A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem
| Autor: | A. V. Petukhov, A. O. Savchenko, V. M. Sveshnikov |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Laplace transform Iterative method Numerical analysis 010102 general mathematics MathematicsofComputing_NUMERICALANALYSIS Domain decomposition methods 02 engineering and technology 01 natural sciences Domain (mathematical analysis) Algebraic equation 020303 mechanical engineering & transports Singularity 0203 mechanical engineering ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Applied mathematics Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | Numerical Analysis and Applications. 11:346-358 |
| ISSN: | 1995-4247 1995-4239 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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