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Zbl 1075.65121
Du, Qikui; Zhang, Mingxin
A non-overlapping domain decomposition algorithm based on the natural boundary reduction for wave equations in an unbounded domain. (English)
[J] Numer. Math., J. Chin. Univ. 13, No. 2, 121-132 (2004). ISSN 1004-8979

Summary: A new domain decomposition method based on the natural boundary reduction, which solves wave problems over an unbounded domain, is suggested. An circular artificial boundary is introduced. The original unbounded domain is divided into two subdomains, an internal bounded region and external unbounded region outside the artificial boundary. A Dirichlet-Neumann (D-N) alternating iteration algorithm is constructed. We prove that the algorithm is equavilent to the preconditioned Richardson iteration method. Numerical studies are performed by the finite element method. The numerical results show that the convergence rate of the discrete D-N iteration is independent of the finite element mesh size.

MSC 2000:: *65M55 Multigrid methods; domain decomposition (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65F10 Iterative methods for linear systems
65F35 Matrix norms, etc. (numerical linear algebra)
35L05 Wave equation

Keywords: Dirichlet-Neumann alternating iteration algorithm; domain decomposition method; boundary reduction; preconditioned Richardson iteration method; finite element method; numerical results; convergence

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