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On Multigrid Methods for Solving Two-Dimensional Boundary-Value Problems. / Gurieva, Y. L.; Il’in, V. P.; Petukhov, A. V.

In: Journal of Mathematical Sciences (United States), Vol. 249, No. 2, 01.08.2020, p. 118-127.

Research output: Contribution to journal › Article › peer-review

Harvard

Gurieva, YL, Il’in, VP & Petukhov, AV 2020, 'On Multigrid Methods for Solving Two-Dimensional Boundary-Value Problems', Journal of Mathematical Sciences (United States), vol. 249, no. 2, pp. 118-127. https://doi.org/10.1007/s10958-020-04926-7

APA

Gurieva, Y. L., Il’in, V. P., & Petukhov, A. V. (2020). On Multigrid Methods for Solving Two-Dimensional Boundary-Value Problems. Journal of Mathematical Sciences (United States), 249(2), 118-127. https://doi.org/10.1007/s10958-020-04926-7

Vancouver

Gurieva YL, Il’in VP, Petukhov AV. On Multigrid Methods for Solving Two-Dimensional Boundary-Value Problems. Journal of Mathematical Sciences (United States). 2020 Aug 1;249(2):118-127. doi: 10.1007/s10958-020-04926-7

Author

Gurieva, Y. L. ; Il’in, V. P. ; Petukhov, A. V. / On Multigrid Methods for Solving Two-Dimensional Boundary-Value Problems. In: Journal of Mathematical Sciences (United States). 2020 ; Vol. 249, No. 2. pp. 118-127.

BibTeX

@article{ce982346518842a69522b015fe94bbd5,
title = "On Multigrid Methods for Solving Two-Dimensional Boundary-Value Problems",
abstract = "Various methods for constructing algebraic multigrid type methods for solving multidimensional boundary-value problems are considered. Two-level iterative algorithms in Krylov subspaces based on approximating the Schur complement obtained by eliminating the edge nodes of the coarse grid are described on the example of two-dimensional rectangular grids. Some aspects of extending the methods proposed to the multilevel case, to nested triangular grids, and also to three-dimensional grids are discussed. A comparison with the classical multigrid methods based on using smoothing, restriction (aggregation), coarse-grid correction, and prolongation is provided. The efficiency of the algorithms suggested is demonstrated by numerical results for some model problems.",
author = "Gurieva, {Y. L.} and Il{\textquoteright}in, {V. P.} and Petukhov, {A. V.}",
year = "2020",
month = aug,
day = "1",
doi = "10.1007/s10958-020-04926-7",
language = "English",
volume = "249",
pages = "118--127",
journal = "Journal of Mathematical Sciences (United States)",
issn = "1072-3374",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - On Multigrid Methods for Solving Two-Dimensional Boundary-Value Problems

AU - Gurieva, Y. L.

AU - Il’in, V. P.

AU - Petukhov, A. V.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - Various methods for constructing algebraic multigrid type methods for solving multidimensional boundary-value problems are considered. Two-level iterative algorithms in Krylov subspaces based on approximating the Schur complement obtained by eliminating the edge nodes of the coarse grid are described on the example of two-dimensional rectangular grids. Some aspects of extending the methods proposed to the multilevel case, to nested triangular grids, and also to three-dimensional grids are discussed. A comparison with the classical multigrid methods based on using smoothing, restriction (aggregation), coarse-grid correction, and prolongation is provided. The efficiency of the algorithms suggested is demonstrated by numerical results for some model problems.

AB - Various methods for constructing algebraic multigrid type methods for solving multidimensional boundary-value problems are considered. Two-level iterative algorithms in Krylov subspaces based on approximating the Schur complement obtained by eliminating the edge nodes of the coarse grid are described on the example of two-dimensional rectangular grids. Some aspects of extending the methods proposed to the multilevel case, to nested triangular grids, and also to three-dimensional grids are discussed. A comparison with the classical multigrid methods based on using smoothing, restriction (aggregation), coarse-grid correction, and prolongation is provided. The efficiency of the algorithms suggested is demonstrated by numerical results for some model problems.

UR - http://www.scopus.com/inward/record.url?scp=85088525954&partnerID=8YFLogxK

U2 - 10.1007/s10958-020-04926-7

DO - 10.1007/s10958-020-04926-7

M3 - Article

AN - SCOPUS:85088525954

VL - 249

SP - 118

EP - 127

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 2

ER -

ID: 24832668