Strongly coupled partitioned fluid-structure interaction problems require multiple coupling iterations per time step. The fluid domain and the structure domain are solved multiple times in each time step such that the kinematic and dynamic interface conditions on the fluid-structure interface are satisfied. Quasi-Newton methods have been successfully applied in case the fluid and structure solvers are considered as black boxes, i.e. only input and output information of the solvers are used by the coupling techniques. In this contribution a computationally inexpensive low-fidelity model is combined with a high-fidelity model in order to accelerate the convergence of the high-fidelity model. This is achieved by applying the manifold mapping algorithm on the fluid-structure interaction problem in order to minimize the fluid-structure interface residual. Originating from multi-fidelity optimization, the manifold mapping algorithm is applied for the first time in a simulation context, instead of an optimization context. The manifold mapping algorithm is applied on a standard fluid-structure interaction benchmark, namely the cylinder flap FSI3 case. A reduction of 48% in terms of high fidelity iterations is achieved compared with the inverse least squares Quasi-Newton algorithm, resulting in a 42% decrease in computational costs.