Matrix Norms and the Condition Number: A General Framework to Improve Mesh Quality via Node-Movement

Conference · Mon Sep 27 00:00:00 EDT 1999

OSTI ID:14064

KNUPP, PATRICK

Objective functions for unstructured hexahedral and tetrahedral mesh optimization are analyzed using matrices and matrix norms. Mesh untangling objective functions that create valid meshes are used to initialize the optimization process. Several new objective functions to achieve element invertibility and quality are investigated, the most promising being the ''condition number''. The condition number of the Jacobian matrix of an element forms the basis of a barrier-based objective function that measures the distance to the set of singular matrices and has the ideal matrix as a stationary point. The method was implemented in the Cubit code, with promising results.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: US Department of Energy (US)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 14064
• Report Number(s): SAND99-2542C; TRN: AH200136%%297
• Resource Relation: Conference: 8th International Meshing Roundtable, South Lake Tahoe, CA (US), 10/10/1999--10/13/1999; Other Information: PBD: 27 Sep 1999
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
MATRICES
OPTIMIZATION
MESH GENERATION
MATRIX ELEMENTS
JACOBIAN FUNCTION
COMPUTER CALCULATIONS
MESH OPTIMIZATION
SHAPE MEASURES
CONDITION NUMBER
MATRIX NORMS
FINITE ELEMENT MESH
TETRAHEDRAL MESH
HEXAHEDRAL MESH
MESH UNTANGLING