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The topological asymptotic. (English) Zbl 1082.93584
Glowinski, Roland (ed.) et al., Computational methods for control applications. Dedicated to Professor Jacques-Louis Lions on the occasion of his 70th birthday. Proceedings of the France-Japan workshop on computational methods for control applications, Tokyo, Japan, October 7–9, 1998. Tokyo: Gakkōtosho (ISBN 4-7625-0425-4/hbk). GAKUTO International Series. Mathematical Sciences and Applications 16, 53-72 (2002).
Summary: The aim of topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole. In this paper we present general mathematical tools to obtain and analyse such expressions: an adaptation of the adjoint method to asymptotic behavior and a domain truncation technique. Then we study a cost function involving the Laplace equation with a Dirichlet type condition on the boundary of the hole.
For the entire collection see [Zbl 1068.93003].

93C95 Application models in control theory
93B40 Computational methods in systems theory (MSC2010)