In the solution of Fluid-Structure Interaction problems, partitioned procedures are modular algorithms that involve separate fluid and structure solvers, that interact, in an iterative framework, through the exchange of suitable transmission conditions at the FS interface. In this work we study, using Fourier analysis, the convergence of partitioned algorithms based on Robin transmission conditions. We derive, for different models of the fluid and the structure, a frequency dependent reduction

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... actor at each iteration of the partitioned algorithm, which is minimized by choosing optimal values * The research of the second and of the third author has been (partially) supported by the ERC Advanced Grant N.227058 MATHCARD. of the coefficients in the Robin transmission conditions. Two-dimensional numerical results are also reported, which highlight the effectiveness of the optimization procedure. Problem setting Let us consider a computational domain Ω t ⊂ R d (d=2, 3, being the space dimension). This domain is divided into a sub-domain Ω t s occupied by an elastic structure and its complement Ω t f occupied by the fluid. The fluid-structure