On a robin iteration method for heterogeneous Helmholtz problems for geophysics applications
Yogi A. Erlangga 1, Cornelis Vuik 2, Cornelis W. Oosterlee 21 Currently at Department of Aerospace Engineering, Institute of Technology at Bandung, Ganesha 10, Bandung 40132, Indonesia
2 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
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)