Abstract
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.
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Original Russian Text © V.M. Sveshnikov, A.O. Savchenko, A.V. Petukhov, 2018, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2018, Vol. 21, No. 4, pp. 435–449.
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Sveshnikov, V.M., Savchenko, A.O. & Petukhov, A.V. A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem. Numer. Analys. Appl. 11, 346–358 (2018). https://doi.org/10.1134/S1995423918040079
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DOI: https://doi.org/10.1134/S1995423918040079