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Free keywords:
Helmholtz equation
Dirichlet-to-Neumann operator
Preconditioning
Domain decomposition
High-frequency waves
Computational seismology
Perfectlymatched layers
Sweeping preconditioner
Abstract:
In this paper we consider sweeping preconditioners for time harmonic wave propagation instratified media, especially in the presence of reflections. In the most famous class ofsweeping preconditioners Dirichlet-to-Neumann operators for half-space problems areapproximated through absorbing boundary conditions. In the presence of reflectionsabsorbing boundary conditions are not accurate resulting in an unsatisfactory performanceof these sweeping preconditioners. We explore the potential of using more accurateDirichlet-to-Neumann operators within the sweep. To this end, we make use of the sep-arability of the equation for the background model. While this improves the accuracy of theDirichlet-to-Neumann operator, we find both from numerical tests and analytical argu-ments that it is very sensitive to perturbations in the presence of reflections. This impliesthat even if accurate approximations to Dirichlet-to-Neumann operators can be devised fora stratified medium, sweeping preconditioners are limited to very small perturbations.
