Numerical Analysis and Applications

, Volume 11, Issue 4, pp 346–358 | Cite as

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

  • V. M. SveshnikovEmail author
  • A. O. Savchenko
  • A. V. Petukhov


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.


exterior boundary value problems non-overlapping decomposition computation of integrals with singularities iterative methods in Krylov subspaces 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. M. Sveshnikov
    • 1
    • 2
    Email author
  • A. O. Savchenko
    • 1
  • A. V. Petukhov
    • 1
  1. 1.Institute of Computational Mathematics and Mathematical Geophysics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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