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A comparison of two optimization methods for mesh quality improvement

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Abstract

We compare inexact Newton and block coordinate descent optimization methods for improving the quality of a mesh by repositioning the vertices, where the overall quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.

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Notes

  1. An important alternative to mesh optimization often used by the unstructured mesh community employs a series of local objective functions.

  2. For hybrid meshes, the exact definition of q can change depending on the element type. However, we assume that the quality metric, shape, for example, is the same for every element.

  3. This approach excludes elements such as pyramids but includes triangles, tetrahedra, wedges, quadrilaterals, and hexahedra.

  4. We show in [6] that averaging is unnecessary in the case of triangular or tetrahedral elements.

  5. Recall that (2) minimizes the inverse mean-ratio objective function, so the stated algorithms use minimization terminology. However, the same algorithms can be used for the maximization problem (1).

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Acknowledgments

The initial version of the analytic gradient for the inverse mean-ratio metric for tetrahedral elements was provided by Paul Hovland (Argonne National Laboratory). The clipped cube mesh image was provided by Carl Ollivier-Gooch (University of British Columbia). The work of the first, second, and third authors was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contracts W-7405-Eng-48 (UCRL-CONF-205150), DE-AC-94AL85000, and W-31-109-Eng-38, respectively. Part of the work of the fourth author was performed while a member of the Center for Applied Mathematics at Cornell University, supported by Sandia National Laboratories, Cornell University, the National Physical Science Consortium, and NSF grant ACI-0085969.

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Authors and Affiliations

  1. Lawrence Livermore National Laboratory, Livermore, CA, USA

    Lori Freitag Diachin

  2. Sandia National Laboratories, Albuquerque, NM, USA

    Patrick Knupp

  3. Argonne National Laboratory, Argonne, IL, USA

    Todd Munson

  4. University of Minnesota, Minneapolis, MN, USA

    Suzanne Shontz

Authors
  1. Lori Freitag Diachin
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  2. Patrick Knupp
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  3. Todd Munson
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  4. Suzanne Shontz
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Correspondence to Lori Freitag Diachin.

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Freitag Diachin, L., Knupp, P., Munson, T. et al. A comparison of two optimization methods for mesh quality improvement. Engineering with Computers 22, 61–74 (2006). https://doi.org/10.1007/s00366-006-0015-0

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  • DOI: https://doi.org/10.1007/s00366-006-0015-0

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