Numerical methods for waveguide modelling

Abstract: Waveguides are used to transmit electromagnetic signals. Their geometry is typically long and slender. This particular shape can be used in the design of efficient computational methods. Only special modes are transmitted and eigenvalue and eigenvector analysis becomes important.We develop finite-element systems for solving electromagnetic field problems in time and frequency domain for closed waveguide cross-sections filled with various materials. The frequency domain discretization of the cross-section for the waveguide produces an algebraic eigenvalue problem. A general program based on Arnoldi's method and ARPACK has been written using node and edge elements to approximate the field. A serious problem with standard node elements is the occurrence of spurious solutions due to improper modeling of the null space of the curl operator. Edge elements remove such non physical spurious solutions. Numerical examples are given for homogeneous and inhomogeneous waveguides. The homogeneous results are compared to analytical solutions to demonstrate that the right order of convergence is achieved.Computations on more complicated inhomogeneous waveguides with and without striplines, are compared to results found in the literature together with grid convergence studies. We also give examples where corner singularities are addressed with $hp$-adaptive methods.The code is used in an industrial environment, together with 3-D time and frequency domain solvers for Maxwell's equations on general domains. For the full 3-D time domain simulations, cross section simulations are used as input on an artificial boundary that we define as a waveguide port. The excitation is done by a Huygens' surface and the backscattered field is taken care of by an unsplit perfectly matched layer. The results have been compared to what analytical input would give.