Uncertainty quantification of EM-circuit systems using stochastic polynomial chaos method

Uncertainties in realistic lumped and distributive circuit systems are of great importance to today´s high yield manufacture demand. However, evaluating the stochastic effect in the time domain for the hybrid electromagnetics (EM)-circuit system was seldom done, especially when Monte Carlo is too expensive to be feasible. In this work, an adaptive hierarchical sparse grid collocation (ASGC) method is presented to quantify the impacts of stochastic inputs on hybrid electromagnetics (EM)-circuit or EM scattering systems. The ASGC method approximates the stochastic observables of interest using interpolation functions over series collocation points. Instead of employing a full-tensor product sense, the collocation points in ASGC method are hierarchically marched with interpolation depth based upon Smolyaks construction algorithm. To further reduce the collocation points, an adaptive scheme is employed by using hierarchical surplus of each collocation point as the error indicator. With the proposed method, the number of collocation points is significantly deduced. To verify the effectiveness and robustness of the proposed stochastic solver, hybrid EM-circuit systems are quantified by a full-wave EM-circuit simulator based upon discontinuous Galerkin time domain (DGTD) method and modified nodal analysis (MNA). The time domain influences of uncertainty inputs such as geometrical information and electrical material properties are thereby benchmarked and demonstrated through this paper.