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Effective Shape Optimization of Laplace Eigenvalue Problems Using Domain Expressions of Eulerian Derivatives

Shengfeng Zhu ()
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Shengfeng Zhu: East China Normal University

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 1, No 2, 17-34

Abstract: Abstract We consider to solve numerically the shape optimization models with Dirichlet Laplace eigenvalues. Both volume-constrained and volume unconstrained formulations of the model problems are presented. Different from the literature using boundary-type Eulerian derivatives in shape gradient descent methods, we advocate to use the more general volume expressions of Eulerian derivatives. We present two shape gradient descent algorithms based on the volume expressions. Numerical examples are presented to show the more effectiveness of the algorithms than those based on the boundary expressions.

Keywords: Shape optimization; Eigenvalue; Eulerian derivative; Shape gradient; Finite element; 65N25; 65N30; 49J20; 49R50 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-017-1198-9

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