Quality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation

Shuli Sun, Haoran Bao, Minghui Liu, Yuan Yuan

State Key Laboratory for Turbulence and Complex System, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, China.

DOI: 10.4236/iim.2013.56021                

Abstract

The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is examined. With regard to its problem of possible producing illegal elements, this paper proposes a modified smoothing scheme with a constrained optimization model for tetrahedral mesh quality improvement. The constrained optimization model is converted to an unconstrained one and then solved by integrating chaos search and BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm efficiently. Quality improvement for tetrahedral mesh is finally achieved by alternately applying the presented smoothing scheme and re-triangulation. Some testing examples are given to demonstrate the effectiveness of the proposed approach.

Keywords

Tetrahedral Mesh; Mesh Quality Improvement; Smoothing; Topological Optimization; Optimal Delaunay Triangulation

Conflicts of Interest

The authors declare no conflicts of interest.

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