电子学报2017，Vol.45Issue(10)：2549-2554,6.DOI:10.3969/j.issn.0372-2112.2017.10.033
正则化预条件方法在矩量法中的应用
Application of the Regularization Preconditioning to the Moment Methods
摘要
Abstract
The system matrices generated by the moment methods are ill-conditioned matrices,which make the iterative methods hardly converge,even accelerated by the existing preconditioning techniques.This paper applies the concept of regularization methods of ill-posed problems,and introduces the so-called regularization matrix as a precondidoner.This preconditioner can shift the eigenvalues of the system matrix directly.And it needs no additional memory to store the preconditioner.Furthermore,this paper proposes to determine the optimized regularization parameter by finding the maximum value of the second derivative of the L-curve of the regularized matrix.Numerical experiments show that the proposed method can converge relatively fast for some matrix equation generated by the electric field integral equation (EFIE) or the magnetic field integral equation (MFIE) solved with the higher order moment method,while iterative methods with the existing preconditioners may converge slowly.关键词
矩量法/病态矩阵/迭代方法/正则化方法Key words
moment methods/ill-conditioned matrix/iterative methods/regularization methods分类
信息技术与安全科学引用本文复制引用
袁浩波,杨蒙,党晓杰,王楠..正则化预条件方法在矩量法中的应用[J].电子学报,2017,45(10):2549-2554,6.基金项目
国家自然科学基金(No.61072018,No.60901030) （No.61072018,No.60901030）
中国博士后基金(No.2014M561211) （No.2014M561211）
中央高校基本科研业务费专项资金(No.JB150223,No.WRYB142105) （No.JB150223,No.WRYB142105）
