Optimized Schwarz methods for spherical interfaces with application to fluid-structure interaction
Friday 5th July 2019
Gigante, G.; Sambataro, G.; Vergara, C.
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, we discuss an optimization procedure for constant interface parameters leading to a Robin-Robin scheme, and 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 optimal choices of constant interface parameters. Finally, we present 3D numerical results inspired by hemodynamic applications, to validate the proposed optimal choices in 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.