水气二相流方程的一种离散数值解法

提出了水气二相流方程的一种数值解法.在利用有限元方法求解水气二相流方程时,引入了离散Newton迭代方法,用于非线性有限元方程组的线性化处理,将这一步计算的收敛阶由原有研究的线性收敛提高到平方收敛,并避免了直接应用Newton迭代方法给编程带来的不便.同时在求解两相的有限元方程组时,采用两相方程组并行迭代的方法,与联立计算相比节省了大量的内存空间.     

解非光滑方程组的Newton-GMRES算法

给出了求解非光滑方程组的Newton—GMRES迭代法。该方法在求解半光滑方程组时，不需要计算广义Jacobi矩阵，同时使求解相应广义Newton方程组也变得容易。尤其对于大型问题，该方法特别适用。数值例子显示了这种方法的有效性。     

基于线性互补的非连续变形分析

非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题,合理设定罚参数很困难,此外,因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代,用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上,综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势,提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序,算例计算结果证明了方法的精度及可行性。     

无导数的大范围平方收敛迭代算法及其数值分析

应用迭代法的困难之处在于：一是迭代公式是否存在导数运算；二是初始值选定是否影响迭代公式的收敛性；三是收敛快速和达到需要精度等问题。我们获得了求方程根不用计算导数的平方收敛迭代公式，并设计了求根的大范围收敛算法，编写了C^ 语言程序，进行了算法和数值分析。与其它算法比较，该算法具有无导数计算、初值任意选定、平方快速收敛、大范围收敛和双精度控制(根的精度和函数值的精度控制)等优点。     

改进模拟退火法在估计河流水质参数中的应用

将模拟退火法应用于求解分析河流水团示踪试验数据，确定河流水质参数的函数优化问题。针对标准SA算法收敛速度缓慢的弱点，采取了增加附加约束条件、设置内阈值提前降温和增加记忆功能等综合措施对算法进行了改进。算例表明，综合改进措施能够明显地提高算法收敛速度，并可以得到满意的参数计算结果。计算结果也表明，内循环次数不会对外循环次数产生明显的影响。由于算法对目标函数没有附加要求，而且算法的收敛性与待估参数的初值无关，因此，改进SA算法在分析河流水质试验数据、确定水质参数方面．将会具有非常广的应用范围。     

准线性级数法在三维电磁正演中的应用

我们最近在三维电磁法正演计算中引入了准线性（ＱＬ）计算法。这篇文章主要讨论提高准线性级数阶次增加计算精度的问题，这种方法可看作是Ｂｏｒｎ级数的推广。利用改进的格林算子，要求它的范数小于１，以确保高阶次ＱＬ级数收敛，并得到起初的计算结果。这种新的方法保证ＱＬ级烽总是收敛，并得到起初的计算结果，这种新的方法保证ＱＬ级数总是收敛，而且可以直接计算ＱＬ法的计算精度，不用与严格的全积分方程（ＩＥ）解比较，使     

重力界面反演改进算法的比较与应用

为得到更接近地下真实分布的反演界面,笔者比较分析Parker-Oldenburg反演和改进迭代反演,发现改进迭代反演方法不仅可以避免计算放大项,而且能够得到更好结果。通过理论模型,对经典Parker-Oldenburg方法和改进迭代反演方法的计算速度、迭代收敛性和结果精确性进行比较,结果表明改进迭代反演方法在保证计算速度和迭代收敛的情况下,能获得更精确的地下界面结构。通过实际数据验证了改进迭代反演的有效性和实用性。     

节理非线性问题的约束函数法

接触非线性主要表现在其接触状态的突变而导致的非光滑性,这种非光滑性可以通过约束函数进行光滑逼近,进而可以用Newton法得到近似解,此方法称之为约束函数法。岩土工程中常用的Goodman单元就是一种类型的接触模型,但其参数的确定及计算的收敛性都存在着一定的困难。然而把约束函数应用到常规的Goodman单元中则可以解决上述困难,在详细地给出了其有限元法后,给出了处理刚体位移的一种简便方法。作为算例,给出了叠梁和三峡3# 坝段坝基稳定性的计算结果。     

非饱和渗流Richards方程数值求解的欠松弛方法

非饱和土渗流理论是岩土工程问题的基础理论,在土石坝渗流、污染物传输、冻土渗流相变和边坡稳定分析等领域有着广泛的应用。非饱和土渗流Richards方程的数值求解过程中,某些参数如水力传导系数计算不当可能引起非线性方法,如Picard方法或Newton方法的迭代收敛震荡,从而导致非线性迭代方法收敛缓慢和精度降低。为了消除或降低迭代收敛震荡对求解精度和计算性能的影响,目前主要采用欠松弛方法。通过一维入渗算例和二维非均质土坝渗流算例演示已有欠松弛方法的局限性,进而提出新的短项混合欠松弛法,并对其实用性和可靠性进行验证。     

一种高频面波频散函数的快速算法—改进的Abo-Zena法

作者在本文中首先介绍了改进的Anas Abo-Zena传递矩阵法面波频散函 数的计算问题。这是一种高频时稳定的算法，适用于一般地基勘查和无损检测的面波频散函数计算。其次，还讨论了用Monte Carlo法求解面波频散函数的问题。并用这种算法和Newton迭代法进行了对比，显示了对于Newton迭代法不能计算的速度逆转剖面（即层速度自上而下逐层减递），Monte Carlo法也适用。     

Numerical solution and convergence analysis of steam injection in heavy oil reservoirs

In this paper, the numerical methods for solving the problem of steam injection in the heavy oil reservoirs are presented. We consider a 3-dimensional model of 3-phase flow, oil, water, and steam, with the effect of 3-phase relative permeability. Interphase mass transfer of water and steam is considered; oil is assumed nonvolatile. We apply the simultaneous solution approach to solve the corresponding nonlinear discretized partial differential equation in the fully implicit form. The convergence of finite difference scheme is proved by the Rosinger theorem. The heuristic Jacobian-Free-Newton-Krylov (HJFNK) method is proposed for solving the system of algebraic equations. The result of this proposed numerical method is well compared with some experimental results. Our numerical results show that the first iteration of the full approximation scheme (FAS) provides a good initial guess for the Newton method. Therefore, we propose a new hybrid-FAS-HJFNK method while there is no steam in the reservoir. The numerical results show that the hybrid-FAS-HJFNK method converges faster than the HJFNK method.     

Mixed finite element discretization and Newton iteration for a reactive contaminant transport model with nonequilibrium sorption: convergence analysis and error estimates

We present a numerical scheme for reactive contaminant transport with nonequilibrium sorption in porous media. The mass conservative scheme is based on Euler implicit, mixed finite elements, and Newton method. We consider the case of a Freundlich-type sorption. In this case, the sorption isotherm is not Lipschitz but just Hölder continuous. To deal with this, we perform a regularization step. The convergence of the scheme is analyzed. An explicit order of convergence depending only on the regularization parameter, the time step, and the mesh size is derived. We give also a sufficient condition for the quadratic convergence of the Newton method. Finally, relevant numerical results are presented.     

A study on iterative methods for solving Richards’ equation

This work concerns linearization methods for efficiently solving the Richards equation, a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media. The discretization of Richards’ equation is based on backward Euler in time and Galerkin finite elements in space. The most valuable linearization schemes for Richards’ equation, i.e. the Newton method, the Picard method, the Picard/Newton method and the L-scheme are presented and their performance is comparatively studied. The convergence, the computational time and the condition numbers for the underlying linear systems are recorded. The convergence of the L-scheme is theoretically proved and the convergence of the other methods is discussed. A new scheme is proposed, the L-scheme/Newton method which is more robust and quadratically convergent. The linearization methods are tested on illustrative numerical examples.     

A parallel, implicit, cell‐centered method for two‐phase flow with a preconditioned Newton–Krylov solver

A new parallel solution technique is developed for the fully implicit three‐dimensional two‐phase flow model. An expandedcell‐centered finite difference scheme which allows for a full permeability tensor is employed for the spatial discretization, and backwardEuler is used for the time discretization. The discrete systems are solved using a novel inexact Newton method that reuses the Krylov information generated by the GMRES linear iterative solver. Fast nonlinear convergence can be achieved by composing inexact Newton steps with quasi‐Newton steps restricted to the underlying Krylov subspace. Furthermore, robustness and efficiency are achieved with a line‐search backtracking globalization strategy for the nonlinear systems and a preconditioner for each coupled linear system to be solved. This inexact Newton method also makes use of forcing terms suggested by Eisenstat and Walker which prevent oversolving of the Jacobian systems. The preconditioner is a new two‐stage method which involves a decoupling strategy plus the separate solutions of both nonwetting‐phase pressure and saturation equations. Numerical results show that these nonlinear and linear solvers are very effective.     

Efficient reservoir history matching using subspace vectors

In this paper, we describe a method of history matching in which changes to the reservoir model are constructed from a limited set of basis vectors. The purpose of this reparameterization is to reduce the cost of a Newton iteration, without altering the final estimate of model parameters and without substantially slowing the rate of convergence. The utility of a subspace method depends on several factors, including the choice and number of the subspace vectors to be used. Computational gains in efficiency result partly from a reduction in the size of the matrix system that must be solved in a Newton iteration. More important contributions, however, result from a reduction in the number of sensitivity coefficients that must be computed, reduction in the dimensions of the matrices that must be multiplied, and elimination of matrix products involving the inverse of the prior model covariance matrix. These factors affect the efficiency of each Newton iteration. Although computation of the optimal set of subspace vectors may be expensive, we show that the rate of convergence and the final results are somewhat insensitive to the choice of subspace vectors. We also show that it is desirable to start with a small number of subspace vectors and gradually increase the number at each Newton iteration until an acceptable level of data mismatch is obtained.     

Solution of Kepler’s Equation with Machine Precision

Astronomy Reports - An algorithm for the numerical solution of Kepler’s equation with machine precision is presented. The convergence of the iterative sequence of Newton’s method is...     

滑坡动态力学监测及破坏过程案例分析

边坡临滑预警一直是地灾研究的难点与热点问题。本文采用一种力学监测方法(牛顿力监测)对雅安宝兴县某傍山公路边坡进行监测,该边坡位于唐包滑坡老滑坡体下缘边界处。经过4个月的连续监测,获取了大量监测数据,并成功预报了两次局部滑坡。本文首先整合牛顿力监测数据和降雨量监测数据,再将监测曲线与滑坡演化过程进行对比分析,揭示滑坡过程中的力学演化规律,对降雨条件下诱发滑坡的原因进行了分析。然后对牛顿力监测预警成功的案例其临滑预警时长与滑坡体量间的关系进行拟合,发现存在明显的正相关关系。最后讨论了牛顿力监测方法与斋藤模型之间的关联性以及优劣势,并根据各自的特点提出了由面到点的监测预警思路。通过分析,牛顿力监测曲线与滑坡演化过程能较好对应,并可将土质滑坡分为3阶段:(1)牛顿力上升阶段; (2)牛顿力突降阶段; (3)滑坡阶段。本文为牛顿力监测系统的推广提供了实践经验,并为力学监测与位移监测结合的研究提供一个新的思路。     

Application and performances of unconstrained optimization methods in seafloor AVO inversion

Seafloor elastic parameters are important for seafloor engineering and geophysical detection beneath the seafloor. We have proposed to use AVO (amplitude variation with offset) theory to estimate seafloor elastic parameters. However, the previous inversion methods are time-consuming. To improve the computing efficiency, we try to solve the inverse problem as an unconstrained optimization problem in this paper. Three kinds of classical unconstrained optimization methods are applied to seafloor AVO inversion, including the steepest descent method, the Newton’s method, and the conjugate gradient method. Then, we design different initial models to test the convergence behaviors of the three methods. Numerical tests show that the perturbation level of the initial models and the noise level of the observed data have a significant effect on the convergence performances of the three methods. Even for the same perturbation and noise levels, the convergence performances differ with different combinations of the perturbed initial elastic parameters. All three methods have higher computing efficiency than the previous methods. This research also offers a strategy to choose a proper optimization method for a specific case in real seafloor AVO inversion.