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Label-Invariant Mesh Quality Metrics

Knupp, Patrick

Proceedings, 18th International Meshing Roundtable, Springer-Verlag, pp.139-155, October 25-28 2009

IMR
PROCEEDINGS

18th International Meshing Roundtable
Salt Lake City, UT, USA.
October 25-28, 2009

Sandia National Laboratories
pknupp@sandia.gov

Abstract
Mappings from a master element to the physical mesh element, in conjunction with local metrics such as those appearing in the Target-matrix paradigm, are used to measure quality at points within an element. The approach is applied to both linear and quadratic triangular elements; this enables, for example, one to measure quality within a quadratic finite element. Quality within an element may also be measured on a set of symmetry points, leading to so-called symmetry metrics. An important issue having to do with the labeling of the element vertices is relevant to mesh quality tools such as Verdict and Mesquite. Certain quality measures like area, volume, and shape should be label-invariant, while others such as aspect ratio and orientation should not. It is shown that local metrics whose Jacobian matrix is non-constant are label-invariant only at the center of the element, while symmetry metrics can be label-invariant anywhere within the element, provided the reference element is properly restricted.

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