Review of methods for numerical solution of the hollow-waveguide problem

A review is given of current methods for numerically solving the hollow-waveguide problem. Attention is drawn to the relative advantages of the various methods, particularly with regard to their performance with different waveguide shapes. Any requirement for a completely automatic algorithm, or for the computation of fields as well as cutoff values, is also found to put some methods to particular advantage. An attempt is made to compare and contrast the various formulations of finite-difference and finite-element methods (and other similar approaches) which result in a standard form of matrix-eigenvalue problem. Other methods studied are those of point-matching, integral equations and conformal transformations.