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Matrix Norms & The Condition Number: A General Framework to Improve Mesh Quality Via Node-Movement

Knupp, Patrick M.

Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.13-22, October 1999


Patrick M. Knupp
Sandia National Laboratories, MIS 0847, P.O. Box 5800 Albuquerque, NM 87185-0847

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.

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