High Order Transparent Boundary Conditions for the Helmholtz Equation
We consider finite element simulations of the Helmholtz equation in unbounded domains. For computational purposes, these domains are truncated to bounded domains using transparent boundary conditions at the artificial boundaries. We present here two numerical realizations of transparent boundary conditions: the complex scaling or perfectly matched layer method and the Hardy space infinite element method. Both methods are Galerkin methods, but their variational framework differs. Proofs of convergence of the methods are given in detail for one dimensional problems. In higher dimensions radial as well as Cartesian constructions are introduced with references to the known theory.
Support from the Austrian Science Fund (FWF) through grant P26252 is gratefully acknowledged.
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