"On acceleration technologies of parallel decomposition methods"
Gurieva Y.L. and Il'in V.P.

One of the main obstacles to the scalable parallelization of the algebraic decomposition methods for solving large sparse systems of linear algebraic equations consists in slowing the convergence rate of the additive iterative Schwarz algorithm in the Krylov subspaces when the number of subdomains increases. The aim of this paper is a comparative experimental analysis of various ways to accelerate the iterations: a parametrized intersection of subdomains, the usage of interface conditions at the boundaries of adjacent subdomains, and the application of a coarse grid correction (aggregation, or reduction) for the original linear system to build an additional preconditioner. The parallelization of algorithms is performed on two levels by programming tools for the distributed and shared memory. The benchmark linear systems under study are formed using the finite difference approximations of the Dirichlet problem for the diffusion-convection equation with various values of the convection coefficients and on a sequence of condensing grids.

Keywords: domain decomposition, additive Schwarz method, reduction algorithms, preconditioned Krylov processes, scalable parallelization, distributed and shared memory, numerical experiments.

  • Gurieva Y.L. – Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of Russian Academy of Sciences; prospekt Lavrentyeva 6, Novosibirsk, 630090, Russia; Ph.D., Senior Scientist, e-mail: yana@lapasrv.sscc.ru
  • Il'in V.P. – Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of Russian Academy of Sciences; prospekt Lavrentyeva 6, Novosibirsk, 630090, Russia; Dr. Sci., Professor, Principal Scientist, e-mail: ilin@sscc.ru