In–out decomposition of boundary integral equations

Creagh, Stephen C.; Hamdin, Hanya Ben; Tanner, Gregor

doi:10.1088/1751-8113/46/43/435203

In–out decomposition of boundary integral equations

Creagh, Stephen C.; Hamdin, Hanya Ben; Tanner, Gregor

Authors

STEPHEN CREAGH STEPHEN.CREAGH@NOTTINGHAM.AC.UK
Associate Professor

Hanya Ben Hamdin

GREGOR TANNER GREGOR.TANNER@NOTTINGHAM.AC.UK
Professor of Applied Mathematics

Abstract

We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features such as diffraction and evanescent coupling; these effects are absent in the well-known semiclassical transfer operators in the sense of Bogomolny. It has long been established that transfer operators are equivalent to the boundary integral approach within semiclassical approximation. Exact treatments have been restricted to specific boundary conditions (such as Dirichlet or Neumann). The approach we propose is independent of the
boundary conditions, and in fact allows one to decouple entirely the problem of propagating waves across the interior from the problem of reflecting waves at
the boundary. As an application, we show how the decomposition may be used to calculate Goos–Haenchen shifts of ray dynamics in billiards with variable boundary conditions and for dielectric cavities.

Citation

Creagh, S. C., Hamdin, H. B., & Tanner, G. (2013). In–out decomposition of boundary integral equations. Journal of Physics A: Mathematical and Theoretical, 46(43), Article 435203. https://doi.org/10.1088/1751-8113/46/43/435203

Journal Article Type	Article
Publication Date	Oct 8, 2013
Deposit Date	Mar 26, 2014
Publicly Available Date	Mar 26, 2014
Journal	Journal of Physics A: Mathematical and Theoretical
Electronic ISSN	1751-8113
Publisher	IOP Publishing
Peer Reviewed	Peer Reviewed
Volume	46
Issue	43
Article Number	435203
DOI	https://doi.org/10.1088/1751-8113/46/43/435203
Public URL	https://nottingham-repository.worktribe.com/output/718920
Publisher URL	http://iopscience.iop.org/1751-8121/46/43/435203/