基于预条件LANCZOS算法快速实现三维地电场正演计算

计算物理 ›› 2009, Vol. 26 ›› Issue (6): 892-896.

基于预条件LANCZOS算法快速实现三维地电场正演计算

宛新林¹, 席道瑛²

1. 安徽建筑工业学院土木工程学院, 安徽合肥 230022;
2. 中国科学技术大学地球与空间科学学院, 安徽合肥 230026

收稿日期:2008-06-18 修回日期:2008-12-12 出版日期:2009-11-25 发布日期:2009-11-25
作者简介:宛新林(1966-),男,安徽庐江,副教授。博士。主要从事应用地球物理与岩土工程教学和科研工作.
基金资助:
国家自然科学基金(40874093);2008安徽省级土木工程教学团队资助项目

Fast Implementation of Forward Modeling of 3-D Geoelectric Field with Precondition Lanczos Method

WAN Xinlin¹, XI Daoying²

1. Department of Civil Engineering, Anhui Institute of Architecture & Industry, Hefei 230022, China;
2. Department of Earth and Space Science, University of Science and Technology of China, Hefei 230026, China

Received:2008-06-18 Revised:2008-12-12 Online:2009-11-25 Published:2009-11-25

摘要/Abstract

摘要： 针对三维地电场正演计算过程中形成的超大规模稀疏线性方程组,采用不完全Cholesky分解方法进行预条件处理,经过条件数改善后形成的新线性方程组的系数矩阵变为一个近似的单位矩阵,再应用Lanczos算法将会提高数值计算的稳定性,加快迭代收敛的速度,通常在迭代次数远小于系数矩阵阶数时就能得到较好精确解的近似值,为下一步的电阻率三维反演计算打下了非常好的基础.

关键词: 三维地电场, 正演计算, 稀疏矩阵, 预条件LANCZOS算法

Abstract: An incomplete Cholesky factorization is used to preconditioning large sparse coefficient matrix in 3-D geoelectric field forward modelling. Coefficient matrix of the new system is an approximate unit matrix. Preconditioned Lanczos algorithm improves stability and convergence of iterative procedures. In the algorithm, as iterative numbers are smaller than dimensions of coefficient matrix, approximation of the exact solution is obtained. Preconditioned Lanczos algorithm is effective in 3-D geoelectric field forward modeling. It makes a foundaiton for 3-D geoelectric inversion.

Key words: 3-D geoelectric field, forward modeling, sparse matrice, preconditioned Lanczos method

中图分类号:

P631.3

宛新林, 席道瑛. 基于预条件LANCZOS算法快速实现三维地电场正演计算[J]. 计算物理, 2009, 26(6): 892-896.

WAN Xinlin, XI Daoying. Fast Implementation of Forward Modeling of 3-D Geoelectric Field with Precondition Lanczos Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(6): 892-896.

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