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Ray Tuminaro
Augmented AMG-Shifted Laplacian Preconditioners for Indefinite Helmholtz Problems

MS 9159
Sandia National Laboratories
PO Box 969
Livermore
CA 94551
rstumin@sandia.gov
Paul Tsuji

The use of shifted Laplacians has become a popular method for preconditioning linear systems coming from the discretization of time-harmonic wave equations. In this talk, we analyze a multilevel Shifted Laplacian procedure that uses polynomial-based smoothers. The analysis reveals both strengths and limitations to the shifted Laplacian idea. Motivated by this analysis, we then propose an additional two-grid error correction step that can be used to further accelerate the convergence of the Shifted Laplacian preconditioner. This correction term is based on a projection of the original Helmholtz operator. Preliminary results indicate that the augmentation can not only improve the convergence but reduce the overall solve time for two and three dimensional problems.





Copper Mountain 2014-02-23