Spectral stochastic finite element method for periodic structure

In this paper we formulate the finite element matrix equations using spectral stochastic methods for plane wave scattering by a periodic structures with uncertain parameters. The input random variable is discretized by Karhunen-Loève expansion method and output random solution is expanded using polynomial chaos method. Stochastic Galerkin method is employed to get least squares solution. We present the method of coupling the plane wave scattering problem with SSFEM and illustrate with a numerical example.