Topological asymptotic analysis of an optimal control problem modeled by a coupled system

Article type: Research Article

Authors: Fernandez, L.^a | Novotny, A.A.^a | Prakash, R.^{b; *}

Affiliations: [a] Laboratório Nacional de Computação Científica LNCC/MCT, Coordenação de Matemática Aplicada e Computacional, Av. Getúlio Vargas 333, 25651-075 Petrópolis – RJ, Brasil. E-mails: lucasf@lncc.br, novotny@lncc.br | [b] Department of Mathematics, Faculty of Physical Science and Mathematics, University of Concepción, Concepción, Chile. E-mail: rprakash@udec.cl

Correspondence: [*] Corresponding author. E-mail: rprakash@udec.cl.

Abstract: In this paper, we deal with the topological asymptotic analysis of an optimal control problem modeled by a coupled system. The control is a geometrical object and the cost is given by the misfit between a target function and the state, solution of the Helmholtz–Laplace coupled system. Higher-order topological derivatives are used to devise a non-iterative algorithm to compute the optimal control for the problem of interest. Numerical examples are presented in order to demonstrate the effectiveness of the proposed algorithm.

Keywords: Control problem, Helmholtz–Laplace coupled system, topological asymptotic analysis, topological derivatives, topology optimization

DOI: 10.3233/ASY-181465

Journal: Asymptotic Analysis, vol. 109, no. 1-2, pp. 1-26, 2018