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 | |
| Publication status | Published - 2005 Jul 29 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - On the boundary element method for billiards with corners
AU - Okada, Y.
AU - Shudo, A.
AU - Tasaki, S.
AU - Harayama, Takahisa
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 -