TY - GEN

T1 - Parallel Methods for Solving Saddle Type Systems

AU - Il’in, V. P.

AU - Kozlov, D. I.

N1 - Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - Parallel methods for solving saddle-type algebraic systems that are relevant for modeling processes and phenomena in the problems of electromagnetism, hydro-gas dynamics, elastoplasticity, filtration and other applications are considered. Preconditioned iterative processes in the Krylov subspaces, including the efficient generalization of the Golub-Kahan-Arioli bidiagonalization method, are investigated as applied to large SLAEs with sparse matrices that arise when approximating multi-dimensional boundary value problems with a complex geometric configuration of computational domains and the contrasting material properties of various media on unstructured grids. It is supposed to store the matrices in compressed formats that require special technologies for working with big data. The parallelization of the proposed class of block algorithms is carried out by means of hybrid programming on supercomputers of a heterogeneous architecture with distributed and hierarchical shared memory, using the means of inter-node message transmission, multi-threaded computing, operation vectorization. A comparative analysis of various algorithmic approaches is carried out on the basis of the estimates of the performance and resource intensity of the corresponding software implementations.

AB - Parallel methods for solving saddle-type algebraic systems that are relevant for modeling processes and phenomena in the problems of electromagnetism, hydro-gas dynamics, elastoplasticity, filtration and other applications are considered. Preconditioned iterative processes in the Krylov subspaces, including the efficient generalization of the Golub-Kahan-Arioli bidiagonalization method, are investigated as applied to large SLAEs with sparse matrices that arise when approximating multi-dimensional boundary value problems with a complex geometric configuration of computational domains and the contrasting material properties of various media on unstructured grids. It is supposed to store the matrices in compressed formats that require special technologies for working with big data. The parallelization of the proposed class of block algorithms is carried out by means of hybrid programming on supercomputers of a heterogeneous architecture with distributed and hierarchical shared memory, using the means of inter-node message transmission, multi-threaded computing, operation vectorization. A comparative analysis of various algorithmic approaches is carried out on the basis of the estimates of the performance and resource intensity of the corresponding software implementations.

KW - algorithm parallelization

KW - computing performance

KW - iterative processes

KW - Krylov subspaces

KW - large sparse SLAEs

KW - saddle matrices

UR - http://www.scopus.com/inward/record.url?scp=85135044868&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e2a681a1-4da4-3b7b-afc4-bf8cd80636fa/

U2 - 10.1007/978-3-031-11623-0_7

DO - 10.1007/978-3-031-11623-0_7

M3 - Conference contribution

AN - SCOPUS:85135044868

SN - 9783031116223

T3 - Communications in Computer and Information Science

SP - 85

EP - 98

BT - Parallel Computational Technologies - 16th International Conference, PCT 2022, Revised Selected Papers

A2 - Sokolinsky, Leonid

A2 - Zymbler, Mikhail

PB - Springer Science and Business Media Deutschland GmbH

T2 - 16th International Conference on Parallel Computational Technologies, PCT 2022

Y2 - 29 March 2022 through 31 March 2022

ER -