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We examine the use of the Dirichlet-to-Neumann coarse space within anadditive Schwarz method to solve the Helmholtz equation in 2D. In particular,we focus on the selection of how many eigenfunctions should go into the coarsespace. We find that wave number independent convergence of a preconditionediterative method can be achieved in certain special cases with an appropriateand novel choice of threshold in the selection criteria. However, this propertyis lost in a more general setting, including the heterogeneous problem.Nonetheless, the approach converges in a small number of iterations for thehomogeneous problem even for relatively large wave numbers and is robust to thenumber of subdomains used.

On the Dirichlet-to-Neumann coarse space for solving the Helmholtz problem using domain decomposition