The overset grid nicknamed ``Yin-Yang'' grid is singularity free and has quasi-uniform grid spacing. It is composed of two identical latitude/longitude orthogonal grid panels that are combined to cover the sphere with partial overlap on their boundaries. The system of shallow-water equations (SWEs) is a hyperbolic system at the core of many models of the atmosphere. In this paper, the SWEs are solved on Yin-Yang grid by using an implicit semi-Lagrangian discretization on a staggered mesh. The resulting scalar elliptic equation is solved using a Schwarz-type domain decomposition method, known as optimized Schwarz method, which gives better performance than the classical Schwarz method by using specific Robin or higher-order transmission conditions.