On the boundary element method for billiards with corners

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

Research output: Contribution to journalArticle

4 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 languageEnglish
Pages (from-to)6675-6688
Number of pages14
JournalJournal of Physics A: Mathematical and General
Volume38
Issue number30
DOIs
Publication statusPublished - 2005 Jul 29
Externally publishedYes

Fingerprint

boundary element method
Billiards
Boundary element method
Boundary Elements
Fredholm Theory
singular integral equations
Helmholtz equation
Helmholtz equations
Helmholtz Equation
Justification
Numerical Scheme
Integral equations
Eigenvalue Problem
Integral Equations
eigenvalues
cut-off

ASJC Scopus subject areas

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

Cite this

On the boundary element method for billiards with corners. / Okada, Y.; Shudo, A.; Tasaki, S.; Harayama, Takahisa.

In: Journal of Physics A: Mathematical and General, Vol. 38, No. 30, 29.07.2005, p. 6675-6688.

Research output: Contribution to journalArticle

Okada, Y. ; Shudo, A. ; Tasaki, S. ; Harayama, Takahisa. / On the boundary element method for billiards with corners. In: Journal of Physics A: Mathematical and General. 2005 ; Vol. 38, No. 30. pp. 6675-6688.
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