三维电磁感应的有限差分法的网格收敛试验

MESH CONVERGENCE TEST FOR THE FINITE DIFFERENCE METHOD IN THREE-DIMENSIONAL ELECTROMAGNETIC MODELLING

本文用三维有限差分法,在计算电导率异常的电磁响应时作了一次网格收敛试验.该收敛解和其它几种数值解法得到的结果作了比较.这些方法是Hohmann的积分方程法、Lee等的混合法和Gupta等的混合法.我们的结果基本上和Hohmann的以及Gupta等的结果一致.试验表明,有限差分法所用的计算机时间比SANGAM混合法的少.为了缩减迭代过程的计算时间,我们使用了一种新的技巧——变区域迭代法,这种方法的收敛速度和一般的(在全区域迭代的)迭代法的收敛速度相同.

We present a mesh convergence test of the 3-D finite difference method for computing the electromagnetic response of a buried conductivity anomaly. The convergent results are compared with those obtained by the other numerical methods--Hohmann's integral equation method, Lee et al's hybrid method and Gupta et al's new hybrid method. Our numerical results are basically in agreement with Hohmann's results and Gupta et al's results. The computer time using the finite difference method is smaller than the computer time using the SANGAM hybrid method developed by Gupta et al. In order to save computer time, we use a new technique called 'iteration method with changed region' for the iterative process. We find that the convergent rate of this new technique is the same as that of the ordinary iteration method. with constant full region, rendering reduction of computer time.