计算物理 ›› 2005, Vol. 22 ›› Issue (1): 88-93.

• 研究简报 • 上一篇    

迭代正则化方法求解电介质中空间电荷分布

扈罗全, 郑飞虎, 张冶文   

  1. 同济大学波尔固体物理研究所, 上海 200092
  • 收稿日期:2003-09-25 修回日期:2004-04-15 出版日期:2005-01-25 发布日期:2005-01-25
  • 作者简介:罗全(1972-),男,江苏宜兴,博士生,从事通信工程中的数学物理问题研究,南京邮电学院280#210003.
  • 基金资助:
    国家自然科学基金(No.50277026);教育部科学技术重点(No.02100);国家重点基础研究发展规划(No.2001CB610406)资助项目

An Iterative Regularization Method for the Space Charge Distribution in Dielectrics

HU Luo-quan, ZHENG Fei-hu, ZHANG Ye-wen   

  1. Pohl Institute of Solid State Physics, Tongji University, Shanghai 200092, China
  • Received:2003-09-25 Revised:2004-04-15 Online:2005-01-25 Published:2005-01-25

摘要: 首先介绍了迭代正则化方法的理论基础,建立了含有空间电荷密度分布的Fredholm第一类积分方程的反卷积算法,利用数值实验研究了加性高斯白噪声对迭代反卷积算法的影响,以及迭代停止标准对非适定问题的数值解的影响,最后使用该方法求解电介质样品中的空间电荷分布.结果表明,在无噪或者低噪环境下,反卷积算法能够非常好地计算出非适定问题的解.当噪声影响增大,信噪比降低时,反卷积的计算结果受到明显的影响.迭代停止标准对数值解的计算精度起着明显的作用.对实际测量数据进行处理表明,迭代正则化反卷积算法能够计算出固体电介质中的空间电荷分布.

关键词: 迭代正则化, 反卷积, 电介质, 空间电荷

Abstract: The application of iterative regularization deconvolution to solve an ill-posed problem is discussed. Firstly, the theoretical foundation of iterative regularization is introduced, and a new Fredholm integral equation of the first kind including space charge distribution is derived .The effect of additive Gaussian white noise for iterative deconvolution algorithm, and the effect of iterative convergence criterion for the numerical solution are studied, respectively. It is shown that the solution of ill-posed problems could be obtained with iterative deconvolution algorithm under lower level noise circumstance. It also indicates that the precision of numerical solution is influenced by the iterative convergence criterion. Finally,the original experimental data are dealt with and the real space charge distribution in dielectrics is obtained.

Key words: iterative regularization, deconvolution, dielectrics, space charge

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