Modeling of Stochastic EMC Problems with Anisotropic Polynomial Chaos Expansions

As the requirements characterizing simulation studies of realistic configurations constantly become more demanding, it is not uncommon that several contemporary electromagnetic problems need to be investigated within a stochastic, rather than a fully deterministic, framework. In this paper, we revise the basic aspects of Polynomial Chaos (PC) methodologies, which currently play a prominent role in the research field of uncertainty quantification. PC techniques enable the representation of the quantities-of-interest (Qol) via polynomial expansions, which facilitate the computation of all the pertinent necessary information, including statistical moments, distributions, and sensitivity indices. As the construction of approximate models with optimal efficiency is always desirable (so that a given level of accuracy is ensured with minimum computational effort), we also pay attention to the development of anisotropic PC.