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Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection. / Gurin, Alexey; Il’in, Valery; Kardash, Ruslan.

Lecture Notes in Computer Science. Vol. 16196 Springer, 2026. p. 274-287 20 (Lecture Notes in Computer Science; Vol. 16196 LNCS).

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

Harvard

Gurin, A, Il’in, V & Kardash, R 2026, Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection. in Lecture Notes in Computer Science. vol. 16196, 20, Lecture Notes in Computer Science, vol. 16196 LNCS, Springer, pp. 274-287, 11th Russian Supercomputing Days, Москва, Russian Federation, 29.09.2025. https://doi.org/10.1007/978-3-032-13127-0_20

APA

Gurin, A., Il’in, V., & Kardash, R. (2026). Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection. In Lecture Notes in Computer Science (Vol. 16196, pp. 274-287). [20] (Lecture Notes in Computer Science; Vol. 16196 LNCS). Springer. https://doi.org/10.1007/978-3-032-13127-0_20

Vancouver

Gurin A, Il’in V, Kardash R. Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection. In Lecture Notes in Computer Science. Vol. 16196. Springer. 2026. p. 274-287. 20. (Lecture Notes in Computer Science). doi: 10.1007/978-3-032-13127-0_20

Author

Gurin, Alexey ; Il’in, Valery ; Kardash, Ruslan. / Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection. Lecture Notes in Computer Science. Vol. 16196 Springer, 2026. pp. 274-287 (Lecture Notes in Computer Science).

BibTeX

@inproceedings{f6c09bb9518d4a80830e52184557d8ff,
title = "Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection",
abstract = "This paper develops and experimentally investigates macrogrid domain decomposition methods for solving large systems of linear algebraic equations (SLAEs) with sparse symmetric matrices obtained from grid approximations of multidimensional boundary value problems. The proposed algorithms are based on constructing two-layer macro-grids and special ordering of nodes according to their belonging to different topological primitives of the macro-grid: macro-nodes, macro-edges, macro-faces, and subdomains. With consistent numbering of vector components, the SLAE matrices in the three-dimensional case take a block-tridiagonal form of fourth order. For its solution, an incomplete factorization algorithm is used, based on block bisection of the original matrix and application of parallel direct or preconditioned iterative algorithms in subdomains. The justification of the proposed methods is given for symmetric positive definite (s.p.d.) matrices.",
author = "Alexey Gurin and Valery Il{\textquoteright}in and Ruslan Kardash",
note = "Gurin, A., Il{\textquoteright}in, V., Kardash, R. (2026). Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection. In: Voevodin, V., Antonov, A., Nikitenko, D. (eds) Supercomputing. RuSCDays 2025. Lecture Notes in Computer Science, vol 16196. Springer, Cham. https://doi.org/10.1007/978-3-032-13127-0_20 The paper was financially supported by the Russian Science Foundation (Project No. 24-21-00402).; 11th Russian Supercomputing Days, RuSCDays 2025 ; Conference date: 29-09-2025 Through 30-09-2025",
year = "2026",
month = jan,
day = "2",
doi = "10.1007/978-3-032-13127-0_20",
language = "English",
isbn = "978-3-032-13126-3",
volume = "16196",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "274--287",
booktitle = "Lecture Notes in Computer Science",
address = "United States",

}

RIS

TY - GEN

T1 - Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection

AU - Gurin, Alexey

AU - Il’in, Valery

AU - Kardash, Ruslan

N1 - Conference code: 11

PY - 2026/1/2

Y1 - 2026/1/2

N2 - This paper develops and experimentally investigates macrogrid domain decomposition methods for solving large systems of linear algebraic equations (SLAEs) with sparse symmetric matrices obtained from grid approximations of multidimensional boundary value problems. The proposed algorithms are based on constructing two-layer macro-grids and special ordering of nodes according to their belonging to different topological primitives of the macro-grid: macro-nodes, macro-edges, macro-faces, and subdomains. With consistent numbering of vector components, the SLAE matrices in the three-dimensional case take a block-tridiagonal form of fourth order. For its solution, an incomplete factorization algorithm is used, based on block bisection of the original matrix and application of parallel direct or preconditioned iterative algorithms in subdomains. The justification of the proposed methods is given for symmetric positive definite (s.p.d.) matrices.

AB - This paper develops and experimentally investigates macrogrid domain decomposition methods for solving large systems of linear algebraic equations (SLAEs) with sparse symmetric matrices obtained from grid approximations of multidimensional boundary value problems. The proposed algorithms are based on constructing two-layer macro-grids and special ordering of nodes according to their belonging to different topological primitives of the macro-grid: macro-nodes, macro-edges, macro-faces, and subdomains. With consistent numbering of vector components, the SLAE matrices in the three-dimensional case take a block-tridiagonal form of fourth order. For its solution, an incomplete factorization algorithm is used, based on block bisection of the original matrix and application of parallel direct or preconditioned iterative algorithms in subdomains. The justification of the proposed methods is given for symmetric positive definite (s.p.d.) matrices.

UR - https://www.scopus.com/pages/publications/105028303286

UR - https://www.mendeley.com/catalogue/b6f51aac-22a0-323c-9d14-f9291655a9c0/

U2 - 10.1007/978-3-032-13127-0_20

DO - 10.1007/978-3-032-13127-0_20

M3 - Conference contribution

SN - 978-3-032-13126-3

VL - 16196

T3 - Lecture Notes in Computer Science

SP - 274

EP - 287

BT - Lecture Notes in Computer Science

PB - Springer

T2 - 11th Russian Supercomputing Days

Y2 - 29 September 2025 through 30 September 2025

ER -

ID: 74290037