Optimized Schwarz Methods for Advection Diffusion Equations in Bounded Domains
Optimized Schwarz methods use better transmission conditions than the classical Dirichlet conditions that were used by Schwarz. These transmission conditions are optimized for the physical problem that needs to be solved to lead to fast convergence. The optimization is typically performed in the geometrically simplified setting of two unbounded subdomains using Fourier transforms. Recent studies for both homogeneous and heterogeneous domain decomposition methods indicate that the geometry of the physical domain has actually an influence on this optimization process. We study here this influence for an advection diffusion equation in a bounded domain using separation of variables. We provide theoretical results for the min-max problems characterizing the optimized transmission conditions. Our numerical experiments show significant improvements of the new transmission conditions which take the geometry into account, especially for strong tangential advection.
- 2.O. Dubois, Optimized Schwarz methods with robin conditions for the advection-diffusion equation, in Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering (Springer, Berlin, 2006)Google Scholar
- 5.M.J. Gander, T. Vanzan, Heterogeneous Optimized Schwarz methods for coupling Helmholtz and Laplace Equations, in Domain Decomposition Methods in Science and Engineering XXIV. Lecture Notes in Computational Science and Engineering (Springer, Berlin, 2018)Google Scholar