基于预处理广义极小残量法的大地电磁正演计算  

Application of generalized minimal residual with preconditioning in the magnetotelluric forward modeling

作　　者：王亮[1] 王鹤[1] 席振铢[1] 冯万杰[1] 

机构地区：[1]中南大学地球科学与信息物理学院,长沙410083

出　　处：《地球物理学进展》2013年第1期165-170,共6页Progress in Geophysics

基　　金："十一五"国家科技支撑计划项目(2006BAB01B07)资助

摘　　要：有限单元法求解大地电磁正演问题,会形成大型稀疏的带状复系数矩阵方程组,其条件数大,易造成病态矩阵,求解极困难.为此,采用每步迭代都具有最优性的广义极小残量法(Generalized Minimal Residual)求解;但是,每步迭代的计算量和存储量都线性增长,造成迭代收敛速度慢,因此,引入不完全LU分解预处理技术以降低矩阵的条件数,加快广义极小残量法的收敛速度.通过二维模型和层状介质模型的电磁响应的计算表明,基于预处理广义最小残量法精确而稳定.Using Finite element method to solve the magnetotelluric forward problem will generate a large sparse complex coefficient matrix equations. Its condition number is great and could easily lead to ill-conditioned matrix which make it difficult to solve. We use the Generalized Minimal Residual method which has the advantage of each iteration with the best resistance to solve it. However the computation and storage are linear growth with the iteration resulting in slow convergence. So we introduce the incomplete LU factorization preconditioning to reduce the condition number of matrix and accelerate the convergence rate of GMRES. This approach is verified through the calculations of layered earth model and 2D earth model. The results show that the GMRES has high precision and stability.

关 键 词：有限元 广义最小残量法 预处理 大地电磁 

分 类 号：P318[天文地球—固体地球物理学] P319[天文地球—地球物理学]