Du, Qikui; Zhang, Mingxin A non-overlapping domain decomposition algorithm based on the natural boundary reduction for wave equations in an unbounded domain. (English) Zbl 1075.65121 Numer. Math., J. Chin. Univ. 13, No. 2, 121-132 (2004). 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. Cited in 3 Documents MSC: 65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems 65F35 Numerical computation of matrix norms, conditioning, scaling 35L05 Wave equation Keywords:Dirichlet-Neumann alternating iteration algorithm; domain decomposition method; boundary reduction; preconditioned Richardson iteration method; finite element method; numerical results; convergence PDF BibTeX XML Cite \textit{Q. Du} and \textit{M. Zhang}, Numer. Math., J. Chin. Univ. 13, No. 2, 121--132 (2004; Zbl 1075.65121) OpenURL