Open AccessIntrusive polynomial‐chaos approach for stochastic problems with axial symmetry
Author(s) -
Zygiridis Theodoros,
Papadopoulos Aristeides,
Kantartzis Nikolaos,
Antonopoulos Christos,
Glytsis Elias N.,
Tsiboukis Theodoros D.
Publication year - 2019
Publication title -
iet microwaves, antennas and propagation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.555
H-Index - 69
eISSN - 1751-8733
pISSN - 1751-8725
DOI - 10.1049/iet-map.2018.5306
Subject(s) - polynomial chaos , axial symmetry , finite difference time domain method , monte carlo method , context (archaeology) , symmetry (geometry) , mathematics , polynomial , uncertainty quantification , computational complexity theory , algorithm , computer science , stochastic process , mathematical analysis , geometry , physics , optics , paleontology , statistics , machine learning , biology
We present and validate a computational approach that enables the quantification of time‐dependent uncertainty in axially symmetric electromagnetic (EM) problems, in the context of a unique simulation. In essence, the finite‐difference time‐domain (FDTD) method, adapted to model bodies of revolution (BOR), is combined with truncated polynomial‐chaos (PC) expansions of the involved field components, so that the stochastic nature of the latter is modelled reliably, when media with random electric properties need to be considered. The developed approach features two distinct advantages: First, by exploiting the azimuthal periodicity of the investigated problems' geometry, the high computational burden of three‐dimensional (3D) simulations is reduced. Second, the large number of simulations that are normally required by Monte–Carlo (MC) methodologies for the extraction of statistical features is avoided, thanks to the integrated PC approximations. A number of numerical tests are conducted, in order to verify the validity and performance of the suggested stochastic algorithm.