Variational regularization method of solving the Cauchy problem for Laplace’s equation： Innovation of the Grad-Shafranov (GS) reconstruction

doi:10.1088/1674-1056/23/10/109402

›› 2014, Vol. 23 ›› Issue (10): 109402-109402.doi: 10.1088/1674-1056/23/10/109402

• GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS • 上一篇

Variational regularization method of solving the Cauchy problem for Laplace’s equation： Innovation of the Grad-Shafranov (GS) reconstruction

颜冰^a, 黄思训^{a b}

a Institute of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China;
b State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China

收稿日期:2014-01-18 修回日期:2014-04-13 出版日期:2014-10-15 发布日期:2014-10-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 41175025).

Variational regularization method of solving the Cauchy problem for Laplace’s equation： Innovation of the Grad-Shafranov (GS) reconstruction

Yan Bing (颜冰)^a, Huang Si-Xun (黄思训)^{a b}

a Institute of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China;
b State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China

Received:2014-01-18 Revised:2014-04-13 Online:2014-10-15 Published:2014-10-15
Contact: Huang Si-Xun E-mail:huangsxp@163.com
About author:94.30.C-; 02.30.Zz; 02.60.Lj; 95.30.Qd
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 41175025).

摘要/Abstract

摘要： The simplified linear model of Grad-Shafranov (GS) reconstruction can be reformulated into an inverse boundary value problem of Laplace's equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace's equation. In the first place, the variational regularization method is used to deal with the ill-posedness of the Cauchy problem for Laplace's equation. Then, the 'L-Curve' principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10 ^-1, the order of the approximate result error can reach 10 ^-3.

关键词: Grad-Shafranov reconstruction, variational regularization method, Cauchy problem

Abstract: The simplified linear model of Grad-Shafranov (GS) reconstruction can be reformulated into an inverse boundary value problem of Laplace's equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace's equation. In the first place, the variational regularization method is used to deal with the ill-posedness of the Cauchy problem for Laplace's equation. Then, the 'L-Curve' principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10 ^-1, the order of the approximate result error can reach 10 ^-3.

Key words: Grad-Shafranov reconstruction, variational regularization method, Cauchy problem

中图分类号: (Magnetospheric configuration and dynamics)

94.30.C-

02.30.Zz (Inverse problems) 02.60.Lj (Ordinary and partial differential equations; boundary value problems) 95.30.Qd (Magnetohydrodynamics and plasmas)

颜冰, 黄思训. Variational regularization method of solving the Cauchy problem for Laplace’s equation： Innovation of the Grad-Shafranov (GS) reconstruction[J]. , 2014, 23(10): 109402-109402.

Yan Bing (颜冰), Huang Si-Xun (黄思训). Variational regularization method of solving the Cauchy problem for Laplace’s equation： Innovation of the Grad-Shafranov (GS) reconstruction[J]. Chin. Phys. B, 2014, 23(10): 109402-109402.

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Variational regularization method of solving the Cauchy problem for Laplace’s equation： Innovation of the Grad-Shafranov (GS) reconstruction

Variational regularization method of solving the Cauchy problem for Laplace’s equation： Innovation of the Grad-Shafranov (GS) reconstruction

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