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Tetrahedral mesh improvement via optimization of the element condition number
Author(s) -
Freitag Lori A.,
Knupp Patrick M.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.341
Subject(s) - tetrahedron , measure (data warehouse) , equilateral triangle , polygon mesh , transformation (genetics) , mathematics , mathematical optimization , set (abstract data type) , element (criminal law) , algorithm , computer science , topology (electrical circuits) , geometry , combinatorics , data mining , biochemistry , chemistry , political science , law , gene , programming language
We 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, we 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. We review the optimization techniques used with each objective function and present experimental results that demonstrate the effectiveness of the mesh improvement methods. We show that a combined optimization approach that uses both objective functions obtains the best‐quality meshes for several complex geometries. Copyright © 2001 John Wiley & Sons, Ltd.