Application of the generalized multiscale finite element method in an inverse random source problem

作     者：Fu, Shubin Zhang, Zhidong 

作者机构：Univ Wisconsin Madison Dept Math Madison WI 53706 USA Sun Yat Sen Univ Sch Math Zhuhai Zhuhai 519082 Guangdong Peoples R China 

出 版 物：《JOURNAL OF COMPUTATIONAL PHYSICS》 (计算物理学杂志)

年 卷 期：2021年第429卷

页      面：110032-110032页

核心收录：

学科分类：07[理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：Academy of Finland [284715, 312110] Atmospheric Mathematics Project of University of Helsinki Academy of Finland (AKA) Funding Source: Academy of Finland (AKA) 

主　　题：Inverse problem Fractional diffusion equation Random source Generalized multiscale finite element method Heterogeneous medium Regularized iterative algorithm 

摘      要：In this work, an inverse random source problem in the fractional diffusion equation with heterogeneous medium is considered. The measurements used are the statistical moments of the realizations of the single point data u(x(0), t, omega). We build the representation of the solution u in integral sense, then prove that the unknowns can be bounded by the moments theoretically. For the numerical reconstruction, to handle the highly heterogeneous medium, the generalized multiscale finite element method (GMsFEM) will be employed in the forward problem solver. With the simulated data, we establish an iterative algorithm of regularized Levenberg-Marquardt type, and some numerical results generated from this algorithm are displayed. (C) 2020 Elsevier Inc. All rights reserved.