Computer Science – Numerical Analysis
Scientific paper
2010-12-24
Computer Science
Numerical Analysis
Scientific paper
In this paper we develop a robust multigrid preconditioned Krylov subspace method for the solution of heterogeneous indefinite Helmholtz problems. The preconditioning operator is constructed by discretizing the original Helmholtz equation on a complex stretched grid. As this preconditioning operator has the same wavenumber as the original problem, and the only difference stems from the complex stretching of the discretization grid, its spectrum closely approximates the spectrum of the original Helmholtz operator, resulting in a fast converging Krylov subspace method. We have analyzed a multigrid cycle based on polynomial smoothers and have found a condition on the parameters used in the complex stretching of the discretization grid such that the existence of a stable third order polynomial smoother is guaranteed. In practice we use three iterations of GMRES as a smoother, and have found this to be a viable smoother for the multigrid preconditioning process. We apply the method to various test problems and report on the observed convergence rate.
Reps Bram
Vanroose Wim
Zubair Hisham bin
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