Optimized Schwarz methods for cilindrical interfaces

Christian Vergara
Politecnico di Milano Dipartimento di Matematica-MOX
Wednesday 21st October 2015
Aula Semnari Saleri VI piano MOX - Dipartimento di Matematica Politecnico di Milano
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. We apply such general results to a simple fluid–structure interaction model problem given by the interaction between an incompressible, inviscid fluid and the wave equation, in the case of cylindrical interfaces. Finally, we assess the effectiveness of the theoretical findings through three-dimensional numerical experiments in the haemodynamic context,obtained by solving the coupling between the Navier–Stokes equations and the linear infinitesimal elasticity. contact: christian.vergara@polimi.it