Optimized Schwarz method for the fluid-structure interaction with cylindrical interfaces

The Optimized Schwarz Method (OSM) is a domain decomposition method based on the introduction of generalized Robin interface conditions obtained by linearly combining the two physical interface conditions through the introduction of suitable symbols, and then on the optimization of such symbols within a proper subset. This method has been considered so far for many problems in the case of flat interfaces. Recently, OSM has been considered and analyzed by the authors for the case of cylindrical interfaces. In particular, we developed a general convergence analysis of the Schwarz method for elliptic problems and an optimization procedure within the constants, with application to the fluid-structure interaction (FSI) problem.
In the present work, we provide a numerical study of the performance of the optimization procedure developed in our previous work for the FSI problem when the solution is characterized by non-null angular frequencies, thus breaking the radial symmetry. The reported 3D numerical results for a cylindrical domain showed the effectiveness of the procedure also in such a case.