title: On the solution of the Helmholtz equation on regions with corners.
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.
authors.affiliation: Department of Mathematics, Yale University, New Haven, CT 06511 kirill.serkh@yale.edu rokhlin@cs.yale.edu.
authors.forename: Kirill
authors.initials: K
authors.lastname: Serkh
authors.affiliation: Department of Mathematics, Yale University, New Haven, CT 06511 kirill.serkh@yale.edu rokhlin@cs.yale.edu.
authors.forename: Vladimir
authors.initials: V
authors.lastname: Rokhlin
keywords: Helmholtz equation; boundary value problems; corners; elliptic partial differential equations; potential theory