[1]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(自然科学版),2008,31(04):29-32.
 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(04):29-32.
点击复制

非薄板腐蚀探测问题的数值解法()
分享到:

《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

卷:
第31卷
期数:
2008年04期
页码:
29-32
栏目:
数学
出版日期:
2008-12-30

文章信息/Info

Title:
Numerical Method for Corrosion Detection Problem in Non-Sheet Case
作者:
陈宇;黄建国;
上海交通大学数学系, 上海200240
Author(s):
Chen Yu Huang Jianguo
Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China
关键词:
有限元 拟牛顿法 反问题 正则化
Keywords:
finite e lem en t Quas-iNew tonM ethod inve rse prob lem s regu la rization
分类号:
O242.23
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.
Abstract:
The problem o f recove ring the corrosion coe ffic ient in an inaccessib le inter ior part from the e lec tric inform ation in an accessible part of a physica l dom ain is studied, wh ich is a typical inv erse prob lem in m a them atical phy sics. U sua-l ly, the prescribed data have no ise erro r. A var ia tiona l form ulation is propo sed to der ive the corro sion coe fficient, based on the Dir ichlet-Neum ann data on the accessib le part. The quas-iN ew ton iterativ em ethod in op tim ization is used to so lve the nume rical so lution o f th is variational prob lem. Som e theoretica l ana lys is is prov ided, and the num erical experim ent show s that the m ethod is effec tive.

参考文献/References:

[ 1] Ing lese G. An inverse prob lem in co rrosion detection[ J]. Inverse Problem s, 1997, 13( 4) : 977-994.
[ 2] Fas ino D, Ing lese G. D iscrete m ethods in the study o f an inverse prob lem fo rLaplace‘s equa tion[ J]. IMA J Num er ica l Analysis, 1999, 19( 1): 105-118.
[ 3] Fas ino D, Ing lese G. An inverse Rob in problem for Lap lace. s equation: theoretica l results and num erical m ethods[ J] . Inverse Problem s, 1999, 15( 1): 41-48.
[ 4] Yang X, Cheng J. An inve rse problem in detecting co rrosion in a pipe[ J]. Jou rnal o fN ingx iaUn ive rs ity: Na tura l Sc ience Edition, 2003, 24( 3) : 215-217.
[ 5] H uang X, H uang J, Chen Y. E rror ana lysis of a param ete r expans ion me thod fo r corro sion detection in a p ipe[ J]. Computers and M a them aticsW ith App lications, 2008, 56( 10): 2 539-2 549.
[ 6] Be lgacem F B, Fekih H E. On C auchy. s prob lem: I. A v ariational Steklov-Poincare theory[ J]. Inverse Prob lem s, 2005,21( 6): 1 915-1 936.
[ 7] A za iezM, Be lgacem F B, Fek ih H E. On Cauchy. s prob lem: II. Com pletion, regu larization and approx im a tion[ J]. Inverse Problem s, 2006, 22( 4): 1 307-1 336.
[ 8] H uang J, Chen Y. A regu lariza tion m e thod fo r the function reconstruction from approx im ate av erage fluxes[ J]. Inverse Problems, 2005, 21( 5) : 1 667-1 684.

备注/Memo

备注/Memo:
通讯联系人: 陈 宇, 博士, 研究方向: 计算数学. E-ma il:dabouxcy@ s jtu. edu. cn
更新日期/Last Update: 2013-05-05