AN EFFICIENT MULTIMODES MONTE CARLO HOMOGENIZATION METHOD FOR RANDOM MATERIALS

doi:10.1137/21M1454237

CSpace

	AN EFFICIENT MULTIMODES MONTE CARLO HOMOGENIZATION METHOD FOR RANDOM MATERIALS
	Yang, Zihao 1; Huang, Jizu 2; Feng, Xiaobing 3; Guan, Xiaofei 4
	2022
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	44 期号:3 页码:A1752-A1774
摘要	In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure. In the first stage, the original oscillatory diffusion equation is approximated, for each fixed random sample omega, by a spatially homogenized diffusion equation with piecewise constant coefficients, resulting in a random diffusion equation. In the second stage, the resulting random diffusion equation is approximated and computed by using an efficient multimodes Monte Carlo method which only requires solving a diffusion equation with a constant diffusion coefficient and a random right-hand side. The main advantage of the proposed method is that it separates the computational difficulty caused by the spatial fast oscillation of the solution and caused by the randomness of the solution, so they can be overcome separately using different strategies. The convergence of the solution of the spatially homogenized equation (from the first stage) to the solution of the original random diffusion equation is established, and the optimal rate of convergence is also obtained for the proposed multimodes Monte Carlo method. Numerical experiments on some benchmark test problems for random composite materials are also presented to gauge the efficiency and accuracy of the proposed two-stage stochastic homogenization method.
关键词	stochastic homogenization multimodes Monte Carlo method finite element method convergence and error estimates random composite materials
DOI	10.1137/21M1454237
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11871069] ; National Natural Science Foundation of China[12131002] ; Strategic Priority Research Program of the Chinese Academy of Sciences[XDC06030101] ; National Key R&D Program of China[2020YFA0713603] ; Natural Science Foundation of Shanghai[21ZR1465800] ; NSF[DMS2012414]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000862824700016
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60893
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Jizu
作者单位	1.Northwestern Polytech Univ, Sch Math & Stat, Xian 710072, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 3.Univ Tennessee, Dept Math, Knoxville, TN 37996 USA 4.Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China
推荐引用方式 GB/T 7714	Yang, Zihao,Huang, Jizu,Feng, Xiaobing,et al. AN EFFICIENT MULTIMODES MONTE CARLO HOMOGENIZATION METHOD FOR RANDOM MATERIALS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2022,44(3):A1752-A1774.
APA	Yang, Zihao,Huang, Jizu,Feng, Xiaobing,&Guan, Xiaofei.(2022).AN EFFICIENT MULTIMODES MONTE CARLO HOMOGENIZATION METHOD FOR RANDOM MATERIALS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,44(3),A1752-A1774.
MLA	Yang, Zihao,et al."AN EFFICIENT MULTIMODES MONTE CARLO HOMOGENIZATION METHOD FOR RANDOM MATERIALS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 44.3(2022):A1752-A1774.