| 非薄板腐蚀探测问题的数值解法 |
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| 引用本文： | 陈宇,黄建国.非薄板腐蚀探测问题的数值解法[J].南京师大学报,2008,31(4). |
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| 作者姓名： | 陈宇 黄建国 |
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| 作者单位： | 上海交通大学数学系 |
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| 摘 要： | 腐蚀探测问题是一个数学物理方程反问题,它通过外边界上可获知的电场数据反演求解腐蚀系数.通常所涉及的数据是带有噪声误差的.在无需假设板或管的厚度很薄的条件下,提出了一个基于Dirichlet-Neumann条件求解腐蚀系数的变分模型.该模型最终由最优化领域中的拟牛顿迭代法实现数值求解.给出若干理论分析,并用数值实验结果说明求解方法的可行有效性.
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| 关 键 词： | 有限元 拟牛顿法 反问题 正则化 |
Numerical Method for Corrosion Detection Problem in Non-Sheet Case |
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| Chen Yu,Huang Jianguo.Numerical Method for Corrosion Detection Problem in Non-Sheet Case[J].Journal of Nanjing Normal University(Natural Science Edition),2008,31(4). |
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| Authors: | Chen Yu Huang Jianguo |
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| Abstract: | The problem of recovering the corrosion coefficient in an inaccessible interior part from the electric information in an accessible part of a physical domain is studied,which is a typical inverse problem in mathematical physics.Usually,the prescribed data have noise error.A variational formulation is proposed to derive the corrosion coefficient,based on the Dirichlet-Neumann data on the accessible part.The quasi-Newton iterative method in optimization is used to solve the numerical solution of this variational problem.Some theoretical analysis is provided,and the numerical experiment shows that the method is effective. |
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| Keywords: | finite element Quasi-Newton Method inverse problems regularization |
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