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In this article, we deal with a numerical method for the approximation of a class of coupled shape optimization problems, which consist in minimizing an appropriate general volume cost functional subjected to coupled boundary value problems by means of a Neumann boundary transmission condition. We show the existence of the shape derivative of the cost functional and express it by means of support functions, using a new formula of shape derivative on a family of convex domains. This allows us to avoid the disadvantages related to the classical shape derivative method using vectors field. Then the numerical discretization is performed using the dual reciprocity boundary element method in order to avert the remeshing task required for the finite element method. Finally, we give some numerical results, based on the gradient method, showing the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

The aim of this paper is to compute the shape derivative of a volume cost functional subject to a Dirich- let boundary value state constraint problem using the shape derivative formula introduced in (Boulkhemair et al., 2020), which concerns star-shaped domains. This allows us to express the shape derivative by means of support functions of convex domains. Then we give a simple algorithm for the numerical resolution of this problem. [ABSTRACT FROM AUTHOR]