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

doi:10.1137/18M1176749

	PARAREAL EXPONENTIAL theta-SCHEME FOR LONGTIME SIMULATION OF STOCHASTIC SCHRODINGER EQUATIONS WITH WEAK DAMPING
	Hong, Jialin 2,3; Wang, Xu 2,3; Zhang, Liying 1
刊名	SIAM JOURNAL ON SCIENTIFIC COMPUTING
	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
DOI	10.1137/18M1176749
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
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000549131500002
内容类型	期刊论文
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.China Univ Min & Technol, Dept Math, Coll Sci, Beijing 100083, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, 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.