Abstract 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.

中文翻译：

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使用 B 样条的任意随机输入的多项式混沌方法

摘要 等几何分析通过使用 B 样条扩展了有限元方法，已在工程分析和设计程序中得到广泛应用。在本文中，这个概念是在应用于计算随机力学的多项式混沌方法的上下文中考虑的。在这方面，注意到在多个应用中使用的许多随机过程可以通过截断相关的级数展开来由混沌表示近似。通常，这些级数的基是正交 Hermite 多项式，由 B 样条基函数代替。此外，B 样条混沌的收敛性被提出并由数值结果证实。此外，还指出，