Anders Andersson, Borje Nilsson, Thomas Biro
Wave scattering problems in variously shaped waveguides with varying boundary conditions is studied with the purpose to investigate what can be done with classical Fourier methods. A set of techniques, including newly developed conformal mapping methods, wave splitting, Fourier series development where non-normal operators have non-real eigenvalues, the building block method, Dirichlet-to-Neumann operators, and reformulation of the differential equtions in terms of equations for reflections and transmission operators, are used to solve the problem. In an example from acoustics, the results are, with good correspondence in the low frequency domain, compared with a finite element method solution to the same problem.
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http://arxiv.org/abs/1307.7911
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