Validating Computational Software With Exact Analytical Solutions: A review of the last three decades

Exact analytical solutions of canonical electromagnetic scattering problems that have been developed in the last 30 years are reviewed to emphasize that many geometrical shapes exist for the validation of computational electromagnetic (CEM) methods. The focus is on exact solutions that can be computed as the sum of series expansions, where the expansion coefficients are known analytically and do not require, for example, the solution of a system of equations. The introduction of a class of artificial materials, known as isorefractive, has enabled the development of new analytical solutions, some of which involve complications not previously found, such as involving different materials, sharp edges, and cavities. In addition, other complicated geometries have been examined to create new exact solutions, without requiring the use of isorefractive materials. Many numerical evaluations exist for the new exact solutions so that for the purposes of numerical validations, one could simply use the existing ones.