A method to estimate the accuracy of numerical models

Determining the accuracy of the results produced by a numerical model remains an ongoing and important problem in computational electromagnetics (CEM) to which perhaps the most desirable and convincing approach is to perform a quantitative comparison between experimental data and the model output. Such a comparison has the disadvantage that it embodies two different kinds of errors, these being the physical modeling error (PME) and the numerical modeling error (NME). Although the PME can normally be expected to be the larger of the two and also the more difficult to evaluate, quantitative knowledge of the NME itself is essential, estimation of which is the topic of this paper. Two approaches are available to estimate the NME, one being internal checks that can be done within a specific model or code (e.g. convergence tests, boundary conditions, power conservation, etc.), and the other the external checks that involve comparing the results of two or more different models. The approach discussed here is another kind of internal check, involving Maxwell's equations, but different from the others in the sense that it seeks a "noise" level in the model output as a measure of the model accuracy.