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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 6392901, 14 pages
Research Article

Efficient Local Level Set Method without Reinitialization and Its Appliance to Topology Optimization

School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China

Received 5 July 2015; Accepted 21 December 2015

Academic Editor: Manuel Pastor

Copyright © 2016 Wenhui Zhang and Yaoting Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The local level set method (LLSM) is higher than the LSMs with global models in computational efficiency, because of the use of narrow-band model. The computational efficiency of the LLSM can be further increased by avoiding the reinitialization procedure by introducing a distance regularized equation (DRE). The numerical stability of the DRE can be ensured by a proposed conditionally stable difference scheme under reverse diffusion constraints. Nevertheless, the proposed method possesses no mechanism to nucleate new holes in the material domain for two-dimensional structures, so that a bidirectional evolutionary algorithm based on discrete level set functions is combined with the LLSM to replace the numerical process of hole nucleation. Numerical examples are given to show high computational efficiency and numerical stability of this algorithm for topology optimization.