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A non-overlapping domain decomposition algorithm based on the natural boundary reduction for wave equations in an unbounded domain. (English) Zbl 1075.65121
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:
65M55Multigrid methods; domain decomposition (IVP of PDE)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
65F10Iterative methods for linear systems
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
35L05Wave equation (hyperbolic PDE)