Abstract:
We propose a method for solving the three-dimensional boundary value problems for the Laplace equation in an unbounded domain. It is based on the non-overlapping decomposition of the exterior domain to the two subdomains such that the initial problem is reduced to the two subproblems, namely, the exterior and the interior boundary value problems on a sphere. To solve the exterior boundary value problem, we propose a singularity isolation method. To cross-link the solutions at the interface of subdomains (a sphere), we introduce a special operator equation that is approximated by the system of linear algebraic equations. Such a system is solved by iterative methods in the Krylov subspaces. The method is illustrated by solving the model problems confirming its operability.
Key words:
exterior boundary value problems, non-overlapping decomposition, computation of integrals with a singularities, iterative methods in Krylov subspaces.
This work was supported by the Russian Science Foundation (project no. 14-11-00485) and the Russian Foundation for Basic Research (project no. 16-01-00168).
Citation:
V. M. Sveshnikov, A. O. Savchenko, A. V. Petukhov, “A new non-overlapping domain decomposition method for the 3-D Laplace exterior problem”, Sib. Zh. Vychisl. Mat., 21:4 (2018), 435–449; Num. Anal. Appl., 11:4 (2018), 346–358
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\by V.~M.~Sveshnikov, A.~O.~Savchenko, A.~V.~Petukhov
\paper A new non-overlapping domain decomposition method for the 3-D Laplace exterior problem
\jour Sib. Zh. Vychisl. Mat.
\yr 2018
\vol 21
\issue 4
\pages 435--449
\mathnet{http://mi.mathnet.ru/sjvm695}
\crossref{https://doi.org/10.15372/SJNM20180407}
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\transl
\jour Num. Anal. Appl.
\yr 2018
\vol 11
\issue 4
\pages 346--358
\crossref{https://doi.org/10.1134/S1995423918040079}
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Linking options:
https://www.mathnet.ru/eng/sjvm695
https://www.mathnet.ru/eng/sjvm/v21/i4/p435
This publication is cited in the following 2 articles:
M. P. Galanin, D. L. Sorokin, “Solving exterior boundary value problems for the Laplace equation”, Differ. Equ., 56:7 (2020), 890–899
A. O. Savchenko, A. V. Petukhov, “A method for solving an exterior boundary value problem for the Laplace equation by overlapping domain decomposition”, J. Appl. Industr. Math., 13:3 (2019), 519–527
Citation in format AMSBIB
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