Abstract
In this paper, an h-adaptive SC-gPC method suited for characterizing rapidly varying and/or discontinuous observables is presented. The proposed extension achieves its efficiency by recursively and adaptively dividing the random domain into sub-domains based on the decay rates of observables' local variances, and constructing separate gPC expansions for each sub-domain. The adaptive SC-gPC method enables the stochastic characterization of electronic systems that involve high-Q resonators and highly non-linear components with discontinuous responses (e.g., rectifier circuits). Due to these systems' high sensitivity to perturbations in excitation or geometry, their stochastic characterization would be impossible using "classical" SC methods without the proposed h-adaptive extension.