  In this work, we consider the solution of fluid-structure interaction
problems using a monolithic approach for the coupling between fluid and solid
subproblems. The coupling of both equations is realized by means of the
arbitrary Lagrangian-Eulerian framework and a nonlinear harmonic mesh motion
model. Monolithic approaches require the solution of large, ill-conditioned
linear systems of algebraic equations at every Newton step. Direct solvers tend
to use too much memory even for a relatively small number of degrees of
freedom, and, in addition, exhibit superlinear grow in arithmetic complexity.
Thus, iterative solvers are the only viable option. To ensure convergence of
iterative methods within a reasonable amount of iterations, good and, at the
same time, cheap preconditioners have to be developed. We study physics-based
block preconditioners, which are derived from the block $LDU$-factorization of
the FSI Jacobian, and their performance on distributed memory parallel
computers in terms of two- and three-dimensional test cases permitting large
deformations.
