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We present Nystr\"om discretizations of multitrace formulations andnon-overlapping Domain Decomposition Methods (DDM) for the solution ofHelmholtz transmission problems for bounded composite scatterers with piecewiseconstant material properties. We investigate the performance of DDM with bothclassical Robin and generalized Robin boundary conditions. The generalizedRobin boundary conditions incorporate square root Fourier multiplierapproximations of Dirichlet to Neumann operators. While the classical versionof DDM is not particularly well suited for Krylov subspace iterative solvers,we show that the associated DDM linear system can be efficiently solved byhierarchical elimination via Schur complements of the Robin data. We showthrough numerical examples that the latter version of DDM gives rise to smallnumbers of Krylov subspace iterations that depend mildly on the frequency andnumber of subdomains.

Multitrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers