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