Optimized Schwarz Methods in Spherical Geometry with an Overset Grid System

In recent years, much attention has been given to domain decomposition methods for solving linear elliptic problems that are based on a partitioning of the domain of the physical problem. More recently, a new class of Schwarz methods known as optimized Schwarz methods was introduced to improve the performance of the classical Schwarz methods. In this paper, we investigate the performance of this new class of methods for solving the model equation (η − ∆)u = f , where η > 0, on spherical geometry. This equation arises in a global weather model as a consequence of an implicit (or semi-implicit) time discretization. We show that the Schwarz methods improved by a non-local transmission condition converges in a finite number of steps. A local approximation permits the use of the new method on a new overset grid system on the sphere called the Yin-Yang grid.