  Fluid-structure interaction models are used to study how a material interacts
with different fluids at different Reynolds numbers. Examining the same model
not only for different fluids but also for different solids allows to optimize
the choice of materials for construction even better. A possible answer to this
demand is parameter-dependent discretization. Furthermore, low-rank techniques
can reduce the complexity needed to compute approximations to
parameter-dependent fluid-structure interaction discretizations.
  Low-rank methods have been applied to parameter-dependent linear
fluid-structure interaction discretizations. The linearity of the operators
involved allows to translate the resulting equations to a single matrix
equation. The solution is approximated by a low-rank method. In this paper, we
propose a new method that extends this framework to nonlinear
parameter-dependent fluid-structure interaction problems by means of the Newton
iteration. The parameter set is split into disjoint subsets. On each subset,
the Newton approximation of the problem related to the upper median parameter
is computed and serves as initial guess for one Newton step on the whole
subset. This Newton step yields a matrix equation whose solution can be
approximated by a low-rank method. The resulting method requires a smaller
number of Newton steps if compared with a direct approach that applies the
Newton iteration to the separate problems consecutively. In the experiments
considered, the proposed method allows to compute a low-rank approximation up
to twenty times faster than by the direct approach.
