  Fluid-structure interaction models involve parameters that describe the solid
and the fluid behavior. In simulations, there often is a need to vary these
parameters to examine the behavior of a fluid-structure interaction model for
different solids and different fluids. For instance, a shipping company wants
to know how the material, a ship's hull is made of, interacts with fluids at
different Reynolds and Strouhal numbers before the building process takes
place. Also, the behavior of such models for solids with different properties
is considered before the prototype phase. A parameter-dependent linear
fluid-structure interaction discretization provides approximations for a bundle
of different parameters at one step. Such a discretization with respect to
different material parameters leads to a big block-diagonal system matrix that
is equivalent to a matrix equation as discussed in [KressnerTobler 2011]. The
unknown is then a matrix which can be approximated using a low-rank approach
that represents the iterate by a tensor. This paper discusses a low-rank GMRES
variant and a truncated variant of the Chebyshev iteration. Bounds for the
error resulting from the truncation operations are derived. Numerical
experiments show that such truncated methods applied to parameter-dependent
discretizations provide approximations with relative residual norms smaller
than $10^{-8}$ within a twentieth of the time used by individual standard
approaches.
