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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一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。
In order to speed up the calculation of 3D forward modeling by DC resistivity method, this paper introduces a new type of algebraic multigrid algorithm-aggregated algebraic multigrid algorithm (AGMG). First of all, based on the field potential quadratic differential equation which is satisfied by the DC resistivity method, the finite difference scheme of seven points is used to discretize the coupled boundary conditions to form a large-scale sparse solution of linear equations. Then, Algorithm and technical process, and the V-loop AGMG preconditioned conjugate gradient (CG) algorithm (AGMG-CG) is used to solve the linear equations. Finally, the DC resistivity 3D forward modeling is achieved. Through the typical numerical simulation of the electric model, the feasibility and accuracy of the proposed algorithm are verified by comparison with the results of 3DDCXH and 3DDCXH. In addition, the numerical simulation of different meshes and different models and comparison with the traditional iterative algorithms (ILU-BCGSTAB, ILU-GCR, SSOR-CG) show that the AGMG-CG algorithm has both iteration times and iterations Significant advantage, at the same time has the almost linear rapid decline, the number of iterations increases with the grid size increases slowly and so on. Therefore, the proposed algorithm has the advantages of high convergence precision, fast convergence and stable iteration, which makes it possible to improve the computational efficiency of the three-dimensional forward modeling of the DC resistivity method.