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.
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