We present a reduced basis stochastic Galerkin method for partial differential equations with random inputs. In this method, the reduced basis methodology is integrated into the stochastic Galerkin method, such that the cost of solvers for the Galerkin system is significantly reduced. To reduce the main cost of matrix-vector manipulation involved in our reduced basis stochastic Galerkin approach, the secant method is applied to identify the number of reduced basis functions. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

翻译：我们为带有随机投入的局部差异方程式提出了一种减少基质吸附Galerkin法,在这种方法中,将减少基数方法纳入Stochatic Galerkin法,从而大幅度降低Galerkin系统溶解器的费用,为了降低我们减少基数吸附Galerkin法所涉矩阵矢量操纵的主要费用,采用分离方法确定减少基数功能的数量。我们提出了方法的一般数学框架,验证其准确性,并以数字实验来证明其效率。