In this talk, I will 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.

王官杰，上海立信会计金融学院讲师。2015年6月毕业于浙江大学数学系，获理学博士学位，2015年7月至2018年3月在中国科学院微系统与信息技术研究所从事博士后研究工作，2018年4月至2020年2月在上海科技大学任助理研究员。他的主要研究方向为微分方程数值解及不确定性量化，目前已发表相关论文多篇。