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.
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U2 - 10.1088/0305-4470/38/30/004
DO - 10.1088/0305-4470/38/30/004
M3 - Article
AN - SCOPUS:22544445234
SN - 0305-4470
VL - 38
SP - 6675
EP - 6688
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 30
ER -