In this paper, an adaptive hierarchical sparse grid collocation (ASGC) method combined with the discontinuous Galerkin time-domain method is leveraged to quantify the impacts of random parameters on the electromagnetics systems. The ASGC method approximates the stochastic observables of interest using interpolation functions over a set of collocation points determined by the Smolyak's algorithm integrated with an adaptive strategy. Instead of resorting to a full-tensor product sense, the Smolyak's algorithm constructs the collocation points in a hierarchical scheme with the interpolation level. Enhanced by an adaptive strategy, the Smolyak's algorithm will sample more points along important dimensions with sharp variations or discontinuities, resulting in a nonuniform sampling scheme. To flexibly handle different stochastic systems, either piecewise linear or Lagrange polynomial basis functions are applied. With these strategies, the number of collocation points is significantly reduced. The statistical knowledge of stochastic observables including the expected value, variance, probability density function, and cumulative distribution function are presented. The accuracy and robustness of the algorithm are demonstrated by various examples.


Electrical and Computer Engineering

Keywords and Phrases

Adaptive hierarchical sparse grid collocation (ASGC) method; DGTD-boundary integral (DGTD-BI) method; discontinuous Galerkin time domain (DGTD) method; modified nodal analysis (MNA); Smolyak's algorithm; statistical knowledge; uncertainty quantification

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Article - Journal

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Publication Date

01 Aug 2015