3X 2H9, Canada.
Email: { paul | julien | vallet | francois | jyves }@cerca.umontreal.ca

Abstract
A method is proposed to measure the difference between a given mesh and the size specification map that this mesh is supposed to satisfy. The size specification map is given in the form of a Riemannian metric that specifies both size and stretching of the mesh to be build. The measure evaluates the difference between the unique metric for which a simplex is a unit equilateral simplex, and the average value over the simplex of the specified Riemannian metric. Analytical and numerical examples illustrate the behavior of this measure. This measure is a unique dimensionless number that characterizes a whole mesh both in size and in shape, be it isotropic or anisotropic, coarse or fine, in a small or a big domain, in two or three dimensions.

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