Optimization of tetrahedral meshes based on element shape measures

Abstract

An element shape optimization procedure is presented, which can be considered as a general post-treatment process for three-dimensional tetrahedral meshes generated by Delaunay triangulation or refinement based on the subdivision of elements. The tetrahedral mesh is optimized with respect to a given element shape measure through a combined iterative scheme of local transformations and node relaxation. From the examples studied, a substantial gain in quality could be achieved in two cycles of iterations based on any valid shape measures, minimum solid angle θ, radius ratio ρ and gamma coefficient γ. Although further research and evidence are required for a more definite conclusion, the γ-coefficient which is more economical to compute, seems to give better results than the other two shape measures. The largest mesh processed which, consists of 67,326 nodes and 360,824 elements, required a CPU time of a little more than 3 min on a IBM Power Station 3BT. © 1997 Elsevier Science Ltd.