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Performance characterization of nonlinear optimization methods for mesh quality improvement

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Abstract

We characterize the performance of gradient- and Hessian-based optimization methods for mesh quality improvement. In particular, we consider the steepest descent and Polack-Ribière conjugate gradient methods which are gradient based. In the Hessian-based category, we consider the quasi-Newton, trust region, and feasible Newton methods. These techniques are used to improve the quality of a mesh by repositioning the vertices, where the overall mesh quality is measured by the sum of the squares of individual elements according to the aspect ratio metric. The effects of the desired degree of accuracy in the improved mesh, problem size, initial mesh configuration, and heterogeneity in element volume on the performance of the optimization solvers are characterized on a series of tetrahedral meshes.

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Acknowledgments

The work of Shankar Prasad Sastry was funded in part by an Institute for CyberScience grant from The Pennsylvania State University. The work of Suzanne M. Shontz was funded in part by NSF grant CNS 0720749 and a Grace Woodward grant from The Pennsylvania State University.

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Authors and Affiliations

  1. The Pennsylvania State University, University Park, PA, 16802, USA

    Shankar Prasad Sastry & Suzanne M. Shontz

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  1. Shankar Prasad Sastry
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  2. Suzanne M. Shontz
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Correspondence to Suzanne M. Shontz.

Additional information

A preliminary version of a portion of these results appeared in shortened form in the Proceedings of the 2009 International Meshing Roundtable.

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Sastry, S.P., Shontz, S.M. Performance characterization of nonlinear optimization methods for mesh quality improvement. Engineering with Computers 28, 269–286 (2012). https://doi.org/10.1007/s00366-011-0227-9

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