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Articles Published in Journal of Scientific Computing

  1. Jardak, M., Su, C.-H., and Karniadakis, G.E.. "Spectral Polynomial Chaos Solutions of the Stochastic Advection Equation" Journal of Scientific Computing. 17 (1-4). 2002. pp. 319--338.

    We present a new algorithm based on Wiener-Hermite functionals combined with Fourier collocation to solve the advection equation with stochastic transport velocity. We develop different stategies of representing the stochastic input, and demonstrate that this approach is orders of magnitude more efficient than Monte Carlo simulations for comparable accuracy.


  2. Wan, X. and Karniadakis, G.E.. "Beyond Wiener---Askey Expansions: Handling Arbitrary PDFs" Journal of Scientific Computing. 27 (1-3). 2006. pp. 455--464.

    In this paper we present a Multi-Element generalized Polynomial Chaos (ME-gPC) method to deal with stochastic inputs with arbitrary probability measures. Based on the decomposition of the random space of the stochastic inputs, we construct numerically a set of orthogonal polynomials with respect to a conditional probability density function (PDF) in each element and subsequently implement generalized Polynomial Chaos (gPC) locally. Numerical examples show that ME-gPC exhibits both p- and h-convergence for arbitrary probability measures.