  The Dirichlet-Neumann scheme is the most common partitioned algorithm for
fluid-structure interaction (FSI) and offers high flexibility concerning the
solvers employed for the two subproblems. Nevertheless, it is not without
shortcomings: to begin with, the inherent added-mass effect often destabilizes
the numerical solution severely. Moreover, the Dirichlet-Neumann scheme cannot
be applied to FSI problems in which an incompressible fluid is fully enclosed
by Dirichlet boundaries, as it is incapable of satisfying the volume
constraint. In the last decade, interface quasi-Newton methods have proven to
control the added-mass effect and substantially speed up convergence by adding
a Newton-like update step to the Dirichlet-Neumann coupling. They are, however,
without effect on the incompressibility dilemma. As an alternative, the
Robin-Neumann scheme generalizes the fluid's boundary condition to a Robin
condition by including the Cauchy stresses. While this modification in fact
successfully tackles both drawbacks of the Dirichlet-Neumann approach, the
price to be paid is a strong dependency on the Robin weighting parameter, with
very limited a priori knowledge about good choices. This work proposes a
strategy to merge these two ideas and benefit from their combined strengths.
The resulting quasi-Newton-accelerated Robin-Neumann scheme is compared to both
Robin- and Dirichlet-Neumann variants. The numerical tests demonstrate that it
does not only provide faster convergence, but also massively reduces the
influence of the Robin parameter, mitigating the main drawback of the
Robin-Neumann algorithm.
