Numerical Simulation of Fluid-Structure Interaction Problems with   Hyperelastic Models: A Monolithic Approach
  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. 
Ulrich Langer and Huidong Yang
math.NA