A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissions and reflections
文献类型：期刊论文
| 作者 | Jin, Shi; Wen, Xin |
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2006 |
| 卷号 | 44期号:5页码:1801-1828 |
| 关键词 | geometrical optics Liouville equation transmission and reflection Hamiltonian-preserving schemes |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/050631343 |
| 英文摘要 | We construct a class of Hamiltonian-preserving numerical schemes for the Liouville equation of geometrical optics, with partial transmissions and reflections. This equation arises in the high frequency limit of the linear wave equation, with a discontinuous index of refraction. In our previous work [Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds, J. Comput. Phys. 214 (2006), pp. 672-697], we introduced the Hamiltonian-preserving schemes for the same equation when only complete transmissions or reflections occur at the interfaces. These schemes are extended in this paper to the general case of partial transmissions and reflections. The key idea is to build into the numerical flux the behavior of waves at the interface, namely, partial transmissions and reflections that satisfy Snell's law of refraction with the correct transmission and reflection coeficients. This scheme allows a hyperbolic stability condition, under which positivity, and stabilities in both l(1) and l(infinity) norms, are established. Numerical experiments are carried out to study the numerical accuracy. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000242572900001 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/3611]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Jin, Shi |
| 作者单位 | 1.Univ Wisconsin, Dept Math, Madison, WI 53706 USA 2.Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China 3.Chinese Acad Sci, Inst Computat Math, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Jin, Shi,Wen, Xin. A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissions and reflections[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2006,44(5):1801-1828. |
| APA | Jin, Shi,&Wen, Xin.(2006).A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissions and reflections.SIAM JOURNAL ON NUMERICAL ANALYSIS,44(5),1801-1828. |
| MLA | Jin, Shi,et al."A Hamiltonian-preserving scheme for the Liouville equation of geometrical optics with partial transmissions and reflections".SIAM JOURNAL ON NUMERICAL ANALYSIS 44.5(2006):1801-1828. |
入库方式： OAI收割
来源：数学与系统科学研究院
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