New approach for solving the inverse boundary value problem of Laplace's equation on a circle: Technique renovation of the Grad-Shafranov (GS) reconstruction
文献类型：期刊论文
| 作者 | Li, H. J.; Feng, X. S.; Xiang, J.; Zuo, P. B. |
| 刊名 | JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS
 |
| 出版日期 | 2013 |
| 卷号 | 118期号:6页码:2876-2881 |
| 关键词 | Grad-Shafranov reconstruction inverse boundary value problems Hilbert transform method of discrete vortex |
| ISSN号 | 2169-9380 |
| 通讯作者 | Feng, XS (reprint author), Chinese Acad Sci, Ctr Space Sci & Appl Res, State Key Lab Space Weather, SIGMA Weather Grp, Beijing 100190, Peoples R China. |
| 英文摘要 | In this paper, the essential technique of Grad-Shafranov (GS) reconstruction is reformulated into an inverse boundary value problems (IBVPs) for Laplace's equation on a circle by introducing a Hilbert transform between the normal and tangent component of the boundary gradients. It is proved that the specified IBVPs have unique solution, given the known Dirichlet and Neumann conditions on certain arc. Even when the arc is reduced to only one point on the circle, it can be inferred logically that the unique solution still exists there on the remaining circle. New solution approach for the specified IBVP is suggested with the help of the introduced Hilbert transform. An iterated Tikhonov regularization scheme is applied to deal with the ill-posed linear operators appearing in the discretization of the new approach. Numerical experiments highlight the efficiency and robustness of the proposed method. According to linearity of the elliptic operator in GS equation, its solution can be divided into two parts. One is solved from a semilinear elliptic equation with an homogeneous Dirichlet boundary condition. The other is solved from the IBVP of Laplace's equation. It is concluded that there exists a unique solution for the so-called elliptic Cauchy problem for the essential technique of GS reconstruction. |
| 收录类别 | SCI |
| 语种 | 英语 |
| 源URL | [http://ir.nssc.ac.cn/handle/122/4993]  |
| 专题 | 国家空间科学中心_空间科学部 |
| 推荐引用方式 GB/T 7714 | Li, H. J.,Feng, X. S.,Xiang, J.,et al. New approach for solving the inverse boundary value problem of Laplace's equation on a circle: Technique renovation of the Grad-Shafranov (GS) reconstruction[J]. JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS,2013,118(6):2876-2881. |
| APA | Li, H. J.,Feng, X. S.,Xiang, J.,&Zuo, P. B..(2013).New approach for solving the inverse boundary value problem of Laplace's equation on a circle: Technique renovation of the Grad-Shafranov (GS) reconstruction.JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS,118(6),2876-2881. |
| MLA | Li, H. J.,et al."New approach for solving the inverse boundary value problem of Laplace's equation on a circle: Technique renovation of the Grad-Shafranov (GS) reconstruction".JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS 118.6(2013):2876-2881. |
入库方式： OAI收割
来源：国家空间科学中心
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