Macro-Modeling of Electromagnetic Domains Exhibiting Geometric and Material Uncertainty

A methodology is presented for the development of stochastic electromagnetic macro-models for domains exhibiting geometric and material uncertainty. Focusing on the case of domains exhibiting geometric/material invariance along one of the axes of the reference coordinate system, the methodology makes use of the theory of polynomial chaos expansion and the concept of a global impedance/admittance matrix relationship defined over a circular surface enclosing the cross-sectional geometry of the domain of interest. The result is a stochastic global impedance/admittance matrix, defined on the enclosing circular surface, whose elements are truncated polynomial chaos expansions over the random space defined by the independent random variables that parameterize the geometric and material uncertainty inside the domain. Use is made of sparse Smolyak grids to reduce the computational cost of constructing the stochastic macro-model. Numerical examples are used to demonstrate some of the attributes of the proposed stochastic macro-models to the numerical solution of electromagnetic scattering problems by an ensemble of cylindrical targets exhibiting uncertainty in their shape and relative positioning.