| Bibliographic Citation | |
| Full Text |  1 Mb |
|---|---|
| Title | Tetrahedral element shape optimization via the Jacobian determinant and condition number. |
| Creator/Author | Freitag, L. A. ; Knupp, P. M. |
| Publication Date | 1999 Jul 30 |
| OSTI Identifier | OSTI ID: 11915 |
| Report Number(s) | ANL/MCS/CP-99689 |
| DOE Contract Number | W-31109-ENG-38 |
| Other Number(s) | TRN: AH200119%%114 |
| Resource Type | Conference |
| Resource Relation | Conference: 8th International Meshing Roundtable, South Lake Tahoe, CA (US), 10/10/1999--10/13/1999; Other Information: PBD: 30 Jul 1999 |
| Research Org | Argonne National Lab., IL (US) |
| Sponsoring Org | US Department of Energy (US) |
| Subject | 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; OPTIMIZATION; SHAPE; TRANSFORMATIONS; JACOBIAN FUNCTION; MESH GENERATION |
| Description/Abstract | 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. |
| Country of Publication | United States |
| Language | English |
| Format | Medium: P; Size: 14 pages |
| Availability | OSTI as DE00011915 To purchase this media from NTIS, click here |
| System Entry Date | 2008 Feb 04 |
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Last Updated: 11/20/2009