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This paper aims to introduce an efficient time-domain formulation of adjustable accuracy for a consistent and trustworthy computation of electromagnetic field characteristics in randomly varying configurations. The developed methodology is carefully certified via comprehensive comparisons with the corresponding outcomes obtained by the Monte Carlo approach.

The presented methodology uses higher-order approximations of Taylor series expansions of stochastic multivariable functions for the rapid estimation of the electromagnetic field component mean value and confidence intervals of their variance. Toward this objective, new time-update equations for the mean value and the variance of the involved electromagnetic field are elaborately derived.

The featured technique presents an efficient alternative to the excessively resource-consuming Monte Carlo finite-difference time-domain (MC–FDTD) implementation, which requires an unduly number of realizations to achieve a satisfying convergence. The higher-order stochastic algorithm retrieves accurately the statistical properties of all electromagnetic field in a single simulation, presenting promising accuracy, stability and convergence.

The adjustable-accuracy higher-order scheme introduces a new framework for the derivation of the stochastic explicit time-update equations and precisely computes the required confidence intervals for the electromagnetic field variance instead of the variance itself, which can be deemed a key advantage over existing schemes. This fully controllable formulation results in significantly more accurate calculations of the electromagnetic field variance, especially for larger fluctuations of the involved electromagnetic media parameters.

The purpose of this paper is to introduce a novel methodology for uncertainty quantification in large-scale systems. It is a non-intrusive approach based on the unscented transform (UT) but it requires far less simulations from a EM solver for certain models.

The methodology of uncertainty propagation is carried out adaptively instead of considering all input variables. First, a ranking of input variables is determined and after a classical UT is applied successively considering each time one more input variable. The convergence is reached once the most important variables were considered.

The adaptive UT can be an efficient alternative of uncertainty propagation for large dimensional systems.

The classical UT is unfeasible for large-scale systems. This paper presents one new possibility to use this stochastic collocation method for systems with large number of input dimensions.