Ingredients for a general purpose stochastic finite elements implementation

Abstract

The Stochastic Finite Element Method has seen a number of incarnations over the past few years, ranging from perturbation-based methods, and Neumann-expansion based methods, to methods for evaluating bounds on the response variability, and more recent functional expansions combined with error minimization techniques. Of these, only the last class of methods provides an explicit expression to the solution of the problem, as opposed to evaluating a global norm of this solution, and can thus be viewed as a rational extension of concepts developed for the deterministic finite element method. The main obstacle in developing a substantial user-community of various stochastic finite element methods has been the lack of a general purpose formalism for addressing issues of general engineering interest. This paper presents the main ingredients for developing a general purpose version of the Spectral Stochastic Finite Element Method.