麦克斯韦方程反演的大范围收敛共轭斜量法  

A Widely Convergent Conjugate Gradient Method for Maxwell Equation Inversion

作　　者：王迎[1] 

机构地区：[1]黑龙江工业学院机械工程系,黑龙江鸡西158100

出　　处：《湖北文理学院学报》2014年第5期5-8,共4页Journal of Hubei University of Arts and Science

摘　　要：针对麦克斯韦方程中的电导率参数反演问题,构造一种具有大范围收敛的正则化共轭斜量反演算法,即将用于求解非线性问题大范围收敛的同伦法、求解大规模优化问题的共轭斜量法与求解不适定问题的Tikhonov正则化方法有机结合,得到解决麦克斯韦方程反演问题大范围收敛的数值方法,以求解电导率参数反演问题,解决了求解过程中局部陷入极小值的困惑.实验结果表明此算法是有效的,可以应用于其他类型的参数识别问题.For the problem of conductivity parameter inversion in the Maxwell equation, It constructs a regularization-conjugate gradient inversion algorithm with a widely convergence. The widely convergent numerical algorithm which can solve the inversion problem of Maxwell equation is gained by organically combining the Homotopy method with global convergence for solving the nonlinear problems, and the conjugate gradient algorithm for solving the large-scale optimization problems with the regularization method Tikhonov for solving the ill-posed problems. The constructed algorithm is used to solve the inverse problem of conductivity parameter and solves the puzzle that the solution falls into the local minimal value in the solving process. The experimental result shows that the algorithm is effective, and can be applied in the parameter identification problems of other types.

关 键 词：麦克斯韦方程 反演 同伦法 共轭斜量法 

分 类 号：O241.82[理学—计算数学]