Coupling iterations in (a time step of) a partitioned simulation can be accelerated using quasi-Newton methods such as IQN-ILS(M), IBQN-LS, MVQN, MVJ and IQN-IMVLS, to name only a few. These methods construct one or more approximate (inverse) Jacobians during the coupling iterations, solely based on the data at the coupling interface. As an exception, IQN-ILSM can also take the Jacobian of a surrogate model into account, constructed based on data at the interface, a simplified physics-based model or any other source. Mostly these methods can be reformulated in the generalized Broyden framework [1], and the behaviour is depending on the number of secant conditions that are respected in the Jacobian approximation. The presented analysis shows how this number also influences how different methods behave when nonlinearity is present in the secant conditions, by either neglecting it or amplifying it [2]. Furthermore, a method to detect and remove nonlinear information in the secant conditions is presented to mitigate related reductions in convergence speed. This approach is subsequently applied to a coupled problem with a fluid flow and a highly elastic structure at the interface, to demonstrate the removal of convergence issues due to the nonlinearities. REFERENCES [1] N. Delaissé, T. Demeester, R. Haelterman, and J. Degroote. Quasi-Newton methods for partitioned simulation of fluid-structure interaction reviewed in the generalized Broyden framework. Archives of Computational Methods in Engineering, 30:3271–3300, 2023. doi: 10.1007/s11831-023-09907-y. [2] T. Demeester, N. Delaissé, E.H. van Brummelen, R. Haelterman, and J. Degroote. On the effect of nonlinearity and Jacobian initialization on the convergence of the generalized Broyden quasi-Newton method. International Journal for Numerical Methods in Engineering, pages 1–19, 2022. doi: 10.1002/nme.6998.