Advances in Computational Mathematics

, Volume 43, Issue 1, pp 45–76 | Cite as

An improved sweeping domain decomposition preconditioner for the Helmholtz equation

  • Christiaan C. StolkEmail author
Open Access


In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries using perfectly matched layers. Simultaneous forward and backward sweeps are introduced, thereby improving the possibilities for parallellization. Finally, the method is combined with an outer two-grid iteration. The method is studied theoretically and with numerical examples. It is shown that the modifications lead to substantial decreases in computation time and memory use, so that computation times become comparable to that of the fastests methods currently in the literature for problems with up to 108 degrees of freedom.


Helmholtz equation Domain decomposition Multigrid method High-frequency waves Perfectly matched layers 

Mathematics Subject Classification (2010)

65N55 65N22 


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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands

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