On radiation conditions for rough surface scattering problems |
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Authors: | Arens, Tilo Hohage, Thorsten |
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Affiliation: | 1 Mathematisches Insitut II, Universität Karlsruhe, 76128 Karlsruhe, Germany, 2 Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, 37083 Göttingen, Germany |
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Abstract: | ** Email: arens{at}numathics.com*** Email: hohage{at}math.uni-goettingen.de It is well known that Sommerfeld's radiation condition is nota valid characterization of outgoing waves for scattering problemsat rough surfaces. Instead, a radiation condition called upwardpropagating radiation condition (UPRC) is commonly used. Recently,a different radiation condition called the pole condition hasbeen investigated for scattering problems at bounded obstacles.In this paper we show the equivalence between the UPRC and thepole condition. In doing so, we give a rigorous interpretationof a formula called the angular spectrum representation forDirichlet data in the space of bounded continuous functions. |
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Keywords: | Helmholtz equation pole condition radiation conditions rough surface scattering. |
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