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Incomplete Factorization Approach in Algebraic Domain Decomposition Methods. / Gurieva, Yana; Il’in, Valery; Kardash, Ruslan.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) . Springer, 2025. p. 362-376 26 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Vol. 15406 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Gurieva, Y, Il’in, V & Kardash, R 2025, Incomplete Factorization Approach in Algebraic Domain Decomposition Methods. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ., 26, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) , vol. 15406 LNCS, Springer, pp. 362-376, 10th Russian Supercomputing Days Conference, Москва, Russian Federation, 23.09.2024. https://doi.org/10.1007/978-3-031-78459-0_26

APA

Gurieva, Y., Il’in, V., & Kardash, R. (2025). Incomplete Factorization Approach in Algebraic Domain Decomposition Methods. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 362-376). [26] (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ; Vol. 15406 LNCS). Springer. https://doi.org/10.1007/978-3-031-78459-0_26

Vancouver

Gurieva Y, Il’in V, Kardash R. Incomplete Factorization Approach in Algebraic Domain Decomposition Methods. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) . Springer. 2025. p. 362-376. 26. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ). doi: 10.1007/978-3-031-78459-0_26

Author

Gurieva, Yana ; Il’in, Valery ; Kardash, Ruslan. / Incomplete Factorization Approach in Algebraic Domain Decomposition Methods. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) . Springer, 2025. pp. 362-376 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ).

BibTeX

@inproceedings{341ea04d77b8434fbd8638edeb5a8257,
title = "Incomplete Factorization Approach in Algebraic Domain Decomposition Methods",
abstract = "Iterative methods for domain decomposition methods in Krylov subspaces to solve large systems of linear algebraic equations arising from grid approximations of multidimensional boundary value problems are considered. The algorithms under study are based on purely algebraic approaches with special variants of approximate factorization of matrices arizing from grid division by a single-layer or two-layer separating macrogrid subsets. Traditional interface boundary conditions between contacting subdomains are replaced by matrix approximations with the compensation principle exploiting. The implementation of preconditioning matrices is carried out by naturally parallelizable forward and back sweep algorithms on the macrogrid. The issues of assessing the efficiency and performance of the proposed methods and technologies for two-dimensional and three-dimensional problems are discussed, including the cases of parallelizing calculations. The results of numerical experiments for a set of methodical problems are presented.",
keywords = "Domain decomposition, Forward and backward sweep, Iterative method, Krylov subspaces, Matrix factorization, Performance",
author = "Yana Gurieva and Valery Il{\textquoteright}in and Ruslan Kardash",
note = "Methodological results of the work were carried out under state contract with ICMMG SB RAS FWNM-2022-0001. Applied part the study was financially supported by RSF (Project No. 24-21-00402).; 10th Russian Supercomputing Days Conference, RuSCDays 2024 ; Conference date: 23-09-2024 Through 24-09-2024",
year = "2025",
doi = "10.1007/978-3-031-78459-0_26",
language = "English",
isbn = "9783031784583",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) ",
publisher = "Springer",
pages = "362--376",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
address = "United States",

}

RIS

TY - GEN

T1 - Incomplete Factorization Approach in Algebraic Domain Decomposition Methods

AU - Gurieva, Yana

AU - Il’in, Valery

AU - Kardash, Ruslan

N1 - Conference code: 10

PY - 2025

Y1 - 2025

N2 - Iterative methods for domain decomposition methods in Krylov subspaces to solve large systems of linear algebraic equations arising from grid approximations of multidimensional boundary value problems are considered. The algorithms under study are based on purely algebraic approaches with special variants of approximate factorization of matrices arizing from grid division by a single-layer or two-layer separating macrogrid subsets. Traditional interface boundary conditions between contacting subdomains are replaced by matrix approximations with the compensation principle exploiting. The implementation of preconditioning matrices is carried out by naturally parallelizable forward and back sweep algorithms on the macrogrid. The issues of assessing the efficiency and performance of the proposed methods and technologies for two-dimensional and three-dimensional problems are discussed, including the cases of parallelizing calculations. The results of numerical experiments for a set of methodical problems are presented.

AB - Iterative methods for domain decomposition methods in Krylov subspaces to solve large systems of linear algebraic equations arising from grid approximations of multidimensional boundary value problems are considered. The algorithms under study are based on purely algebraic approaches with special variants of approximate factorization of matrices arizing from grid division by a single-layer or two-layer separating macrogrid subsets. Traditional interface boundary conditions between contacting subdomains are replaced by matrix approximations with the compensation principle exploiting. The implementation of preconditioning matrices is carried out by naturally parallelizable forward and back sweep algorithms on the macrogrid. The issues of assessing the efficiency and performance of the proposed methods and technologies for two-dimensional and three-dimensional problems are discussed, including the cases of parallelizing calculations. The results of numerical experiments for a set of methodical problems are presented.

KW - Domain decomposition

KW - Forward and backward sweep

KW - Iterative method

KW - Krylov subspaces

KW - Matrix factorization

KW - Performance

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85219209778&origin=inward&txGid=00786e482f7c4be85bdc84d786671354

UR - https://www.mendeley.com/catalogue/ea465d6c-5a51-39c7-98fa-67dde2110945/

U2 - 10.1007/978-3-031-78459-0_26

DO - 10.1007/978-3-031-78459-0_26

M3 - Conference contribution

SN - 9783031784583

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 362

EP - 376

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer

T2 - 10th Russian Supercomputing Days Conference

Y2 - 23 September 2024 through 24 September 2024

ER -

ID: 64991149