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Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method
Authors:Shengfeng Zhu  Chunxiao Liu
Institution:a Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China
b Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, Zhejiang, PR China
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.
Keywords:Shape optimization  Topology optimization  Piecewise constant level set method  Projection Lagrangian method
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