Adaptive wavelet stochastic collocation for resonant transmission line circuits

An adaptive wavelet stochastic collocation method for uncertainty quantification is applied to a resonant circuit with stochastic parameters. The outputs of many electrical systems vary rapidly with respect to internal random parameters, for example due to resonance conditions. Accurate and efficient characterization of output statistics is key in designing systems with irregularities, but poses a challenge for conventional sampling-based stochastic collocation methods. The adaptive method in this paper constructs a hierarchical sparse grid approximation using wavelet basis functions. Since wavelet expansion coefficients are rigorous error estimators, wavelet sparse grids can potentially meet error tolerances with optimal efficiency and outperform local polynomial and other adaptive finite-element methods. The advantages and efficiency of this method is explored in the context of the circuit problem presented.