Geometric integrators for multiple time-scale simulation

doi:10.1088/0305-4470/39/19/S04

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	Geometric integrators for multiple time-scale simulation
	Jia, ZD ; Leimkuhler, B
	2006-05-12
发表期刊	JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN	0305-4470
卷号	39 期号:19 页码:5379-5403
摘要	In this paper, we review and extend recent research on averaging integrators for multiple time-scale simulation such as are needed for physical N-body problems including molecular dynamics, materials modelling and celestial mechanics. A number of methods have been proposed for direct numerical integration of multiscale problems with special structure, such as the mollified impulse method (Garcia-Archilla, Sanz-Serna and Skeel 1999 SIAM J. Sci. Comput. 20 930-63) and the reversible averaging method (Leimkuhler and Reich 2001 J. Comput. Phys. 17195-114). Features of problems of interest, such as thermostatted coarse-grained molecular dynamics, require extension of the standard framework. At the same time, in some applications the computation of averages plays a crucial role, but the available methods have deficiencies in this regard. We demonstrate that a new approach based on the introduction of shadow variables, which mirror physical variables, has promised for broadening the usefulness of multiscale methods and enhancing accuracy of or simplifying computation of averages. The shadow variables must be computed from an auxiliary equation. While a geometric integrator in the extended space is possible, in practice we observe enhanced long-term energy behaviour only through use of a variant of the method which controls drift of the shadow variables using dissipation and sacrifices the formal geometric properties such as time-reversibility and volume preservation in the enlarged phase space, stabilizing the corresponding properties in the physical variables. The method is applied to a gravitational three-body problem as well as a partially thermostatted model problem for a dilute gas of diatomic molecules.
DOI	10.1088/0305-4470/39/19/S04
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000238383700005
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2750
专题	中国科学院数学与系统科学研究院
通讯作者	Jia, ZD
作者单位	1.Chinese Acad Sci, Inst Computat Math, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 2.Univ Leicester, Dept Math, Leicester LE1 7RH, Leics, England
推荐引用方式 GB/T 7714	Jia, ZD,Leimkuhler, B. Geometric integrators for multiple time-scale simulation[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL,2006,39(19):5379-5403.
APA	Jia, ZD,&Leimkuhler, B.(2006).Geometric integrators for multiple time-scale simulation.JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL,39(19),5379-5403.
MLA	Jia, ZD,et al."Geometric integrators for multiple time-scale simulation".JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 39.19(2006):5379-5403.