发布时间：2025-09-09
Polynomial chaos expansions for stiff random ODEs
主讲人：史文杰
摘要：In this talk, we investigate the impact of stiffness of random ODEs on the gPC performance. We start by extending pragmatic definitions of stiffness used in deterministic ODEs to their random counterparts. Then, we introduce gPC with parallel MIRK schemes to solve random stiff ODEs, in which a suitable parallelism partially alleviates the curse of dimensionality. Our stiffness analysis comprises two parts: (i) the relationship between Jacobians of random ODEs and the corresponding gPC equations and (ii) stiffness of the gPC equations. It provides a direct way to determine whether a random ODE and/or the corresponding gPC equations are stiff. This theoretical analysis plays a key role in designing numerical implementations not only of gPC but also of other methods of stochastic computation, e.g., Monte Carlo simulations and stochastic collocation. A series of computational experiments is used to demonstrate the agreement between our theoretical analysis and numerical results and to establish gPC with parallel MIRK as a feasible and effective tool for solving stiff random ODEs.
主讲人简介：史文杰，武汉纺织大学数学与统计学院副教授。2014年6月毕业于华中科技大学，获理学博士学位。2012年7月至2013年10月为美国加州大学圣地亚哥分校联合培养博士研究生。已主持国家自然科学基金青年基金项目1项，并参与国家自然科学基金面上项目多项。主要从事随机微分方程数值解的研究工作。以第一作者或通讯作者在SIAM J. Sci. Comput.、Appl. Numer. Math.等国际重要期刊发表多篇SCI收录论文
邀请人：张诚坚
时间： 2025年9月12日16:00-18:00
地点： 科技楼南楼811室