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

V. M. Sveshnikov, A. O. Savchenko, A. V. Petukhov

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)346-358
Number of pages13
JournalNumerical Analysis and Applications
Volume11
Issue number4
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

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

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