Measuring the Metric Conformity of a Mesh
Labbe, Paul; Dompierre, Julien; Vallet, Marie-Gabrielle; Guibalt, Francois; Trepanier, Jean-Yves
Numerical Grid Generation in Computational Field Simulations, The International Society of Grid Generation, pp.809-818, September 2000
Centre de recherche en calcul appliqué (CERCA),
5160, boul. Décarie, bureau 400, Montréal (Québec), H3X, Canada.
E-mail: [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 satisty. The size specification map is given in the form of a Riemannian metric that specifies both size and stretching of the mesh to be built. 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. It is sensitive to discrepancies in both shape and size between the simplices of the mesh and the Riemannian metric that the mesh is supposed to satisfy.
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