skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Tetrahedral mesh improvement via optimization of the element condition number

Abstract

The authors present a new shape measure for tetrahedral elements that is optimal in that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. Using this shape measure, they formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the tetrahedral mesh; the second aims to improve the worst-quality element in the mesh. They review the optimization techniques used with each objective function and presents experimental results that demonstrate the effectiveness of the mesh improvement methods. They show that a combined optimization approach that uses both objective functions obtains the best-quality meshes for several complex geometries.

Authors:
;
Publication Date:
Research Org.:
Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
755616
Report Number(s):
SAND2000-1276J
TRN: AH200021%%359
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Other Information: Submitted to International Journal for Numerical Methods in Engineering; PBD: 22 May 2000
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MESH GENERATION; GEOMETRY; ALGORITHMS; OPTIMIZATION; NUMERICAL SOLUTION; MESH IMPROVEMENT; OPTIMIZATION-BASED MESH SMOOTHING; MESH QUALITY; ELEMENT CONDITION NUMBER

Citation Formats

FREITAG,LORI A., and KNUPP,PATRICK. Tetrahedral mesh improvement via optimization of the element condition number. United States: N. p., 2000. Web.
FREITAG,LORI A., & KNUPP,PATRICK. Tetrahedral mesh improvement via optimization of the element condition number. United States.
FREITAG,LORI A., and KNUPP,PATRICK. Mon . "Tetrahedral mesh improvement via optimization of the element condition number". United States. https://www.osti.gov/servlets/purl/755616.
@article{osti_755616,
title = {Tetrahedral mesh improvement via optimization of the element condition number},
author = {FREITAG,LORI A. and KNUPP,PATRICK},
abstractNote = {The authors present a new shape measure for tetrahedral elements that is optimal in that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. Using this shape measure, they formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the tetrahedral mesh; the second aims to improve the worst-quality element in the mesh. They review the optimization techniques used with each objective function and presents experimental results that demonstrate the effectiveness of the mesh improvement methods. They show that a combined optimization approach that uses both objective functions obtains the best-quality meshes for several complex geometries.},
doi = {},
journal = {International Journal for Numerical Methods in Engineering},
number = ,
volume = ,
place = {United States},
year = {2000},
month = {5}
}