A Method for Solving an Exterior Boundary Value Problem for the Laplace Equation by Overlapping Domain Decomposition
- Authors: Savchenko A.O.1, Petukhov A.V.1
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Affiliations:
- Institute of Computational Mathematics and Mathematical Geophysics
- Issue: Vol 13, No 3 (2019)
- Pages: 519-527
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213233
- DOI: https://doi.org/10.1134/S1990478919030128
- ID: 213233
Cite item
Abstract
We propose a numerical method for solving an exterior three-dimensional boundary value problem for the Laplace equation based on the overlapping decomposition of the computational domain. The initial boundary value problem is reduced to solving an operator equation for the sought values of the function on an auxiliary sphere enclosing the interior boundary. This equation is approximated by a system of linear algebraic equations which is solved by iterative methods in the Krylov subspaces. A series of numerical experiments for model problems with known solutions demonstrates not only the convergence of the method and the attained accuracy of the calculations but also a sufficiently short runtime.
About the authors
A. O. Savchenko
Institute of Computational Mathematics and Mathematical Geophysics
Author for correspondence.
Email: savch@ommfao1.sscc.ru
Russian Federation, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090
A. V. Petukhov
Institute of Computational Mathematics and Mathematical Geophysics
Author for correspondence.
Email: petukhov@lapasrv.sscc.ru
Russian Federation, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090