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Published on: February 3, 2014
On the solution of the Helmholtz equation on regions with corners
Kirill Serkh1, Vladimir Rokhlin1
1Department of Mathematics, Yale University, New Haven, CT 06511 kirill.serkh@yale.edu rokhlin@cs.yale.edu.
Abstract:
In this paper we solve several boundary value problems for the Helmholtz equation on polygonal domains. We observe that when the problems are formulated as the boundary integral equations of potential theory, the solutions are representable by series of appropriately chosen Bessel functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.
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