求解时谐涡流模型鞍点问题的分块交替分裂隐式迭代算法的改进  

THE IMPROVEMENT OF BLOCK ALTERNATING IMPLICIT ITERATION METHODS FOR SADDLE-POINT PROBLEMS FROM TIME-HARMONIC EDDY CURRENT MODELS

作　　者：刘忠祥 王翠薇 王增琦 Liu Zhongxiang;Wang Cuiwei;Wang Zengqi(Shanghai Jiao Tong University,School of Mathematical Sciences,Shanghai 200240,Chin)

机构地区：[1]上海交通大学数学科学学院

出　　处：《计算数学》2018年第3期271-286,共16页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11371022)资助项目

摘　　要：分块交替分裂隐式迭代方法是求解具有鞍点结构的复线性代数方程组的一类高效迭代法．本文通过预处理技巧得到原方法的一种加速改进方法，称之为预处理分块交替分裂隐式迭代方法．理论分析给出了新方法的收敛性结果．对于一类时谐涡旋电流模型问题，我们给出了若干满足收敛条件的迭代格式．数值实验验证了新型算法是对原方法的有效改进．Block alternating splitting implicit iteration method is the effective iteration methods for solving the complex saddle point linear systems. In the present paper, we accelerate the method with the preconditioning technique and obtain a new iteration methods, called preconditioned block alternating splitting implicit iteration method. By suitable splitting of the coefficient matrix, we obtain several iteration schemes for the complex linear systems arising from a class of time-harmonic eddy current problems. The comparison with the orig- inal methods illustrates that the accelerating technique improve the numerical performance significantly.

关 键 词：时谐涡流模型 复线性鞍点问题 交替分裂隐式迭代法 预处理技术 

分 类 号：O241.6[理学—计算数学]