| Variational regularization method of solving the Cauchy problem for Laplace＇s equation： Innovation of the Grad-Shafranov （GS） reconstruction |
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| 引用本文： | 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].中国物理 B,2014(10):654-662. |
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| 作者姓名： | 颜冰 黄思训 |
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| 作者单位： | Institute of Meteorology and Oceanography, PLA University of Science and Technology;State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration |
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| 基金项目： | Project supported by the National Natural Science Foundation of China(Grant No.41175025) |
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| 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.
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| 关 键 词： | 拉普拉斯方程 正则化方法 柯西问题 GS 毕业 变分 创新 求解 |
Variational regularization method of solving the Cauchy problem for Laplace’s equation: Innovation of the Grad–Shafranov(GS)reconstruction |
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| Yan Bing;Huang Si-Xun.Variational regularization method of solving the Cauchy problem for Laplace’s equation: Innovation of the Grad–Shafranov(GS)reconstruction[J].Chinese Physics B,2014(10):654-662. |
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| Authors: | Yan Bing;Huang Si-Xun |
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| Abstract: | Grad-Shafranov reconstruction, variational regularization method, Cauchy problem |
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| Keywords: | Grad-Shafranov reconstruction variational regularization method Cauchy problem |
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