Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Uncertainty propagation using Wiener-Haar expansions
Journal of Computational Physics
Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
SIAM Journal on Scientific Computing
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Uncertainty analysis for the steady-state flows in a dual throat nozzle
Journal of Computational Physics
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Computational Modeling of Uncertainty in Time-Domain Electromagnetics
SIAM Journal on Scientific Computing
A stochastic variational multiscale method for diffusion in heterogeneous random media
Journal of Computational Physics
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We investigate the evolution of the probability distribution function in time for some wave and Maxwell equations in random media for which the parameters, e.g. permeability, permittivity, fluctuate randomly in space; more precisely, two different media interface randomly in space. We numerically compute the probability distribution and density for output solutions. The underlying numerical and statistical techniques are the so-called polynomial chaos Galerkin projection, which has been extensively used for simulating partial differential equations with uncertainties, and the Monte Carlo simulations.