Optimized Schwarz methods with Ventcell transmission condition for Stokes-Darcy coupling (Yingxiang Xu, Changchun, China)

15.11.2019 13:45 – 14:45

Stokes-Darcy coupling is an important multi-physics model where domain decomposition methods can be specifically designed to reduce the computational complexity. In this talk, we design Ventcell transmission condition for the framework of optimized Schwarz methods (OSMs) for Stokes-Darcy coupling. The convergence behavior is then analyzed in the Fourier frequency domain, where we find that the convergence factor tends to zero for large frequencies, which is a typical behavior for overlapping domain decomposition and is quite different from the Robin transmission condition for Stokes-Darcy coupling. We determine the transmission parameters by minimizing the convergence factor over all the involved frequencies and find that the optimized parameters can be obtained by solving a nonlinear system. Theoretically we find that the convergence behavior of the OSMs with Ventcell transmission condition does not depend on the mesh size and outperforms that for Robin transmission conditions. Numerically we find that the optimized Ventcell transmission condition leads to very fast convergence of subdomain iterations.

Lieu

Room 624, Séminaire d'analyse numérique

entrée libre