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Numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points
  • ISSN号：1005-1031
  • 期刊名称：《高校应用数学学报：英文版（B辑）》
  • 分类：O175.1[理学—数学;理学—基础数学] TS77[轻工技术与工程—制浆造纸工程]
  • 作者机构：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China.
  • 相关基金：Supported by the Key Project of the Major Research Plan of the NSFC （91130004）.Acknowledgement. We thank the referee for valuable comments and remarks.
作者： CHENG Xiao-liang YU Yuan-jie[1]
关键词： 数值估计, 不连续点, 分段常数, 数值方法, 椭圆方程, 最小二乘, 目标函数, 牛顿法, Inverse problem, Robin coefficient, differentiability, the Gauss-Newton method.
中文摘要：

我们为从边界大小在二维的椭圆形的方程估计 piecewise 常数罗宾系数建议一个新数字方法。知更鸟逆问题被重做进产量的最小化最少平方的明确的表达。一种技术基于决定未知系数的不连续的点被建议，并且我们调查答案和关于不连续的点功能的目的可辨性。然后，我们为重建使用高斯牛顿方法未知罗宾系数的形状。数字例子说明它的效率和稳定性。

英文摘要：

We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin in- verse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.

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期刊信息
  • 《高校应用数学学报：英文版（B辑）》
  • 主管单位:教育部
  • 主办单位:浙江大学 中国工业与应用数学学会
  • 主编：林正炎 李大潜
  • 地址：杭州玉泉浙江大学数学系
  • 邮编：310027
  • 邮箱：amjcu B@eju.edu.cn
  • 电话：0571-87951602
  • 国际标准刊号：ISSN：1005-1031
  • 国内统一刊号：ISSN：33-1171/O
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国科学引文索引（扩展库）
  • 被引量:26