An FMM for waveguide problems of 2-D Helmholtz' equation and its application to eigenvalue problems

This paper discusses an FMM for solving waveguide problems and associated eigenvalue problems for Helmholtz' equation in a two dimensional infinite strip with homogeneous Neumann boundary condition on the sides. Layer potentials with Green's function for this problem are evaluated efficiently with the help of the method of images and FMM. We apply FMM to solve some boundary value problems in waveguides and associated resonance frequency problems using the Sakurai-Sugiura projection method after discussing the required analytic continuation of the solutions to complex frequencies. Some numerical examples show the accuracy and the efficiency of the proposed method.