论文部分内容阅读
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.
The multi-grid method has a very high computational efficiency when solving the discrete linear system derived from the boundary value problem of partial differential equations, but the common geometric multigrid method has some shortcomings when dealing with the partial differential equations with transition coefficients, Which limits its application.In this paper, the algebraic multigrid (AMG) method is used to solve the finite difference linear equations formed by the forward modeling of the three-dimensional direct resistivity method. By solving the secondary field method, the singularity So as to obtain a fast and accurate numerical simulation of three-dimensional resistivity.The two models with large electrical differences were simulated to verify the convergence efficiency of the algebraic multi-grid method.The calculated results show that, compared with the incomplete Cholesky Compared with the ICCG method, the algebraic multi-grid method has higher computational efficiency and stability. Moreover, with the increase of the number of three-dimensional grid nodes, the computational efficiency of the algebraic multi-grid method becomes more obvious.