多物理耦合非线性偏微分方程与数值解不确定度量化数学方法  

Mathematical methods for uncertainty quantification in nonlinear multi-physics systems and their numerical simulations

作　　者：王瑞利[1] 江松[1] 

机构地区：[1]北京应用物理与计算数学研究所,北京100094

出　　处：《中国科学：数学》2015年第6期723-738,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11372051和11201035);中国工程物理研究院科学基金(批准号:2011B0202043)资助项目

摘　　要：多物理耦合的非线性偏微分方程和数值解在众多实际工程领域扮演重要角色,对其不确定度量化的数学方法已成为具有挑战性的难题.本文结合爆轰流体力学多物理耦合的非线性偏微分方程和数值求解,介绍多物理耦合数学建模与模拟中的不确定性及复杂工程建模与模拟不确定度量化常用数学方法的优缺点,提出未来多物理耦合数学建模与模拟中不确定度量化所面临的一些未解决的重要问题及困难.Nonlinear multi-physics systems and their numerical simulations play an important role in many practical engineering fields, and the development of reliable mathematical methods for uncertainty quantification of such multi-physics systems is still facing great challenges. In this paper, taking the multi-physics models from detonation mechanics and their numerical solution, we briefly introduce recently developed mathematical meth- ods for uncertainty quantification in both complex multi-physics engineering modeling and associated numerical simulation. Also, the strengths and weaknesses of the methods will be discussed, and open problems as well as mathematical challenges will be underlined.

关 键 词：多物理耦合 非线性 偏微分方程 数值解 不确定度量化 数学方法 

分 类 号：O241.82[理学—计算数学]