【摘要】 应用交错网格有限差分法计算三维复杂环境中的感应测井响应 .其中 ,利用Krylov子空间不变性求解离散得到的大型稀疏复对称线性方程组 .在构造Krylov子空间时使用其系数矩阵的伪逆以改善迭代的收敛性 .迭代中 ,使用不完全Cholesky分解共轭梯度法求解 4个三维Poisson方程以得到新的Lanczos向量 .通常迭代不超过 2 0次可得到理想结果 .另外 ,提出一种新的物质平均公式以计算电导率平均值 ,可保证电流守恒 .更多还原

【Abstract】 The finite difference method using staggered grid is applied to simulate the induction logging response in 3D media. The invariance property of the Krylov subspace is used to solve the large sparse complex symmetric linear system. To improve iteration convergence the pseudo inverse of the coefficient matrix is employed when constructing the Krylov subspace instead of the coefficient matrix itself. In each iteration four 3D Poisson equations are computed to get a new Lanczos vector with incomplete Cholesky decomposition conjugate method. Generally, the desirable solution is achieved with no more than 20 times of iteration. Also, a new material averaging formula is presented to get a reasonable average of the conductivity, which guarantees the conservation of the electric current.更多还原