Parallel Approaches and Technologies of Domain Decomposition Methods

Abstract

The efficiency of two-level iterative processes in the Krylov subspaces is investigated, as well as their parallelization in solving large sparse nonsymmetric systems of linear algebraic equations arising from grid approximations of two-dimensional boundary-value problems for convectiondiffusion equations with various coefficient values. Special attention is paid to optimization of the sizes of subdomain intersections, to the types of boundary conditions on adjacent boundaries in the domain decomposition method, and to the aggregation (or coarse grid correction) algorithms. The outer iterative process is based on the additive Schwarz algorithm, whereas parallel solution of the subdomain algebraic systems is effected by using a direct or a preconditioned Krylov method. The key point in the programming realization of these approaches is the 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 based on numerical experiments. Some issues related to the scalability of parallelization are discussed. Bibliography: 13 titles.