Analysis of the Cutoff Wavenumber for Arbitrarily Shaped Waveguides Using Method of Dipole Representations with an Excitation Source

In this study, a new meshless technique named the method of dipole representation (MDPR) is proposed for numerically solving cutoff wavenumbers (eigenfrequency) of arbitrarily shaped waveguides with an excitation source. MDPR belongs to the de-singularized method like the method of auxiliary sources. Based on the solution of the 2D Laplace boundary-value problem with rational functions (dipole representation) as basis functions, this study gives the form of dipole representation for the problem under consideration. In MDPR, determining the location of the singularities (called poles in this study) is crucial, and a placement scheme for pole location is given by exponential clustering. Numerical results show that the proposed method can effectively solve the arbitrarily shaped waveguide eigenvalue problem. It also shows that MDPR can achieve root-exponential convergence.