用于电介质中空间电荷分布测量的Tikhonov反卷积算法  

The Application of Tikhonov Deconvolution Algorithm for Space Charge Distribution in Dielectrics

作　　者：扈罗全[1] 郑飞虎[1] 张冶文[1] 

机构地区：[1]同济大学波尔固体物理研究所,上海200092

出　　处：《计算物理》2004年第5期432-438,共7页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(No.50277026);教育部科学技术重点项目(No.02100);国家重点基础研究发展规划项目(No.2001CB610406)资助项目

摘　　要：　研究了使用压力波法测量平板电介质试样的空间电荷分布的数值解法,使用基于Tikhonov正则化方法的反卷积算法得到了真实的空间电荷分布.在反卷积算法中使用了相关的技术处理,如小波包过滤高频噪音,Tikhonov正则化方法处理积分方程等.利用数值实验研究了噪声对反卷积算法的影响,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电介质中的空间电荷分布;在处理有噪数据时,反卷积的结果受到明显的影响,但仍然有较高的计算精度.正则化参数α对空间电荷分布的数值解起着明显的光滑作用,但是对于解的积分值却影响不大.对实际测量数据进行处理的结果表明,反卷积算法成功地计算出了固体电介质中的空间电荷分布和电场分布.A numerical algorithm for space charge distribution in the planar dielectric sample by Pressure Wave Propagation(PWP)method is presented. The real space charge distribution is obtained from the deconvolution based on Tikhonov regularization method.Several technical treatments related to the deconvolution technique have been adopted,such as erasing the high frequency noise with wavelet packet filters,treating with integral equation using Tikhonov regularization method etc..The affect of noise for deconvolution algorithm is studied indetail by numerical experiments. It is shown that deconvolution algorithm for solving space charge distribution in dielectric can obtain very good results under low noise circumstance,however the numerical results are affected significantly under high noise circumstance,although they are still acceptable. There is evident smoothing effect for numerical solutions using regularization parameter α,but there is no significant effect for integral of numerical solution. Applying the deconvolution method to analyse experimental data,space charge distribution and electric field distribution are as well obtained successfully.

关 键 词：电介质 空间电荷 积分方程 数值实验 TIKHONOV正则化方法 数值解法 固体 反卷积算法 电场分布 测量 

分 类 号：O241[理学—计算数学] TM935.38[理学—数学]