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PARAREAL EXPONENTIAL theta-SCHEME FOR LONGTIME SIMULATION OF STOCHASTIC SCHRODINGER EQUATIONS WITH WEAK DAMPING

文献类型：期刊论文

作者Hong, Jialin1,3; Wang, Xu1,3; Zhang, Liying2
刊名SIAM JOURNAL ON SCIENTIFIC COMPUTING
出版日期2019
卷号41期号:6页码:B1155-B1177
关键词stochastic Schrodinger equation parareal algorithm exponential theta-scheme invariant measure
ISSN号1064-8275
DOI10.1137/18M1176749
英文摘要A parareal algorithm based on an exponential theta-scheme is proposed for the stochastic Schrodinger equation with weak damping and additive noise. It proceeds as a two-level temporal parallelizable integrator with the exponential theta-scheme as the integrator on the coarse grid. The proposed algorithm in the linear case increases the convergence order from one to k for theta is an element of [0, 1] \ {1/2}. In particular, the convergence order increases to 2k when theta = 1/2 due to the symmetry of the algorithm. The convergence condition for longtime simulation is also established for the proposed algorithm in the nonlinear case, which indicates the superiority of implicit schemes. Numerical experiments are dedicated to illustrating the convergence order of the algorithm for different choices of theta, as well as the error for different iterated number k.
资助项目National Natural Science Foundation of China[11601514] ; National Natural Science Foundation of China[11801556] ; National Natural Science Foundation of China[11771444] ; National Natural Science Foundation of China[11971458]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000549131500002
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/51801]  
专题中国科学院数学与系统科学研究院
通讯作者Hong, Jialin
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
2.China Univ Min & Technol, Dept Math, Coll Sci, Beijing 100083, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式
GB/T 7714		 Hong, Jialin,Wang, Xu,Zhang, Liying. PARAREAL EXPONENTIAL theta-SCHEME FOR LONGTIME SIMULATION OF STOCHASTIC SCHRODINGER EQUATIONS WITH WEAK DAMPING[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2019,41(6):B1155-B1177.
APA Hong, Jialin,Wang, Xu,&Zhang, Liying.(2019).PARAREAL EXPONENTIAL theta-SCHEME FOR LONGTIME SIMULATION OF STOCHASTIC SCHRODINGER EQUATIONS WITH WEAK DAMPING.SIAM JOURNAL ON SCIENTIFIC COMPUTING,41(6),B1155-B1177.
MLA Hong, Jialin,et al."PARAREAL EXPONENTIAL theta-SCHEME FOR LONGTIME SIMULATION OF STOCHASTIC SCHRODINGER EQUATIONS WITH WEAK DAMPING".SIAM JOURNAL ON SCIENTIFIC COMPUTING 41.6(2019):B1155-B1177.

入库方式： OAI收割

来源：数学与系统科学研究院

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