Transactions of the Japan Society for Industrial and Applied Mathematics
Online ISSN : 2424-0982
ISSN-L : 0917-2246
Calculation of Eigenvalues Related to 2 Dimensional Periodic Boundary Value Problems for the Helmholtz Equation Using the Sakurai-Sugiura Method and Periodic Fast Multipole Method(Practice)
Taichiro NoseNaoshi Nishimura
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2014 Volume 24 Issue 3 Pages 185-201

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Abstract

This paper presents a method of eigenvalue calculation related to periodic boundary value problems for the Helmholtz equation in two dimensions based on the Sakurai-Sugiura projection method and periodic FMM. The Sakurai-Sugiura projection method solves nonlinear eigenvalue problems using contour integrals and is considered to be suitable for solving eigenvalue problems in conjuction with boundary element methods. We apply this method to eigenvalue problems specific to periodic boundary value problems related to guided waves and anomalies. We then validate the proposed method with numerical examples.

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© 2014 The Japan Society for Industrial and Applied Mathematics
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