Extension of a Coarse Grid Preconditioner to Non-symmetric Problems

The Optimized Order 2 (OO2) method is a non-overlapping domain decomposition method with differential interface conditions of order 2 along the interfaces which approximate the exact artificial boundary conditions [13, 9]. The convergence of Schwarz type methods with these interface conditions is proved in [12]. There already exists applications of the OO2 method to convection-diffusion equation [9] and Helmholtz problem [3]. We first recall the OO2 method and present numerical results for the convection-diffusion equation discretized by a finite volume scheme. The aim of this paper is then to provide an extension of a preconditioning technique introduced in [7, 5] based upon a global coarse problem to non-symmetric problems like convection-diffusion problems. The goal is to get the independence of the convergence upon the number of subdomains. Numerical results on convectiondiffusion equation will illustrate the efficiency of the OO2 algorithm with this coarse grid preconditioner.