| A Regularized Newton Method in Inverse Scattering Problem from Cavities |
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| 引用本文： | 冯立新 马富明. A Regularized Newton Method in Inverse Scattering Problem from Cavities[J]. 东北数学, 2007, 23(6): 479-490 |
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| 作者姓名： | 冯立新 马富明 |
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| 作者单位： | [1]School of Mathematical Sciences, Heilongjiang University, Harbin, 150080 [2]Institute of Mathematics, Jilin University, Changchun, 130012 |
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| 基金项目： | Foundation item： The NNSF （10626017） of China, the Science Foundation （11511276） of the Education Committee of Heilongjiang Province and the Foundation （LBH-Q05114） of Heilongjiang Province. |
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| 摘 要： | We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization.For its approximate solution we propose a regularized Newton iteration scheme.For a foundation of Newton type methods we establish the Fréchet differentiability of solution to the scattering problem with respect to the boundary of the cavity.Some numerical examples of the feasibility of the method are presented.
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| 关 键 词： | 解洞穴逆散射问题 正则化 Newton方法 数值分析 |
| 文章编号： | 1000-1778（2007）06-0479-12 |
| 收稿时间： | 2006-04-04 |
| 修稿时间： | 2006-04-04 |
A Regularized Newton Method in Inverse Scattering Problem from Cavities |
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| FENG Li-xin MA Fu-ming. A Regularized Newton Method in Inverse Scattering Problem from Cavities[J]. Northeastern Mathematical Journal, 2007, 23(6): 479-490 |
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| Authors: | FENG Li-xin MA Fu-ming |
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| Affiliation: | School of Mathematical Sciences, Heilongjiang University, Harbin, 150080;Institute of Mathematics, Jilin University, Changchun, 130012 |
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| Abstract: | We consider the inverse problem to determine the shape of a open cavity embedded in the infinite ground plane from knowledge of the far-field pattern of the scattering of TM polarization. For its approximate solution we propose a regularized Newton iteration scheme. For a foundation of Newton type methods we establish the Fr~chet differentiability of solution to the scattering problem with respect to the boundary of the cavity. Some numerical examples of the feasibility of the method are presented. |
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| Keywords: | inverse scattering problem regularization Newton method |
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