A new non-overlapping domain decomposition method for the 3-D Laplace exterior problem
V.M. Sveshnikov1,2, A.O. Savchenko1, A.V. Petukhov1
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Acad. Lavrentieva 6, Novosibirsk, 630090, Russia
2Novosibirsk State University, Pirogova st., 2, Novosibirsk, 630090, Russia
Keywords: внешние краевые задачи, декомпозиция расчетной области, вычисление интегралов с особенностями, итерационные методы в подпространствах Крылова, exterior boundary value problems, non-overlapping decomposition, computation of integrals with a singularities, iterative methods in Krylov subspaces
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.
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