An Efficient Optimization Procedure for Tetrahedral Meshes by Chaos Search Algorithm

A simple and efficient localoptimization-based procedure for node repositioning/smoothing ofthree-dimensional tetrahedral meshes is presented. The initialtetrahedral mesh is optimized with respect to a specified element shapemeasure by chaos search algorithm, which is very effective for theoptimization problems with only a few design variables. Examples showthat the presented smoothing procedure can provide favorable conditionsfor local transformation approach and the quality of mesh can besignificantly improved by the combination of these two procedures withrespect to a specified element shape measure. Meanwhile, severalcommonly used shape measures for tetrahedral element, which areconsidered to be equivalent in some weak sense over a long period oftime, are briefly re-examined in this paper. Preliminary study indicatesthat using different measures to evaluate the change of element shapewill probably lead to inconsistent result for both well shaped andpoorly shaped elements. The proposed smoothing approach can be utilizedas an appropriate and effective tool for evaluating element shapemeasures and their influence on mesh optimization process and optimalsolution.