Stochastic PEEC Method Based on Polynomial Chaos Expansion

The new stochastic partial element equivalent circuit (PEEC) method is proposed for uncertainty quantification in electromagnetic problems when material parameters are considered as random variables. The proposed formulation is derived using polynomial chaos expansion (PCE) and Galerkin projection. For the first time, the well-known advantages of PEEC are combined with those of PCE techniques, which can tackle also large variations in the random parameters. Volume conductive media are first considered in the formulation, which is then extended to dielectric, magnetic, and surface conductive media.