Achieving Finite Element Mesh Quality via Optimization of the Jacobian Matrix Norm and Associated Quantities, Part 1 - A Framework for Surface Mesh Optimization

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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 ... continued below

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Knupp, P.M. January 18, 1999.

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This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 77 times , with 5 in the last month . More information about this article can be viewed below.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Laboratories, Albuquerque, NM, and Livermore, CA
    Place of Publication: Albuquerque, New Mexico

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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.

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  • Journal Name: International Journal Numerical Methods in Engineering

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  • Other: DE00003213
  • Report No.: SAND99-0110J
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 3213
  • Archival Resource Key: ark:/67531/metadc682780

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  • January 18, 1999

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  • July 25, 2015, 2:20 a.m.

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  • Nov. 22, 2016, 2:24 p.m.

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Knupp, P.M. Achieving Finite Element Mesh Quality via Optimization of the Jacobian Matrix Norm and Associated Quantities, Part 1 - A Framework for Surface Mesh Optimization, article, January 18, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc682780/: accessed October 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.