中文摘要：

引入外推瀑布式多重网格法（EXCMG）求解2.5维直流电阻率有限元计算形成的大型稀疏线性方程组,结合基于地址矩阵的压缩存贮方式以及最优化离散波数,使得2.5维电阻率正演程序的计算速度大大提高而内存需求大大减小.研究结果表明：EXCMG法的收敛速度与网格尺寸无关,计算速度明显优于不完全Cholesky共轭梯度（ICCG）法.并且,随着问题规模的增大,EXCMG法的效率优势更加明显.对1600×1600网格的2.5维电阻率法模拟问题,正演程序仅耗时28s,视电阻率平均相对误差控制在0.22%以内,为进一步研究快速反演奠定了基础.

英文摘要：

Combining the compression storage mode based on address matrix with the optimized discrete wave-number,an extrapolation cascadic multigrid（EXCMG） method was introduced to solve the large sparse systems of linear equations resulting from 2.5D finite-element direct current（DC） resistivity modeling,which greatly increased the computing speed and significantly reduced the memory requirements of 2.5D forward modeling program.The research results showed that EXCMG method,which converged at a rate independent of the mesh size,was much more efficient than the incomplete Cholesky conjugate gradient（ICCG） method.Moreover,as the size of the problem increases,the efficiency advantage of EXCMG over other methods becomes more obvious.The EXCMG program for 2.5D DC resistivity modeling with a grid of 1600×1600 only took 28 seconds,and the average relative error of apparent resistivity was less than 0.22%,which laid the foundation for the latter studies of rapid inversion.