TY - GEN

T1 - Conjugate Direction Methods for Parallel Deflation

AU - Gurieva, Yana

AU - Il’in, Valery

N1 - Funding Information: The theoretical part of the study was carried out under a government contract with the ICMMG SB RAS (0315-2019-0008). The computational experiments were supported by the Russian Foundation for Basic Research (project No. 18-01-00295). Funding Information: Acknowledgements. The theoretical part of the study was carried out under a government contract with the ICMMG SB RAS (0315-2019-0008). The computational experiments were supported by the Russian Foundation for Basic Research (project No. 18-01-00295). Publisher Copyright: © 2021, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - We consider parallel iterative processes in Krylov subspaces for solving symmetric positive definite systems of linear algebraic equations (SLAEs) with sparse ill-conditioned matrices arising under grid approximations of multidimensional initial-boundary value problems. Furthermore, we research the efficiency of the methods of moments for choosing an initial guess and constructing a projective-type preconditioner based on a known basis formed by the direction vectors. As a result, the reduction in the number of iterations implies an increase in their computational complexity, which is effectively minimized by parallelizing vector operations. The approaches under consideration are relevant for the multiple solution of SLAEs with the same matrices and different sequentially determined right-hand sides. Such systems arise in multilevel iterative algorithms, including additive domain decomposition and multigrid approaches. The efficiency of the suggested methods is demonstrated by the results of numerical experiments involving methodological examples.

AB - We consider parallel iterative processes in Krylov subspaces for solving symmetric positive definite systems of linear algebraic equations (SLAEs) with sparse ill-conditioned matrices arising under grid approximations of multidimensional initial-boundary value problems. Furthermore, we research the efficiency of the methods of moments for choosing an initial guess and constructing a projective-type preconditioner based on a known basis formed by the direction vectors. As a result, the reduction in the number of iterations implies an increase in their computational complexity, which is effectively minimized by parallelizing vector operations. The approaches under consideration are relevant for the multiple solution of SLAEs with the same matrices and different sequentially determined right-hand sides. Such systems arise in multilevel iterative algorithms, including additive domain decomposition and multigrid approaches. The efficiency of the suggested methods is demonstrated by the results of numerical experiments involving methodological examples.

KW - Conjugate directions

KW - Deflation

KW - Iterative algorithms

KW - Krylov subspaces

KW - Numerical experiments

KW - Preconditioning matrix

UR - http://www.scopus.com/inward/record.url?scp=85112292501&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-81691-9_14

DO - 10.1007/978-3-030-81691-9_14

M3 - Conference contribution

AN - SCOPUS:85112292501

SN - 9783030816902

T3 - Communications in Computer and Information Science

SP - 194

EP - 207

BT - Parallel Computational Technologies - 15th International Conference, PCT 2021, Revised Selected Papers

A2 - Sokolinsky, Leonid

A2 - Zymbler, Mikhail

PB - Springer Science and Business Media Deutschland GmbH

T2 - 15th International Conference on Parallel Computational Technologies, PCT 2021

Y2 - 30 March 2021 through 1 April 2021

ER -