An efficient optimization procedure for tetrahedral meshes by chaos search algorithm

A simple and efficient local optimization-based procedure for node repositioning/smoothing of three-dimensional tetrahedral meshes is presented. The initial tetrahedral mesh is optimized with respect to a specified element shape measure by chaos search algorithm, which is very effective for the optimization problems with only a few design variables. Examples show that the presented smoothing procedure can provide favorable conditions for local transformation approach and the quality of mesh can be significantly improved by the combination of these two procedures with respect to a specified element shape measure. Meanwhile, several commonly used shape measures for tetrahedral element, which are considered to be equivalent in some weak sense over a long period of time, are briefly re-examined in this paper. Preliminary study indicates that using different measures to evaluate the change of element shape will probably lead to inconsistent result for both well shaped and poorly shaped elements. The proposed smoothing approach can be utilized as an appropriate and effective tool for evaluating element shape measures and their influence on mesh optimization process and optimal solution.