In this work we address the numerical solution of large scale fluid-structure interaction problems when nonconforming grids and⁄or nonconforming finite elements discretizations are used at the interface separating the fluid and structure physical domains. To deal with nonconforming fluid-structure discretizations we use the INTERNODES method (INTER-polation for NOnconforming DEcompositionS) formerly introduced in [6] for the solution of elliptic PDEs on nonconforming domain decomposition. To cope with the high computational complexity of the three dimensional FSI problem obtained after spatial and temporal discretization, we use the block parallel preconditioner FaCSI [7]. A numerical investigation of the accuracy properties of INTERNODES applied to the nonconforming FSI problem is carried out for the simulation of the pressure wave propagation in a straight elastic cylinder. Finally, we study the scalability performance of the FaCSI preconditioner in the nonconforming case by solving a large-scale nonconforming FSI problem in a patients-pecific arterial bypass.