An Experimental Study of the Efficiency of Solving 2D Boundary Value Problems on Subgrids of Quasi-Structured Rectangular Grids

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An Experimental Study of the Efficiency of Solving 2D Boundary Value Problems on Subgrids of Quasi-Structured Rectangular Grids. / Kozyrev, A. N.; Sveshnikov, V. M.

In: Numerical Analysis and Applications, Vol. 14, No. 3, 07.2021, p. 238-248.

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

BibTeX

@article{9be84bd4ec854a5799286a4649e170a4,

title = "An Experimental Study of the Efficiency of Solving 2D Boundary Value Problems on Subgrids of Quasi-Structured Rectangular Grids",

abstract = "An experimental study of the efficiency of solvers of 2D boundary value problems on subgrids of quasi-structured rectangular grids is carried out. A solver means a solution method and its software implementation. The following three solvers are considered: a direct solver (Buneman{\textquoteright}s cyclic reduction method) and two iterative ones (the alternative direction method of Peaceman and Rachford and the successive overrelaxation method). Characteristic features of the study are as follows: 1) the subgrids have a small number of nodes, namely 8 × 8, 16 × 16, 32 × 32, and 64 × 64; 2) the efficiency is estimated not only for single calculations, but also for series of calculations; in each of them the problem is repeatedly solved with different boundary conditions on the same subgrid. Based on a series of calculations, a combined method is proposed, and recommendations on using the solvers are given.",

keywords = "direct methods, experimental studies, iterative methods, solvers of boundary value problems, subgrids of quasi-structured grids",

author = "Kozyrev, {A. N.} and Sveshnikov, {V. M.}",

note = "Funding Information: This work was performed within the framework of the budget project no. 0315-2019-0008 of the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences. Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = jul,

doi = "10.1134/S1995423921030046",

language = "English",

volume = "14",

pages = "238--248",

journal = "Numerical Analysis and Applications",

issn = "1995-4239",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - An Experimental Study of the Efficiency of Solving 2D Boundary Value Problems on Subgrids of Quasi-Structured Rectangular Grids

AU - Kozyrev, A. N.

AU - Sveshnikov, V. M.

N1 - Funding Information: This work was performed within the framework of the budget project no. 0315-2019-0008 of the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences. Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/7

Y1 - 2021/7

N2 - An experimental study of the efficiency of solvers of 2D boundary value problems on subgrids of quasi-structured rectangular grids is carried out. A solver means a solution method and its software implementation. The following three solvers are considered: a direct solver (Buneman’s cyclic reduction method) and two iterative ones (the alternative direction method of Peaceman and Rachford and the successive overrelaxation method). Characteristic features of the study are as follows: 1) the subgrids have a small number of nodes, namely 8 × 8, 16 × 16, 32 × 32, and 64 × 64; 2) the efficiency is estimated not only for single calculations, but also for series of calculations; in each of them the problem is repeatedly solved with different boundary conditions on the same subgrid. Based on a series of calculations, a combined method is proposed, and recommendations on using the solvers are given.

AB - An experimental study of the efficiency of solvers of 2D boundary value problems on subgrids of quasi-structured rectangular grids is carried out. A solver means a solution method and its software implementation. The following three solvers are considered: a direct solver (Buneman’s cyclic reduction method) and two iterative ones (the alternative direction method of Peaceman and Rachford and the successive overrelaxation method). Characteristic features of the study are as follows: 1) the subgrids have a small number of nodes, namely 8 × 8, 16 × 16, 32 × 32, and 64 × 64; 2) the efficiency is estimated not only for single calculations, but also for series of calculations; in each of them the problem is repeatedly solved with different boundary conditions on the same subgrid. Based on a series of calculations, a combined method is proposed, and recommendations on using the solvers are given.

KW - direct methods

KW - experimental studies

KW - iterative methods

KW - solvers of boundary value problems

KW - subgrids of quasi-structured grids

UR - http://www.scopus.com/inward/record.url?scp=85113948903&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/670f1ab8-8d4f-35db-b00c-54c03f6a428f/

U2 - 10.1134/S1995423921030046

DO - 10.1134/S1995423921030046

M3 - Article

AN - SCOPUS:85113948903

VL - 14

SP - 238

EP - 248

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 3

ER -

ID: 34152486