Analysis and optimization of the generalized Schwarz method for elliptic problems with application to fluid-structure interaction (Q495545)

The authors consider the generalized Schwarz method applied to a linear elliptic problem for a general interface in any dimension. They provide a unified convergence analysis including the exact convergence set of the interface symbols related to the operators involved in the transmission conditions. A general procedure to obtain estimates of the optimized interface symbols within the constants is described. This procedure is applied to a simple fluid-structure interaction model problem given by the interaction between an incompressible, inviscid fluid and the wave equation. Some three-dimensional numerical experiments in the haemodynamic context, obtained by solving the coupling between the Navier-Stokes equations and the linear infinitesimal elasticity are presented.