Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics

To account for uncertainties on model parameters, the stochastic approach can be used. The model parameters as well as the outputs are then random fields or variables. Several methods are available in the literature to solve stochastic models like sampling methods, perturbation methods or approximation methods. In this paper, we propose an overview on the solution of stochastic problems in computational electromagnetics using approximation methods. Some applications will be presented in order to illustrate the possibilities offered by the approximation methods but also their current limitations due to the curse of dimensionality. Finally, recent numerical techniques proposed in the literature to face the curse of dimensionality are presented for non-intrusive and intrusive approaches.This work has been supported by the pole MEDEE funded by the Nord Pas de Calais Region and the European Union and also by the Arts et M´etiers Fundation