| In this dissertation, we consider an overlapping domain decomposition method for the solution of a non-symmetric singularly perturbed advection-diffusion equation. The problem originates from the implicit temporal discretization schemes for parabolic equations. The main goal of this work is to apply the method to solve the problem of modeling the atmospheric dispersion of pollutants.; For spatial approximation, different approaches were considered, such as the finite element, finite difference and finite volume methods. Each discretization was applied to approximate the problem on locally refined spatial meshes. For advection dominated flows, the discrete problem was stabilized by upwinding or artificial viscosity.; The domain decomposition algorithm is based on the use of the rapid exponential decrease property of grid Green's function. The size of the overlap is estimated in terms of the parameters of the problem and values of the coefficients.; The algorithm can be used for the non-iterative solution of time-dependent advection and advection-diffusion problems on parallel computers, because they require global communication only once per time-step. |
