Non-linear optimization for field, scattering and SEM problems

It is pointed out that many difficult problems in fields, scattering and singularity expansion methods (SEM) can be quite simple when a set of transcendental simultaneous equations can be used. Four examples of this are examined, and general conclusions are drawn. The examples demonstrate that many difficult problems in electromagnetics are indeed simple when they are formulated into a set of transcendental simultaneous equations and solved by a nonlinear optimization routine. It is suggested that the simplicity may derive from the requirement that most of the methods in electromagnetics (from the classical variable separation to the spectral domain, variational techniques and numerical moment methods) have for linear operations. Significant simplification is therefore to be expected in a number of problems when a nonlinear operation, such as the optimization routine, is used.