Some parallel methods and technologies of domain decomposition

The efficiency of two-level iterative processes in Krylov subspaces is investigated, as well as their parallelization in solving large sparse non-symmetric systems of linear algebraic equations arising from grid approximations of two-dimensional boundary value problems for diffusion-convection equations with different coefficient values. Special attention is paid to optimization of the subdomain intersection size, to the types of boundary conditions on adjacent boundaries in the domain decomposition method, and to the aggregation (or coarse grid correction) algorithms. Outer iterative process is based on the additive Schwarz algorithm, while parallel solution of the subdomain algebraic systems is effected by a direct or a preconditioned Krylov method. A crucial point in programming realization of these approaches is a technology of forming the so-called extended algebraic subsystems in the compressed sparse row format. A comparative analysis of the influence of various parameters is carried out basing on numerical experiments data. Some issues related to the scalability of parallelization are discussed.