共轭梯度法

This paper discusses the nonlinear inversion algorithms instructively andmainlystudytwokinds ofnonlinearinversionalgorithms: SimulatedAnnealingConjugate Grads and Artificial Neural Network Genetic Algorithms, these two methods can decrease the iteration times and avoiddroppinginto the local extremum, we do the model calculation and confirm thevalidityofthealgorithm.

对非线性反演算法进行了有益的探讨，主要研究了两种非线性混合优化反演算法：模拟退火共轭梯度混合反演和神经网络遗传反演算法，两种混合算法都达到了减少迭代次数、避免陷入局部极值的目的，并进行了模型试算，验证了算法的有效性。

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

The mixed method raise the convergent rate of the conjugate gradient method, and solve the problem which the steepest descent method can not solve in the condition with badly characteristics for the objective function.

混合算法既提高了共轭梯度算法的收敛速度，又解决了目标函数"性态不优"时，最速下降法难以求解的问题。

The obtained results a re compared with analytic solution and those from integral equation and other me ans. It is shown that the staggered grid finite difference method combined with the Biconjugate gradient iterative solver processed with divergence correction and incomplete Cholesky decomposition procedures can efficiently improve the three dimensional electromagnetic calculation with high accuracy and stability.

经与解析方法、积分方程等其他方法的计算结果对比表明，交错网格有限差分法结合散度校正和不完全乔累斯基分解预处理的双共轭梯度迭代方法进行正演计算，速度快、精度高、结果稳定，能适应三维复杂介质的数值模拟，为三维电磁反演奠定了基础。

In this paper, the following progress has been discussed:(1) the improved conjugate gradient algorithm which combines the inversion equation;(2) the formulation for velvet gene at all directions and the approximation method of Jacobian matrics based on disturbance method;(3) the model is adjusted by analyzing the influence of damp coefficient and correction factor to inversion result ;(4) the influence of damp coefficient to the resolution of inversion is studied. to some degree, we improved the problem of "barycenter ascending shift" to electric anomalous body in 3-D resistivity inversion.

本文主要讨论了以下几个方面的内容：（1）结合反演方程式改进的共轭梯度算法；（2）基于扰动法的线源Jacobi矩阵的近似计算方法及光滑系数矩阵在各个方向上的光滑因子的计算公式；（3）通过分析阻尼系数与修改量校正量对反演结果的影响，提出了利用校正系数对模型修正量进行校正；（4）较为系统的讨论了阻尼系数λ对反演分辨能力的影响，较好的改善了三维电阻率反演中的电性异常体重心的&上漂&现象。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。