On the solution of the Helmholtz equation on regions with corners.
basic_science · Level V
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- Record sourced from PubMed, PMID 27482110.
- Also identified by DOI 10.1073/pnas.1609578113 and PMC identifier 4995988.
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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.