On the boundary element method for billiards with corners

Y. Okada; A. Shudo; S. Tasaki; T. Harayama

doi:10.1088/0305-4470/38/30/004

On the boundary element method for billiards with corners

Y. Okada, A. Shudo, S. Tasaki, T. Harayama

School of Advanced Science and Engineering

Research output: Contribution to journal › Article

5 Citations (Scopus)

Abstract

The boundary element method is one of the reliable numerical schemes to solve the eigenvalue problem of the Helmholtz equation, which is justified by the Fredholm theory for domains with a smooth boundary. When a domain has corners, however, the corresponding integral equation is singular, so that the boundary element method lacks its well-established base. Employing a cutoff technique, we here formulate a well-grounded version of the boundary element method, and also give a certain justification to the standard boundary element method even for domains with corners.

Original language	English
Pages (from-to)	6675-6688
Number of pages	14
Journal	Journal of Physics A: Mathematical and General
Volume	38
Issue number	30
DOIs	https://doi.org/10.1088/0305-4470/38/30/004
Publication status	Published - 2005 Jul 29

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ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

Cite this

Okada, Y., Shudo, A., Tasaki, S., & Harayama, T. (2005). On the boundary element method for billiards with corners. Journal of Physics A: Mathematical and General, 38(30), 6675-6688. https://doi.org/10.1088/0305-4470/38/30/004

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10.1088/0305-4470/38/30/004