Eduard Frick, David Dahl, Katharina Klioba, Christian Seifert, Marko Lindner, Christian Schuster
Quantitative Error Bounds of Polynomial Chaos Expansion and their Application to Resonant Systems
Type : PREPRINT
Language : ENGLISH
Format : application/pdf
Upload : 02/21/2019
Abstract:
The polynomial chaos expansion (PCE) has become a method of significant research interest for uncertainty quantification in the context of electrical and electromagnetic systems. This is due to several advantages including the fast convergencerate of PCE that is observed for many applications. In resonantsystems however the PCE convergence slows down significantly for frequencies in the vicinity of the resonances. This problem is well known but a quantitative analysis that would allow for aprediction of the PCE convergence speed has not been presented yet. This paper introduces quantitative upper bounds for the PCE approximation error resulting from a general application with a single random uniformly or Gaussian distributed input parameter. Many resonant systems can be locally approximated by a RLC parallel circuit. In some of these systems the upperbounds can be used for the estimation of the polynomial degree that is required for the reduction of the PCE error below a prescribed precision. This is demonstrated on the contour integral method (CIM) where a non-intrusive PCE is used for modeling the absolute value of a stochastic crosstalk impedance in a via array.
Keywords:
polynomial chaos expansion, resonant systems, parallel circuit, contour integral method, convergence, error bounds