自然科学版 英文版
自然科学版 英文版
自然科学版 英文版

您目前所在的位置:首页 - 期刊简介 - 详细页面

中南大学学报(自然科学版)

Journal of Central South University

第40卷    第2期    总第186期    2009年4月

[PDF全文下载]    [Flash在线阅读]

    

文章编号:1672−7207(2009)02−0484−08
不完全LU分解预处理的BICGSTAB算法在
大地电磁二维正演模拟中的应用
柳建新,蒋鹏飞,童孝忠,徐凌华,谢 维,王 浩

(中南大学 信息物理工程学院,湖南 长沙,410083)

摘 要: 基于双二次插值的有限单元法求解大地电磁二维正演问题,以不均匀网格剖分为基础,推导出大地电磁响应的计算公式。针对有限单元法最后形成一个线性方程组,系数矩阵是大型稀疏的带状对称正定复系数矩阵,并且其条件数远大于1,为严重病态矩阵,求解其对应方程组会遇到很多困难等问题,采用不完全LU分解(即上三角与下三角分解)处理的稳定双共轭梯度算法(BICGSTAB算法)求解该线性方程组,通过对层状介质和二维模型电磁响应进行计算,获得二维大地电磁的视电阻率曲线和阻抗相位曲线。研究结果表明,BICGSTAB算法具有速度快、精度高和稳定性好等优点。

 

关键字: 大地电磁;有限单元法;二维正演;不完全LU分解;BICGSTAB算法

Application of BICGSTAB algorithm with incomplete LU decomposition preconditioning to two-dimensional magnetotelluric forward modeling
LIU Jian-xin, JIANG Peng-fei, TONG Xiao-zhong, XU Ling-hua, XIE Wei, WANG Hao

School of Info-physics and Geomatics Engineering, Central South University, Changsha 410083, China

Abstract:Based on the finite element method of quadratic interpolation in a rectangular element to solve the two-dimensional magnetotelluric forward problem, no-uniform mesh based magnetotelluric responses calculation formula was derived. Based on the fact that the finite element method was used to form a linear equation, and the coefficient matrix was a large sparse, banded, symmetric, conditioned and complex matrix, its condition number is far larger than 1, and it was an ill-conditioned matrix, solving large scale ill-conditioned linear equation was very difficult, and so the BICGSTAB (Bi-conjugate gradient stabilized method) algorithm with incomplete LU decomposition for preconditioning was used to solve this system linear equation. This approach was verified through the calculations of layered earth model and two-dimensional earth model. The results show that the BICGSTAB algorithm has high speed, high precision and stability. The apparent resistivity curves and the impedance phase curves are very accurate to synthetic magnetotelluric responses.

 

Key words: magnetotelluric; finite element method; two-dimensional forward modeling; incomplete LU decomposition; BICGSTAB algorithm

中南大学学报(自然科学版)
  ISSN 1672-7207
CN 43-1426/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
版权所有:《中南大学学报(自然科学版、英文版)》编辑部
地 址:湖南省长沙市中南大学 邮编: 410083
电 话: 0731-88879765 传真: 0731-88877727
电子邮箱:zngdxb@csu.edu.cn 湘ICP备09001153号