A non-overlapping domain decomposition algorithm based on the natural boundary reduction for wave equations in an unbounded domain. (English) Zbl 1075.65121

Du, Qikui; Zhang, Mingxin

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.

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