Strongly coupled fluid-structure interaction simulations often suffer from slow convergence, limited parallel scalability or difficulties in using black-box solvers. As partitioned simulations still play an important role in cases where new combinations of models, discretizations and codes have to be tested in an easy and fast way, we propose a combination of a parallel black-box coupling with a manifold mapping algorithm as an acceleration method. In this approach, we combine a com- putationally inexpensive low-fidelity FSI model with a high-fidelity FSI model to reduce the number of coupling iterations of the high fidelity FSI model. Information from previous time steps is taken into account with a secant update step similar to the Broyden update. The used black-box approach is applied for an incompressible laminar flow over a fixed cylinder with an attached flexible flap and a wave prop- agation in a three-dimensional elastic tube problem. A reduction of approximately 55 % in terms of high fidelity iterations is achieved compared to the Anderson mix- ing method if the fluid and the structure solvers are executed in parallel.