Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation

Authors:
Y. A. Erlangga;C. Vuik;C. W. Oosterlee
Affiliations:
Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
Venue:
Applied Numerical Mathematics
Year:
2006

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Abstract

Within the framework of shifted-Laplace preconditioners [Y.A. Erlangga, C. Vuik, C.W. Oosterlee, On a class of preconditioners for the Helmholtz equation, Appl. Numer. Math. 50 (2004) 409-425] for the Helmholtz equation, different methods for the approximation of the inverse of a complex-valued Helmholtz operator are discussed. The performance of the preconditioner for Helmholtz problems at high wavenumbers in heterogeneous media is evaluated. Comparison with other preconditioners from the literature is also presented.