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 ^[1]

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1. Sandia National Laboratories

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 Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
• Sponsoring Organization: US Department of Energy (US)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 14064
• Report Number(s): SAND99-2542C
• Country of Publication: United States
• Language: English

Related Subjects

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