Algebraic mesh quality metrics

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Description

Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element ... continued below

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29 p.

Creation Information

Knupp, Patrick April 24, 2000.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 18 times . More information about this article can be viewed below.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.

Physical Description

29 p.

Notes

OSTI as DE00754328

Medium: P; Size: 29 pages

Source

  • Journal Name: SIAM Journal of Scientific Computing; Other Information: Submitted to SIAM Journal of Scientific Computing

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  • Report No.: SAND2000-1033J
  • Report No.: 0000035207-000
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 754328
  • Archival Resource Key: ark:/67531/metadc706326

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  • April 24, 2000

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • April 10, 2017, 7:05 p.m.

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Knupp, Patrick. Algebraic mesh quality metrics, article, April 24, 2000; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc706326/: accessed September 26, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.