TY - JOUR

T1 - Two-level iterative methods for solving the saddle point problems

AU - Il'in, V. P.

N1 - Funding Information: The work is supported by grants RFBR N 18-01-00295 and RSF N 19-11-00048 Publisher Copyright: © 2021 Institute of Physics Publishing. All rights reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1/4

Y1 - 2021/1/4

N2 - Iterative processes in the Krylov subspaces for solving large ill conditioned saddle-type SLAEs with sparse matrices arising in finite difference, finite volume, and finite element approximations of multidimensional boundary value problems with complex geometric and functional properties of the initial data, characteristic of many relevant applications are studied. Combined two-level iterative algorithms using efficient Chebyshev acceleration and variational the conjugate directions methods, as well as the Golub-Kahan bi-diagonalization algorithms in the Krylov subspaces are considered. Examples of two-dimensional and three-dimensional filtration problems are used to study the resource consumption and computational performance of the proposed algorithms, as well as their scalable parallization on the multiprocessor systems with distributed and hierarchical shared memory.

AB - Iterative processes in the Krylov subspaces for solving large ill conditioned saddle-type SLAEs with sparse matrices arising in finite difference, finite volume, and finite element approximations of multidimensional boundary value problems with complex geometric and functional properties of the initial data, characteristic of many relevant applications are studied. Combined two-level iterative algorithms using efficient Chebyshev acceleration and variational the conjugate directions methods, as well as the Golub-Kahan bi-diagonalization algorithms in the Krylov subspaces are considered. Examples of two-dimensional and three-dimensional filtration problems are used to study the resource consumption and computational performance of the proposed algorithms, as well as their scalable parallization on the multiprocessor systems with distributed and hierarchical shared memory.

UR - http://www.scopus.com/inward/record.url?scp=85100791694&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1715/1/012004

DO - 10.1088/1742-6596/1715/1/012004

M3 - Conference article

AN - SCOPUS:85100791694

VL - 1715

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012004

T2 - International Conference on Marchuk Scientific Readings 2020, MSR 2020

Y2 - 19 October 2020 through 23 October 2020

ER -