Assessment of Adaptive Sparse Grid Collocation Methods in Wave Propagation Environments With Uncertainty

Sparse grid collocation methods are used for uncertainty quantification in electromagnetic propagation problems. The first application here involves waves propagating in lossy media with uncertain permittivities and permeabilities, for which several cases with increasing random-space dimensionality are exemplified. The objective in the second application is to compute expected signal strength above flat Earth surface at ranges far from transmitter location, where randomness is present due to uncertain refractivity of the atmosphere. Two different sparse grid algorithms are demonstrated throughout the paper, and the deterministic evaluators are accessed as a black box by the sparse grid algorithms. The difficult task of a priori method adaption is overcome by a first order check that enforces the black box solver only a few times. Through the results considered, strengths of the two algorithms are differentiated depending on the characteristics of the randomness. The advantage of a new routine used in this work is emphasized by showing its numerical contribution to the field estimation problem in a specific example. By means of the sparse grid methods used, we quantitatively provide the relative importance of each RV in contributing to the changes in the field distribution received at the observation range.