A multilevel, level-set method for optimizing eigenvalues in shape design problems

Authors:
E. Haber
Affiliations:
Department of Mathematics and Computer Science, Emory University, 400 Downman Drive, Suite W 401, Atlanta, GA
Venue:
Journal of Computational Physics
Year:
2004

Citing 6
Cited 16

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A boundary piecewise constant level set method for boundary control of eigenvalue optimization problems

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A critical comparative assessment of differential equation-driven methods for structural topology optimization

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A survey of structural and multidisciplinary continuum topology optimization: post 2000

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Abstract

In this paper, we consider optimal design problems that involve shape optimization. The goal is to determine the shape of a certain structure such that it is either as rigid or as soft as possible. To achieve this goal we combine two new ideas for an efficient solution of the problem. First, we replace the eigenvalue problem with an approximation by using inverse iteration. Second, we use a level set method but rather than propagating the front we use constrained optimization methods combined with multilevel continuation techniques. Combining these two ideas we obtain a robust and rapid method for the solution of the optimal design problem.