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A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem. / Sveshnikov, V. M.; Savchenko, A. O.; Petukhov, A. V.

In: Numerical Analysis and Applications, Vol. 11, No. 4, 01.10.2018, p. 346-358.

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

Harvard

Sveshnikov, VM, Savchenko, AO & Petukhov, AV 2018, 'A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem', Numerical Analysis and Applications, vol. 11, no. 4, pp. 346-358. https://doi.org/10.1134/S1995423918040079

APA

Sveshnikov, V. M., Savchenko, A. O., & Petukhov, A. V. (2018). A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem. Numerical Analysis and Applications, 11(4), 346-358. https://doi.org/10.1134/S1995423918040079

Vancouver

Sveshnikov VM, Savchenko AO, Petukhov AV. A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem. Numerical Analysis and Applications. 2018 Oct 1;11(4):346-358. doi: 10.1134/S1995423918040079

Author

Sveshnikov, V. M. ; Savchenko, A. O. ; Petukhov, A. V. / A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem. In: Numerical Analysis and Applications. 2018 ; Vol. 11, No. 4. pp. 346-358.

BibTeX

@article{e04f84db34964f589d92d9ef574c8909,
title = "A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem",
abstract = "We propose a method for solving three-dimensional boundary value problems for Laplace{\textquoteright}s equation in an unbounded domain. It is based on non-overlapping decomposition of the exterior domain into two subdomains so that the initial problem is reduced to two subproblems, namely, exterior and interior boundary value problems on a sphere. To solve the exterior boundary value problem, we propose a singularity isolation method. To match the solutions on the interface between the subdomains (the sphere), we introduce a special operator equation approximated by a system of linear algebraic equations. This system is solved by iterative methods in Krylov subspaces. The performance of the method is illustrated by solving model problems.",
keywords = "computation of integrals with singularities, exterior boundary value problems, iterative methods in Krylov subspaces, non-overlapping decomposition",
author = "Sveshnikov, {V. M.} and Savchenko, {A. O.} and Petukhov, {A. V.}",
year = "2018",
month = oct,
day = "1",
doi = "10.1134/S1995423918040079",
language = "English",
volume = "11",
pages = "346--358",
journal = "Numerical Analysis and Applications",
issn = "1995-4239",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "4",

}

RIS

TY - JOUR

T1 - A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem

AU - Sveshnikov, V. M.

AU - Savchenko, A. O.

AU - Petukhov, A. V.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We propose a method for solving three-dimensional boundary value problems for Laplace’s equation in an unbounded domain. It is based on non-overlapping decomposition of the exterior domain into two subdomains so that the initial problem is reduced to two subproblems, namely, exterior and interior boundary value problems on a sphere. To solve the exterior boundary value problem, we propose a singularity isolation method. To match the solutions on the interface between the subdomains (the sphere), we introduce a special operator equation approximated by a system of linear algebraic equations. This system is solved by iterative methods in Krylov subspaces. The performance of the method is illustrated by solving model problems.

AB - We propose a method for solving three-dimensional boundary value problems for Laplace’s equation in an unbounded domain. It is based on non-overlapping decomposition of the exterior domain into two subdomains so that the initial problem is reduced to two subproblems, namely, exterior and interior boundary value problems on a sphere. To solve the exterior boundary value problem, we propose a singularity isolation method. To match the solutions on the interface between the subdomains (the sphere), we introduce a special operator equation approximated by a system of linear algebraic equations. This system is solved by iterative methods in Krylov subspaces. The performance of the method is illustrated by solving model problems.

KW - computation of integrals with singularities

KW - exterior boundary value problems

KW - iterative methods in Krylov subspaces

KW - non-overlapping decomposition

UR - http://www.scopus.com/inward/record.url?scp=85058296584&partnerID=8YFLogxK

U2 - 10.1134/S1995423918040079

DO - 10.1134/S1995423918040079

M3 - Article

AN - SCOPUS:85058296584

VL - 11

SP - 346

EP - 358

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 4

ER -

ID: 17896761