Reduced-order models of finite element approximations of electromagnetic devices exhibiting statistical variability

A methodology is proposed for the development of reduced-order models of finite element approximations of electromagnetic devices exhibiting uncertainty or statistical variability in their input parameters. In this approach, the reduced order system matrices are represented in terms of their orthogonal polynomial chaos expansions on the probability space defined by the input random variables. The coefficients of these polynomials, which are matrices, are obtained through the repeated, deterministic model order reduction of finite element models generated for specific values of the input random parameters. These values are chosen efficiently in a multi-dimensional grid using a Smolyak algorithm. The generated stochastic reduced order model is represented in the form of an augmented system that lends itself to the direct generation of the desired statistics of the device response. The accuracy and efficiency of the proposed method is demonstrated through its application to the reduced-order finite element modeling of a terminated coaxial cable and a circular wire loop antenna.