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

doi:10.1137/18M1176749

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	PARAREAL EXPONENTIAL theta-SCHEME FOR LONGTIME SIMULATION OF STOCHASTIC SCHRODINGER EQUATIONS WITH WEAK DAMPING
	Hong, Jialin 1,2; Wang, Xu 1,2; Zhang, Liying 3
	2019
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	41 期号:6 页码:B1155-B1177
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.
关键词	stochastic Schrodinger equation parareal algorithm exponential theta-scheme invariant measure
DOI	10.1137/18M1176749
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000549131500002
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/51802
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.China Univ Min & Technol, Dept Math, Coll Sci, Beijing 100083, 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.