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Title: Algebraic mesh quality metrics

Abstract

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.

Authors:
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
754328
Report Number(s):
SAND2000-1033J; 0000035207-000
0000035207-000; TRN: AH200016%%219
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article
Journal Name:
SIAM Journal of Scientific Computing
Additional Journal Information:
Other Information: Submitted to SIAM Journal of Scientific Computing; PBD: 24 Apr 2000
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MESH GENERATION; EVALUATION; METRICS; MATRICES; UNSTRUCTURED MESH GENERATION; MESH QUALITY METRICS; CONDITION NUMBER; SHAPE MEASURES

Citation Formats

KNUPP, PATRICK. Algebraic mesh quality metrics. United States: N. p., 2000. Web.
KNUPP, PATRICK. Algebraic mesh quality metrics. United States.
KNUPP, PATRICK. 2000. "Algebraic mesh quality metrics". United States. https://www.osti.gov/servlets/purl/754328.
@article{osti_754328,
title = {Algebraic mesh quality metrics},
author = {KNUPP, PATRICK},
abstractNote = {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.},
doi = {},
url = {https://www.osti.gov/biblio/754328}, journal = {SIAM Journal of Scientific Computing},
number = ,
volume = ,
place = {United States},
year = {2000},
month = {4}
}