Analysis and optimization of the generalized Schwarz method for elliptic problems with application to fluid-structure interaction

We propose a unified convergence analysis of the generalized Schwarz method applied to a linear elliptic problem for a general interface (flat, cylindrical or spherical) in any dimension. In particular, we provide the exact convergence set of the interface symbols related to the operators involved in the transmission conditions. We also provide a general procedure to obtain estimates of the optimized interface symbols within the constants. Finally, we apply such general results to a fluid-structure interaction model problem, and we assess the effectiveness of the theoretical findings through three-dimensional numerical experiments in the haemodynamic context.