Optimized Schwarz methods for spherical interfaces with application to fluid-structure interaction

Abstract

In this work we consider the optimized Schwarz method designed for computational domains that feature spherical or almost spherical interfaces. In the first part, we consider the diffusion-reaction problem. We provide a convergence analysis of the generalized Schwarz method and, following [G. Gigante and C. Vergara, Numer. Math., 131 (2015), pp. 369–404], we discuss an optimization procedure for constant interface parameters leading to a Robin–Robin scheme. Finally, we present some numerical results both in spherical and in ellipsoidal domains. In the second part of the work, we address the fluid-structure interaction problem. Again, we provide a convergence analysis and discuss optimized choices of constant interface parameters. Finally, we present three- dimensional numerical results inspired by hemodynamic applications, to validate the proposed choices in the presence of large added mass effect. In particular, we consider numerical experiments both in an ideal spherical domain and in a realistic abdominal aortic aneurysm.

Key words. Optimized Schwarz method; Spherical interfaces; Fluid structure interaction; Abdominal aortic aneurysm