A multilevel, level-set method for optimizing eigenvalues in shape design problems
نویسندگان
چکیده
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 the 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 together we obtain a robust and rapid method for the solution of the problem.
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