Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum

被引:21
|
作者
Zhu, Shengfeng [1 ]
Liu, Chunxiao [2 ]
Wu, Qingbiao [1 ]
机构
[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
[2] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China
基金
中国国家自然科学基金;
关键词
Shape optimization; Eigenvalue; Topology optimization; Binary level set method; Augmented Lagrangian method; Projection Lagrangian method; 2-DIMENSIONAL PHOTONIC CRYSTALS; MAXIMIZING BAND-GAPS; INVERSE PROBLEMS; DERIVATIVES; SCHEMES; DESIGN; EIGENVALUES; ALGORITHMS; LOADS; MODEL;
D O I
10.1016/j.cma.2010.06.007
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
We optimize eigenvalues in optimal shape design using binary level set methods. The interfaces of sub-regions are represented implicitly by the discontinuities of binary level set functions taking two values 1 or 1 at convergence. A binary constraint is added to the original model problems. We propose two variational algorithms to solve the constrained optimization problems. One is a hybrid type by coupling the Lagrange multiplier approach for the geometry constraint with the augmented Lagrangian method for the binary constraint. The other is devised using the Lagrange multiplier method for both constraints. The two iterative algorithms are both largely independent of the initial guess and can satisfy the geometry constraint very accurately during the iterations. Intensive numerical results are presented and compared with those obtained by level set methods, which demonstrate the effectiveness and robustness of our algorithms. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码:2970 / 2986
页数:17
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