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

Research output: Contribution to journal › Article › peer-review

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
Externally published	Yes

ASJC Scopus subject areas

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

Access to Document

10.1088/0305-4470/38/30/004

Fingerprint Dive into the research topics of 'On the boundary element method for billiards with corners'. Together they form a unique fingerprint.

Cite this

@article{a004749a8a604e64a98ff52d27abb4dc,

title = "On the boundary element method for billiards with corners",

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.",

author = "Y. Okada and A. Shudo and S. Tasaki and T. Harayama",

year = "2005",

month = jul,

day = "29",

doi = "10.1088/0305-4470/38/30/004",

language = "English",

volume = "38",

pages = "6675--6688",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "30",

}

TY - JOUR

T1 - On the boundary element method for billiards with corners

AU - Okada, Y.

AU - Shudo, A.

AU - Tasaki, S.

AU - Harayama, T.

PY - 2005/7/29

Y1 - 2005/7/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=22544445234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22544445234&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/38/30/004

DO - 10.1088/0305-4470/38/30/004

M3 - Article

AN - SCOPUS:22544445234

VL - 38

SP - 6675

EP - 6688

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 30

ER -