title: Achieving Finite Element Mesh Quality via Optimization of the Jacobian
 Matrix Norm and Associated Quantities, Part 1 - A Framework for Surface Mesh
 Optimization
creator: Knupp, P.M.
contributor: United States. Department of Energy.
publisher: Sandia National Laboratories
date: 1999-01-18
language: English
description: Structured mesh quality optimization methods are extended to
 optimization of unstructured triangular, quadrilateral, and mixed finite
 element meshes. N"ew interpretations of well-known nodally-bssed objective
 functions are made possible using matrices and matrix norms. The matrix
 perspective also suggests several new objective functions. Particularly
 significant is the interpretation of the Oddy metric and the Smoothness
 objective functions in terms of the condition number of the metric tensor and
 Jacobian matrix, respectively. Objective functions are grouped according to
 dimensionality to form weighted combinations. A simple unconstrained local
 optimum is computed using a modiiied N-ewton iteration. The optimization
 approach was implemented in the CUBIT mesh generation code and tested on
 several problems. Results were compared against several standard element-based
 quaIity measures to demonstrate that good mesh quality can be achieved with
 nodally-based objective functions.
subject: Optimization
subject: 99 Mathematics, Computers, Information Science, Management, Law,
 Miscellaneous
subject: Finite Element Method
subject: Mesh Generation
source: Journal Name: International Journal Numerical Methods in Engineering
type: Article
format: Text
identifier: other: DE00003213
identifier: rep-no: SAND99-0110J
identifier: grantno: AC04-94AL85000
identifier: osti: 3213
identifier: https://digital.library.unt.edu/ark:/67531/metadc682780/
identifier: ark: ark:/67531/metadc682780