Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium
文献类型：期刊论文
| 作者 | Gao LiPing1; Zhang Bo2,3
|
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2011-12-01 |
| 卷号 | 54期号:12页码:2693-2712 |
| 关键词 | Maxwell equations finite-difference time-domain method stability superconvergence perfectly electric conducting boundary conditions energy identities |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-011-4305-7 |
| 英文摘要 | This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D Maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L (2) and H (1) norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L (2) and H (1) norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis. |
| 资助项目 | Shandong Provincial Natural Science Foundation[Y2008A19] ; Research Reward for Excellent Young Scientists from Shandong Province[2007BS01020] ; Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry ; National Natural Science Foundation of China[11071244] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000297735900013 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/11878]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Gao LiPing |
| 作者单位 | 1.China Univ Petr, Sch Sci, Dept Computat & Appl Math, Qingdao 266555, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Gao LiPing,Zhang Bo. Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium[J]. SCIENCE CHINA-MATHEMATICS,2011,54(12):2693-2712. |
| APA | Gao LiPing,&Zhang Bo.(2011).Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium.SCIENCE CHINA-MATHEMATICS,54(12),2693-2712. |
| MLA | Gao LiPing,et al."Stability and superconvergence analysis of the FDTD scheme for the 2D Maxwell equations in a lossy medium".SCIENCE CHINA-MATHEMATICS 54.12(2011):2693-2712. |
入库方式： OAI收割
来源：数学与系统科学研究院
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