Sweeping preconditioners for stratified media in the presence of reflections

Janosch Preuß (), Thorsten Hohage () and Christoph Lehrenfeld ()
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Janosch Preuß: Max-Planck-Institut für Sonnensystemforschung
Thorsten Hohage: Max-Planck-Institut für Sonnensystemforschung
Christoph Lehrenfeld: Institut für Numerische und Angewandte Mathematik

Partial Differential Equations and Applications, 2020, vol. 1, issue 4, 1-17

Abstract: Abstract In this paper we consider sweeping preconditioners for time harmonic wave propagation in stratified media, especially in the presence of reflections. In the most famous class of sweeping preconditioners Dirichlet-to-Neumann operators for half-space problems are approximated through absorbing boundary conditions. In the presence of reflections absorbing boundary conditions are not accurate resulting in an unsatisfactory performance of these sweeping preconditioners. We explore the potential of using more accurate Dirichlet-to-Neumann operators within the sweep. To this end, we make use of the separability of the equation for the background model. While this improves the accuracy of the Dirichlet-to-Neumann operator, we find both from numerical tests and analytical arguments that it is very sensitive to perturbations in the presence of reflections. This implies that even if accurate approximations to Dirichlet-to-Neumann operators can be devised for a stratified medium, sweeping preconditioners are limited to very small perturbations.

Keywords: Helmholtz equation; Dirichlet-to-Neumann operator; Preconditioning; Domain decomposition; High-frequency waves; Computational seismology; Perfectly matched layers; Sweeping preconditioner; 65F08; 65N30; 35L05; 86-08; 86A15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-020-00019-x

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