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2012 | OriginalPaper | Chapter
Scattering Problems in Periodic Media with Local Perturbations
Authors : Therese Pollok, Lin Zschiedrich, Frank Schmidt
Published in: Scientific Computing in Electrical Engineering SCEE 2010
Publisher: Springer Berlin Heidelberg
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Within this paper we consider scattering problems with periodic exterior domains, modeled by the Helmholtz equation. Most current works on this subject make specific assumptions on the geometry of the periodic cell, e.g. special symmetries or shapes, and cannot be generalized to higher space dimensions in an easy way. In contrast our goal is the realization of an easy dimension independent concept which is valid for all kinds of periodic structures with local defects. We will first give a general analytical formulation and then present an algorithmic realization. At the end of the paper we will also depict a 1D and 2D example.