摘要
多重网格方法在求解由偏微分方程的边值问题离散所得线性系统时,具有非常高的计算效率.但常用的几何多重网格法在处理带跃变系数的偏微分方程时存在一定缺陷,限制了其应用.本文应用代数多重网格(AMG)方法求解三维直流电阻率法正演模拟形成的有限差分线性方程组,通过求解二次场的方法消除了总场中由点电源导致的奇异性,从而获得快速、精确的三维电阻率数值模拟.对两个存在大的电性差异的模型进行了模拟计算,以验证代数多重网格法的收敛效率.计算结果表明,与不完全Cholesky共轭梯度(ICCG)方法相比,代数多重网格方法具有更高的计算效率及稳定性.而且,随着三维网格节点数的增加,代数多重网格方法计算的高效性更加明显.
Multigrid method is of high numerical efficiency in solving linear equations arisen from boundary value problem of partial differential equation（PDE）. The usual geometrical muhigrid has some defects which restrict its application in PDE with jumping coefficient. In this paper, algebraic multigrid （AMG） method is used to solve finite difference linear equations which are derived from 3D DC resistivity modelling. We solve the secondary potential to remove the singularity of the primary potential caused by source current, resulting in an accurate 3D resistivity modelling. Two models with high conductivity contrast are used to demonstrate convergence and efficiency of the AMG method. Our results show that AMG methods are very efficient and robust in comparison with incomplete cholesky conjugate gradient （ICCG） methods. Moreover, the AMG method becomes more efficient as the number of 3D grid nodes increases.
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2010年第3期700-707,共8页
Chinese Journal of Geophysics
基金
supported by funds from the Natural Sciecne Foundation of China (No.40674037,40874034)
