We consider the numerical solution of scalar wave equations in domains whichare the union of a bounded domain and a finite number of infinite cylindricalwaveguides. The aim of this paper is to provide a new convergence analysis ofboth the Perfectly Matched Layer (PML) method and the Hardy space infiniteelement method in a unified framework. We treat both diffraction and resonanceproblems. The theoretical error bounds are compared with errors in numericalexperiments.
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