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a r t i c l e i n f o a b s t r a c t We develop a multi-element probabilistic collocation method (ME-PCM) for arbitrary discrete probability measures with finite moments and apply it to solve partial differential equations with random parameters. The method is based on numerical construction of orthogonal polynomial bases in terms of a discrete probability… (More)

- Mengdi Zheng, Boris Rozovsky, George E. Karniadakis
- SIAM J. Scientific Computing
- 2015

We propose an adaptive Wick–Malliavin (WM) expansion in terms of the Malli-avin derivative of order Q to simplify the propagator of general polynomial chaos (gPC) of order P (a system of deterministic equations for the coefficients of gPC) and to control the error growth with respect to time. Specifically, we demonstrate the effectiveness of the WM method… (More)

- Mengdi Zheng, George E. Karniadakis
- SIAM J. Scientific Computing
- 2015

We develop new probabilistic and deterministic approaches for moment statistics of stochastic partial differential equations with pure jump tempered α-stable (TαS) Lévy processes. With the compound Poisson (CP) approximation or the series representation of the TαS process, we simulate the moment statistics of stochastic reaction-diffusion equations with… (More)

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