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Articles written by Jardak, M.

  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. Jardak, M. and Ghanem, R.G.. "Spectral stochastic homogenization of divergence-type PDEs" Computer Methods in Applied Mechanics and Engineering. 193 (6--8). 2004. pp. 429-447.

    This paper presents a formulation and numerical analysis of the homogenization of stochastic PDEs. The framework of homogenization is adopted to describe an effective medium that is equivalent in some sense to a heterogeneous medium of interest. The parameters of the resulting homogeneous medium are described as stochastic processes characterized by their polynomial chaos decomposition. The formulation yields a chaos decomposition for the predicted behavior of the homogeneous medium that captures, in addition to the effect of heterogeneity, the effect of variability. Once this description has been computed, various statistics of the solution can be efficiently evaluated. (C) 2003 Elsevier B.V. All rights reserved.