中文摘要：

为加快直流电阻率法三维正演模拟的计算速度，本文引入一种新型的代数多重网格算法—聚集代数多重网格算法（AGMG）。首先从直流电阻率法满足的电位二次场微分方程出发，采用七点有限差分格式进行离散，结合混合边界条件形成大型稀疏求解线性方程组；然后详细给出AGMG法聚集粗化的成对聚集算法及技术流程，并采用V循环AGMG预处理共轭梯度（CG）算法（AGMG-CG）求解线性方程组，最终实现直流电阻率三维正演模拟。通过典型地电模型数值模拟研究，并与成熟的直流电阻率三维正演模拟程序（3DDCXH）结果及解析结果对比验证了本文给出算法可行性和准确性。另外通过对不同剖分网格和不同模型的数值模拟，并与传统迭代算法（ILU-BCGSTAB、ILU-GCR、SSOR-CG）对比表明，AGMG-CG算法不论从迭代次数还是迭代时间上都有显著优势，同时具有近乎线性快速下降、迭代次数随网格大小增加而缓慢增加等优点。因此，本文算法具有收敛精度高、收敛快、迭代稳定等优点，为提高直流电阻率法三维正演模拟的计算效率提供了可能。

英文摘要：

To speed up three-dimensional （3D） DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method （AGMG）. We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner （AGMG-CG） to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling （3DDCXH）. In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.