Two-level preconditioners for the Helmholtz equation
For researchers solving large-scale Helmholtz problems, this provides a practical comparison of preconditioner strategies, though the results are incremental and domain-specific.
The paper numerically compares two coarse space definitions for two-level domain decomposition preconditioners for the Helmholtz equation in 2D and 3D, finding that the DtN-based coarse space yields better convergence than the coarse mesh approach, especially for high wavenumbers.
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.