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Int. J. Numer. Anal. Mod., 2 (2005), pp. 197-208. |
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On a robin iteration method for heterogeneous Helmholtz problems for geophysics applications Yogi A. Erlangga 1, Cornelis Vuik 2, Cornelis W. Oosterlee 2 1 Currently at Department of Aerospace Engineering, Institute of Technology at Bandung, Ganesha 10, Bandung 40132, Indonesia2 Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands Received by the editors January 1, 2004 and, in revised form, March 22, 2004 Abstract In this paper, a robust iterative method for the 2D heterogeneous Helmholtz equation is discussed. Two important ingredients of the method are evaluated, namely the Krylov subspace iterative methods and multigrid based preconditioners. For the Krylov subspace methods we evaluate GM-RES and Bi-CGSTAB. The preconditioner used is the complex shifted Laplace preconditioner [Erlangga, Vuik, Oosterlee, Appl. Numer. Math. 50(2004) 409-425] which is approximately solved using multigrid. Numerical examples which mimic geophysical applications are presented. AMS subject classifications: 65N55, 65F10, 65N22, 78A45, 76Q05 Key words: Helmholtz equation; Krylov subspace methods; preconditioner; multigrid Email: Y.A.Erlangga@tudelft.nl (Y. A. Erlangga), C.Vuik@tudelft.nl (C. Vuik), C.W.Oosterlee@tudelft.nl (C. W. Oosterlee) |