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Articles Published in Physica D

  1. Ghanem, R.G. and Red-Horse, J.R. "Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach" Physica D. 133 (1-4). 1999. pp. 137--144.

    This paper presents an efficient procedure for characterizing the solution of evolution equations with stochastic coefficients. These typically model the behavior of physical systems whose properties are modeled as spatially or temporally varying stochastic processes described within the framework of probability theory. The concepts of projection, orthogonality and weak convergence are exploited in a manner which directly mimics deterministic finite element solutions except that, in the stochastic case, inner products refer to expectation operations. Specifically, the Karhunen–Loève expansion is used to discretize these processes into a denumerable set of random variables, thus providing a denumerable function space in which the problem is cast. The polynomial chaos expansion is then used to represent the solution in this space, and the coefficients in the expansion are evaluated as generalized Fourier coefficients via a Galerkin procedure in the Hilbert space of random variables.