Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection

Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection Full article

Conference

Суперкомпьютерные дни в России 2025
20-30 Sep 2025 , Москва

Source

Supercomputing. 11th Russian Supercomputing Days, RuSCDays 2025, Moscow, Russia, September 29–30, 2025, Revised Selected Papers. Conference proceedings
Compilation, Springer Cham. Switzerland.2026. 534 c. ISBN 978-3-032-13126-3.

Output data

Year: 2026, Pages: 274-287 Pages count : 14 DOI: 10.1007/978-3-032-13127-0_20

Authors

Gurin Alexey ¹ , Il’in Valery ² , Kardash Ruslan ^2,3

Affiliations

1	Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the RAS, Novosibirsk, Russia
2	Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia
3	Novosibirsk State University, Novosibirsk, Russia

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.

Gurin A. , Il’in V. , Kardash R.
Experimental Study of Macrogrid Domain Decomposition Methods with Approximate Block Bisection
In compilation Supercomputing. 11th Russian Supercomputing Days, RuSCDays 2025, Moscow, Russia, September 29–30, 2025, Revised Selected Papers. Conference proceedings. – Springer Cham., 2026. – C.274-287. – ISBN 978-3-032-13126-3. DOI: 10.1007/978-3-032-13127-0_20 OpenAlex

Published online:

Jan 2, 2026

OpenAlex:

W7117968379

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