Engineering with Computers

, Volume 22, Issue 2, pp 61–74 | Cite as

A comparison of two optimization methods for mesh quality improvement

  • Lori Freitag Diachin
  • Patrick Knupp
  • Todd Munson
  • Suzanne Shontz
Original Article


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.


Mesh quality improvement Mesh optimization Mesh smoothing 



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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Copyright information

© Springer-Verlag London Limited 2006

Authors and Affiliations

  • Lori Freitag Diachin
    • 1
  • Patrick Knupp
    • 2
  • Todd Munson
    • 3
  • Suzanne Shontz
    • 4
  1. 1.Lawrence Livermore National LaboratoryLivermoreUSA
  2. 2.Sandia National LaboratoriesAlbuquerqueUSA
  3. 3.Argonne National LaboratoryArgonneUSA
  4. 4.University of MinnesotaMinneapolisUSA

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