Abstract
The uncertainties in various Electromagnetic (EM) problems may present a significant effect on the properties of the involved field components, and thus, they must be taken into consideration. However, there are cases when a number of stochastic inputs may feature a low influence on the variability of the outputs of interest. Having this in mind, a dimensionality reduction of the Polynomial Chaos (PC) technique is performed, by firstly applying a sensitivity analysis method to the stochastic inputs of multi-dimensional random problems. Therefore, the computational cost of the PC method is reduced, making it more efficient, as only a trivial accuracy loss is observed. We demonstrate numerical results about EM wave propagation in two test cases and a patch antenna problem. Comparisons with the Monte Carlo and the standard PC techniques prove that satisfying outcomes can be extracted with the proposed dimensionality-reduction technique.
Highlights
Uncertainty quantification in the context of an Electromagnetic (EM) problem is of vital significance, as the calculation of the involved field quantities can be a challenging task
A sensitivity analysis algorithm has been implemented, in order to reduce the computational cost of the Polynomial Chaos (PC) scheme
The selection of the most important random variables in a given problem can be performed with the proposed heuristic, which is based on the Morris method
Summary
Uncertainty quantification in the context of an Electromagnetic (EM) problem is of vital significance, as the calculation of the involved field quantities can be a challenging task. Other problems involve the geometrical uncertainties introduced due to fabrication tolerances during the construction of printed circuit board antennas, which may have a significant impact on their performance [2]. Neglecting those random fluctuations can lead to unrealistic outcomes; deterministic schemes are not sufficient in such cases. For this reason, various techniques have been proposed that deal with uncertainty problems more efficiently. The most common method for assessing EM uncertainties is the Monte Carlo (MC) approach [3]
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