# CEM for Harmonic Problem Solving in Frequency, Time and Harmonic Domains

## Computational Electromagnetics (CEM) Techniques and Validation

A number of computational electromagnetics (CEM) techniques have been developed, and numerical codes have been generated to analyze various electromagnetics problems since the mid-1960s. While each is based on classical electromagnetic theory, and implements Maxwell’s equations in one form or another, these techniques, and the manner in which they are used to analyze a given problem, can produce quite different results. The results are affected by the way in which the underlying physic formalisms have been implemented within the codes, including the mathematical basis functions, numerical solution methods, numerical precision, and the use of building blocks (primitives) to generate computational models.

Despite all CEM codes having their basis in Maxwell’s equations of one form or another, their accuracy and convergence rate depends on how the physics equations are cast (e.g., integral or differential form, frequency or time domain), what numerical solver approach is used, inherent modeling limitations, approximations, and so forth. Although these techniques and codes have been applied to a myriad of electromagnetic problems, uncertainty still exists, and current validation practices have not always proved to be reliable. Computer predictions have been compared to measurements to provide a first-order validation, but there is also much interest in how the techniques, when applied to a given problem or a class of problems, compare to each other and the fundamental theory upon which they are based. Hence, additional efforts are needed

to establish a standardized method for validating these techniques and to instill confidence in them [6, 7].

The physics formalism, available modeling primitives, analysis frequency, and time or mesh discretization further affect accuracy, solution convergence, and overall validity of the computer model. The critical areas that must be addressed include model accuracy, convergence, and techniques or code validity for a given set of canonical, standard validation, and benchmark models. For instance, uncertainties may arise when the predicted results using one type of CEM technique do not agree favorably or consistently with the results of other techniques or codes of comparable type, or even against measured data on benchmark models.

Furthermore, it can be difficult to compare the results between certain techniques or codes, despite their common basis in Maxwell’s equations. Exceptions can be cited, in particular, when comparing the results of “similar” codes grouped according to their physics, solution methods, and modeling element domains. Nevertheless, disparities among codes in a certain “class” have been observed. Many examples can be cited where fairly significant deviations have been observed between analytical or computational techniques and empirical-based methods. Differences are not unexpected, but the degree of disparity in certain cases cannot be readily explained, nor easily discounted, which has led to the often asked-question, *“Which result is accurate*?” [6, 7]