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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2014 Volume 428, Pages 89–106 (Mi znsl6054)

This article is cited in 6 papers

Some parallel methods and technologies of domain decomposition

Y. L. Gurievaab, V. P. Il'inab

a Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: 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.

Key words and phrases: domain decomposition, parallel two-level methods, Krylov subspaces, preconditioning matrices, aggregation algorithms, subdomain intersections, interface conditions.

UDC: 519.612

Received: 10.11.2014


 English version:
Journal of Mathematical Sciences (New York), 2015, 207:5, 724–735

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