Tetrahedral element shape optimization via the Jacobian determinant and condition number.

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We present a new shape measure for tetrahedral elements that is optimal in the sense 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. We use this shape measure to 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. Because the element condition number is not defined ... continued below

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14 p.

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Freitag, L. A. & Knupp, P. M. July 30, 1999.

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We present a new shape measure for tetrahedral elements that is optimal in the sense 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. We use this shape measure to 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. Because the element condition number is not defined for tetrahedral with negative volume, these objective functions can be used only when the initial mesh is valid. Therefore, we formulate a third objective function using the determinant of the element Jacobian that is suitable for mesh untangling. We review the optimization techniques used with each objective function and present experimental results that demonstrate the effectiveness of the mesh improvement and untangling methods. We show that a combined optimization approach that uses both condition number objective functions obtains the best-quality meshes.

Physical Description

14 p.

Notes

OSTI as DE00011915

Medium: P; Size: 14 pages

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  • 8th International Meshing Roundtable, South Lake Tahoe, CA (US), 10/10/1999--10/13/1999

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  • Report No.: ANL/MCS/CP-99689
  • Grant Number: W-31109-ENG-38
  • Office of Scientific & Technical Information Report Number: 11915
  • Archival Resource Key: ark:/67531/metadc626288

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  • July 30, 1999

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

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  • April 7, 2017, 2:32 p.m.

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Freitag, L. A. & Knupp, P. M. Tetrahedral element shape optimization via the Jacobian determinant and condition number., article, July 30, 1999; Illinois. (digital.library.unt.edu/ark:/67531/metadc626288/: accessed December 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.