The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
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We introduce a fast method for the stochastic analysis of systems with continuous stochastic parameters. This involves non-intrusive Polynomial Chaos, a concept related to generalized Polynomial Chaos. A single polynomial basis corresponding to a probability distribution is used, where the support of its probability density function allows the application of simple quadrature rules for the calculation of Polynomial Chaos expansion coefficients. Through these steps, we obtain a method which allows the use of Polynomial Chaos with black boxes. In this way, Polynomial Chaos is made significantly more attractive, since the new method will neither require deep understanding of its mathematical foundation, nor the usual adjustments of the polynomial basis for every problem, but allows users to run fast simulations with a Polynomial Chaos approach, for the stochastic analysis of systems. As well as a mathematically detailed explanation and an application example with a single-phase rectifier, we will describe advantages and challenges of this method.