Eigenvalue analysis with the boundary element method and the Sakurai-Sugiura method for periodic boundary value problems for Helmholtz' equation in 3D

An eigenvalue analysis of periodic boundary value problems for Helmholtz' equation in 3D with the boundary element method (BEM) and the Sakurai-Sugiura (SS) method is proposed. The SS method is one of numerical methods for non-linear eigenvalue problems. This method obtains eigenvalues inside a fixed contour in the complex plane by calculating an integral along the contour. In this paper, we extend integral operators in the BEM to complex phase factor in order to calculate the integral along the contour, which is used in the SS method. With this calculation, we develop an eigenvalue analysis for Helmholtz' equation in 3D with the BEM and the SS method.