| ON THE TIME SPLITTING SPECTRAL METHOD FOR THE COMPLEX GINZBURG-LANDAU EQUATION IN THE LARGE TIME AND SPACE SCALE LIMIT | |
| Degond, Pierre ; Jin, Shi ; Tang, Min | |
| 2010-05-06 ; 2010-05-06 | |
| 关键词 | asymptotic preserving scheme complex Ginzburg-Landau equation asymptotic limit time splitting spectral method NONLINEAR SCHRODINGER-EQUATIONS SYSTEM APPROXIMATIONS ATTRACTORS CONVECTION DYNAMICS SCHEMES REGIMES Mathematics, Applied |
| 中文摘要 | We are interested in the numerical approximation of the complex Ginzburg-Landau equation in the large time and space limit. There are two interesting regimes in this problem, one being the large space time limit, and one being the nonlinear Schrodinger limit. These limits have been studied analytically in, for example, T. Colin and A. Soyeur, Asymptot. Anal., 13 ( 1996), pp. 361-372; F. H. Lin, Comm. Pure Appl. Math., 51 (1998), pp. 385-441; F. H. Lin and J. X. Xin, Comm. Math. Phys., 200 ( 1999), pp. 249-274. We study a time splitting spectral method for this problem. In particular, we are interested in whether such a scheme is asymptotic preserving (AP) with respect to these two limits. Our results show that the scheme is AP for the first limit but not the second one. For the large space time limit, our numerical experiments show that the scheme can capture the correct physical behavior without resolving the small scale dynamics, even for transitional problems, where small and large scales coexist. |
| 语种 | 英语 ; 英语 |
| 出版者 | SIAM PUBLICATIONS ; PHILADELPHIA ; 3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA |
| 内容类型 | 期刊论文 |
| 源URL | [http://hdl.handle.net/123456789/13737]  |
| 专题 | 清华大学 |
| 推荐引用方式 GB/T 7714 | Degond, Pierre,Jin, Shi,Tang, Min. ON THE TIME SPLITTING SPECTRAL METHOD FOR THE COMPLEX GINZBURG-LANDAU EQUATION IN THE LARGE TIME AND SPACE SCALE LIMIT[J],2010, 2010. |
| APA | Degond, Pierre,Jin, Shi,&Tang, Min.(2010).ON THE TIME SPLITTING SPECTRAL METHOD FOR THE COMPLEX GINZBURG-LANDAU EQUATION IN THE LARGE TIME AND SPACE SCALE LIMIT.. |
| MLA | Degond, Pierre,et al."ON THE TIME SPLITTING SPECTRAL METHOD FOR THE COMPLEX GINZBURG-LANDAU EQUATION IN THE LARGE TIME AND SPACE SCALE LIMIT".(2010). |
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