报告主题：An alternating low-rank projection approach for partial differential equations with random inputs

时间：2026年3月12日12:30-13:15

地点：腾讯会议 会议号：875-6589-8473

报告人：王官杰

报告内容简介：

It is known that standard stochastic Galerkin methods face challenges when solving partial differential equations (PDEs) with random inputs. These challenges are typically attributed to the large number of required physical basis functions and stochastic basis functions. Therefore, it becomes crucial to select effective basis functions to properly reduce the dimensionality of both the physical and stochastic approximation spaces. In this study, our focus is on the stochastic Galerkin approximation associated with generalized polynomial chaos (gPC). We delve into the low-rank approximation of the quasimatrix, whose columns represent the coefficients in the gPC expansions of the solution. We conduct an investigation into the singular value decomposition (SVD) of this quasimatrix, proposing a strategy to identify the rank required for a desired accuracy. Subsequently, we introduce both a simultaneous low-rank projection approach and an alternating low-rank projection approach to compute the low-rank approximation of the solution for PDEs with random inputs. Numerical results demonstrate the efficiency of our proposed methods for both diffusion and Helmholtz problems.

主讲人简介：

王官杰，上海立信会计金融学院教师。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2020年2月在上海科技大学先后任博士后、任助理研究员，2020年3月至今在上海立信会计金融学院任教师。他的主要研究方向为微分方程数值解及不确定性量化，目前已在Journal of Computational Physics（JCP）、Journal of Scientific Computing（JSC）和International Journal for Uncertainty Quantification（IJ4UQ）等重要期刊上发表相关论文十余篇。