On the Various Applications of Stochastic Collocation in Computational Electromagnetics

The application of deterministic-stochastic models in some areas of computational electromagnetics is presented. Namely, in certain problems there is an uncertainty in the input data set as some system properties are partly or entirely unknown. Thus, a simple stochastic collocation (SC) method is used to determine the relevant statistics about the given responses. The SC approach also provides the assessment of the related confidence intervals in the set of calculated numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via SC method, is shown to be robust and efficient approach providing a satisfactory convergence rate. The presented stochastic framework provides means for sensitivity analysis enabling a better insight into the relationship between the input parameters and the output of interest. This chapter provides certain computational examples from the previous work by the authors illustrating successful application of SC technique in the areas of: human exposure to electromagnetic fields, transcranial magnetic stimulation (TMS), transient analysis of buried wires and design of instrumental landing system (ILS).