An Adaptive Sparse Anisotropic Polynomial-Chaos Expansion Algorithm Applied to EMC Problems

Various popular methods for Uncertainty Quantification (UQ) rely on the computation of Polynomial-Chaos (PC) expansions, which represent stochastic processes via convergent polynomial series. The computational cost for determining the expansion coefficients in such methods is related to the number of input variables, and is significantly enlarged in high-dimensional problems. On the other hand, the PC coefficients of the basis functions can be considered, in many cases, to form a sparse vector. This property is exploited in this paper to build PC models that are accurate and computationally efficient, by implementing the Orthogonal Matching Pursuit (OMP) as the solver, which can deal with underdetermined linear systems, assuming that their solution is sparse. In order to enhance the computational efficiency even further, the presented PC method is applied adaptively for various PC model orders, and the best solution is chosen according to a leave-one-out criterion. Finally, an optimally-designed multilayer electromagnetic filter for EMC applications is examined, considering ten or twenty stochastic design variables.