A polynomial chaos method for arbitrary random inputs using B-splines

Isogeometric analysis which extends the finite element method through the usage of B-splines has become well established in engineering analysis and design procedures. In this paper, this concept is considered in context with the methodology of polynomial chaos as applied to computational stochastic mechanics. In this regard it is noted that many random processes used in several applications can be approximated by the chaos representation by truncating the associated series expansion. Ordinarily, the basis of these series are orthogonal Hermite polynomials which are replaced by B-spline basis functions. Further, the convergence of the B-spline chaos is presented and substantiated by numerical results. Furthermore, it is pointed out, that the B-spline expansion is a generalization of the Legendre multi-element generalized polynomial chaos expansion, which is proven by solving several stochastic differential equations.