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Two-level preconditioners for the Helmholtz equation

Bonazzoli, Marcella and Dolean, Victorita and Graham, Ivan G. and Spence, Euan A. and Tournier, Pierre-Henri (2018) Two-level preconditioners for the Helmholtz equation. In: Lecture Notes in Computational Science and Engineering. Lecture Notes in Computational Science and Engineering . Springer, Cham, Switzerland. (In Press)

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Abstract

In this paper we compare numerically two different coarse space definitions for two-level domain decomposition preconditioners for the Helmholtz equation, both in two and three dimensions. While we solve the pure Helmholtz problem without absorption, the preconditioners are built from problems with absorption. In the first method, the coarse space is based on the discretization of the problem with absorption on a coarse mesh, with diameter constrained by the wavenumber. In the second method, the coarse space is built by solving local eigenproblems involving the Dirichlet-to-Neumann (DtN) operator.