A comparison of two optimization methods for mesh quality improvement
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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.
KeywordsMesh 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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