| 利用不完全Cholesky共轭梯度法求解点源三维地电场 |
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| 引用本文： | 吴小平,徐果明.利用不完全Cholesky共轭梯度法求解点源三维地电场[J].地球物理学报,1998,41(6):848-855. |
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| 作者姓名： | 吴小平 徐果明 |
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| 作者单位： | 中国科技大学地球与空间科学系,合肥230026 |
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| 摘 要： | 点源三维地电场的求解是一大型数值计算问题．本文用有限差分方法求解，最后形成一个线性方程组Ax＝b，这里A是大型稀疏的带状对称矩阵．解大型稀疏方程组的完全Cholesky分解直接算法，一般要求巨大的机器内存来存储系数矩阵A，而且计算速度极慢．因此引入不完全Cholesky共轭梯度（ICCG）算法及按行索引的稀疏存储模式，充分利用A的稀疏性，使得计算速度大大提高，而内存要求则大大减少，因此ICCG算法是地电三维正演的强有力工具．
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| 关 键 词： | 共轭梯度法 不完全Cholesky共轭梯度法 按行索引稀疏存储模式 地电三维正演 |
| 收稿时间： | 1998-06-12 |
THE CALCULATION OF THREE-DIMENSIONAL GEOELECTRIC FIELD OF POINT SOURCE BY INCOMPLETE CHOLESKY CONJUGATE GRADIENT METHOD |
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| WU XIAO-PING, XU GUO-MING, LI SHI-CAN.THE CALCULATION OF THREE-DIMENSIONAL GEOELECTRIC FIELD OF POINT SOURCE BY INCOMPLETE CHOLESKY CONJUGATE GRADIENT METHOD[J].Chinese Journal of Geophysics,1998,41(6):848-855. |
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| Authors: | WU XIAO-PING XU GUO-MING LI SHI-CAN |
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| Institution: | Department of Earth and Space Science, University of Science andTechnology of China. Hefei 230026, China |
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| Abstract: | The calculation of three-dimensional geoelectric field of point-source is in fact an exhausting numerical computation problem. In thes paper, finite difference method is used to form a linear equation Ax = b, in which A is a large sparse band symmetric matrix. In solving the large sparse equations, the direct method with Complete Cholesky decomposition is quite slow and reqinres much more storage of computer for coefficient matrix A. Therefore, we introduced incomplete Cholesky Conjugate Gradient (ICCG) method and row-indexed sparse storage mode. By taking advantage of the sparseness of A, the ICCG method converges much quickly and requires much less storage of computer. So it is a robust method for 3-D geoelectric modelling. |
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| Keywords: | Conjugate gradient (CG) method Incomplete Cholesky conjugate gradient (ICCG) method Row-indexed sparse storage mode 3-D geoelectric forward |
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