  In this paper, we consider a monolithic approach to handle coupled
fluid-structure interaction problems with different hyperelastic models in an
all-at-once manner. We apply Newton's method in the outer iteration dealing
with nonlinearities of the coupled system. We discuss preconditioned Krylov
sub-space, algebraic multigrid and algebraic multilevel methods for solving the
linearized algebraic equations. Finally, we compare the results of the
monolithic approach with those of the corresponding partitioned approach that
we studied in our previous work.
