Abstract. We introduce and study numerically a two-level Schwarz preconditioner for NewtonKrylov methods for fluid-structure interaction, with special consideration of the application area of simulating blood flow. Our approach monolithically couples the fluid to the structure on both fine and coarse grids and in the subdomain solves, insuring that there is multiphysics coupling during all aspects of the algorithm. The fluid-structure system is discretized on unstructured nonnested meshes, with an overlapping additive domain decomposition on both coarse and fine levels and multiplicative Schwarz preconditioning between levels. We investigate the effect of different coarse discretization sizes, solver stopping criteria, and overlap size, and we demonstrate that the method is robust to physical parameters including the structure's Young's modulus and the timestep size. Finally, we show effective preconditioning of the complicated coupled system, with nearly perfect weak scaling to a thousand processors and millions of unknowns.Key words. fluid-structure interaction, blood flow, multilevel methods, arbitrary LagrangianEulerian, restricted additive Schwarz, domain decomposition, parallel computing, preconditioning AMS subject classifications. 65M55, 65M60, 65Y05, 76Z05 DOI. 10.1137/0907794251. Introduction. Fluid-structure interaction problems are difficult enough that simulations of realistic phenomena often require parallel processing. In this paper we consider scalable and efficient two-level Newton-Krylov-Schwarz algorithms for monolithic coupling in fluid-structure interaction. The target application is blood flow in arteries, which is a computationally difficult and practically important application area [15,36]. In particular, the similar densities of blood and artery wall make the coupling between fluid and structure strong in both directions, so that partitioned or iterative procedures have difficulties due to the added-mass effect [1,8]. Instead of a partitioned procedure, we adopt a monolithic computational approach, coupling fluid to structure in one large system that is solved all at once. This tight coupling allows for robustness to parameters and makes our method immune to the addedmass effect. The resulting system is difficult to solve, but we show here that it can be solved efficiently with effective preconditioning strategies. For more on monolithic coupling, see [5,16,21]. Though we focus on the blood-flow problem, our algorithm could be used for more general fluid-structure interaction problems, including ones with deformable structures inside the fluid domain [25].Besides monolithic coupling in all aspects of the numerical algorithm, the other emphasis of our approach is parallel scalability. Fluid-structure interaction problems in general, and the blood-flow problem in particular, are very computationally demanding and require parallel computing in order to achieve useful resolution and accuracy. In order to use large supercomputers for large problems, we need innovative
