Polynomial chaos for multirate partial differential algebraic equations with random parameters

In radio frequency applications, a multivariate model yields an efficient representation of signals with amplitude modulation and/or frequency modulation. Periodic boundary value problems of multirate partial differential algebraic equations (MPDAEs) have to be solved to reproduce the quasiperiodic signals. Typically, technical parameters appear in the system, which may exhibit some uncertainty. Substitution by random variables results in a corresponding stochastic model. We apply the technique of the generalised polynomial chaos to obtain according solutions. A Galerkin approach yields larger coupled systems of MPDAEs. We analyse the properties of the coupled systems with respect to the original formulations. Thereby, we focus on the case of frequency modulation, since the case of amplitude modulation alone is straightforward.