A comparison of two optimization methods for mesh quality improvement

Abstract

We compare inexact Newton and 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.

A dual element based geometric element transformation method for all-hexahedral mesh smoothing

“…The other identities can be deduced analogously. h In order to judge the regularizing effect of the transformation the quality of a hexahedral element will be measured by the mean ratio quality criterion given in [33,34]. This criterion is particularly suited for element regularizing approaches, since it measures the deviation of an arbitrary tetrahedron from a given reference tetrahedron.…”

Implementation and evaluation of automated tetrahedral–prismatic mesh generation software

“…Within the scope of the present work, the Mesquite toolkit was evaluated as well [16,26]. For the limited task of envelope optimization, however, MMA achieved better results within practical optimization time limits.…”

The geometric element transformation method for tetrahedral mesh smoothing

“…That is, if the transformation is applied iteratively, the resulting tetrahedra become more and more regular. In order to assess the regularity of a tetrahedron T numerically, the mean ratio quality criterion [18,20] will be used. It is given by…”

“…This leads to methods which can be combined with classical Laplacian smoothing in order to moderate the higher computational complexity [14] or even be used to untangle 0045 meshes [16]. The good quality achieved by local optimizationbased methods can be further improved by using global optimization-based methods, which incorporate all mesh elements into the objective function [17,18]. Naturally, this leads to a higher implementational and computational complexity.…”