Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

Authors:
Shengfeng Zhu;Qingbiao Wu;Chunxiao Liu
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China;Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China;Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, Zhejiang, PR China
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm.