Solution of solute transport in unsaturated porous media by the method of characteristics

A degenerate convection‐diffusion problem is approximated using the scheme that is based on the relaxation method and also the method of characteristics. A mathematical model for solute transport in unsaturated porous media is included. Moreover, multiple site adsorption is considered. Convergence of the scheme is proved and numerical experiments in 1D and 2D are presented. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 732–761, 2003.     

动态特性的参数设计在差示光度法测金中的应用

本文提出对动态特性参数设计使用相关系数与信噪比作为内表指标进行分析 ,并使用该分析方法优化了差示光度法测较高浓度金矿样的试验条件。     

求动态规划最优解的一种简便新方法——图解法

离散型确定性的动态规划问题，是运筹学规划论中一个重要的组成部分，其内容包含的问题比较多．求其最优解的方法，叫逆序法(又叫回推法)．本提出一种统一的解法——图解法．其优点是：方便简便，计算简单．     

二维热传导型半导体瞬态问题的二次元特征有限体积元方法

将特征线方法与有限体积元方法相结合,采用Lagrange型分片二次多项式空间和分片常数函数空间分别作为试探函数和检验函数空间构造了二维热传导型半导体瞬态问题的全离散二次元特征有限体积元格式,并进行误差分析,得到了次优阶L^2模误差估计结果．     

动态特性稳健设计中的响应曲面分析

针对含有单个噪声因素的动态特性的稳健设计，建立了响应曲面模型，给出了模型的统计分析方法，得到了有关统计量的统计分布及效的估计。     

Derivation of the method of characteristics for the fluid dynamic solution of flow advection along porous wall channels

This paper describes in detail a novel formulation of the method of characteristics for its application to solve one-dimensional compressible unsteady non-homentropic flow advected along porous wall channels. In particular, the method is implemented into a wall-flow monolith Diesel particulate filter model whose purpose is the pressure drop prediction. The flow inside the monolith channels is considered to be one-dimensional and the flow through the porous wall treated as a source term agree with the Darcy’s law. The flow dynamic behaviour at internal nodes of the channels is solved by means of shock capturing methods, whereas the end nodes, or boundary conditions, are solved applying the method of characteristics. The derived solution in this study of the Riemann variables and the entropy level includes the variation along the space–time plane due to cross-section area changes, friction and heat transfer as traditionally stated, but also takes into account the key influence on every line of the flow leaving or entering to the channels through the porous walls.     

Analysis of incompressible miscible displacement in porous media by characteristics collocation method

Miscible displacement of one incompressible fluid by another in a porous medium is modelled by a coupled system of two partial differential equations. The pressure equation is elliptic, whereas the concentration equation is parabolic but normally convection‐dominated. In this article, the collocation scheme is used to approximate the pressure equation and another characteristics collocation scheme to treat concentration equation. Existence and uniqueness of solutions of the algorithm are proved. Optimal order error estimate is demonstrated. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

An approximation of incompressible miscible displacement in porous media by mixed finite elements and symmetric finite volume element method of characteristics

A nonlinear system of two coupled partial differential equations models miscible displacement of one incompressible fluid by another in a porous medium. A sequential implicit time‐stepping procedure is defined, in which the pressure and Darcy velocity of the mixture are approximated by a mixed finite element method and the concentration is approximated by a combination of a modified symmetric finite volume element method and the method of characteristics. Optimal order convergence in H¹ and in L² are proved for full discrete schemes. Finally, some numerical experiments are presented. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Efficient dynamic programming implementations of Newton's method for unconstrained optimal control problems

Naive implementations of Newton's method for unconstrainedN-stage discrete-time optimal control problems with Bolza objective functions tend to increase in cost likeN ³ asN increases. However, if the inherent recursive structure of the Bolza problem is properly exploited, the cost of computing a Newton step will increase only linearly withN. The efficient Newton implementation scheme proposed here is similar to Mayne's DDP (differential dynamic programming) method but produces the Newton step exactly, even when the dynamical equations are nonlinear. The proposed scheme is also related to a Riccati treatment of the linear, two-point boundary-value problems that characterize optimal solutions. For discrete-time problems, the dynamic programming approach and the Riccati substitution differ in an interesting way; however, these differences essentially vanish in the continuous-time limit.This work was supported by the National Science Foundation, Grant No. DMS-85-03746.     

A dynamic meshless method for the least squares problem with some noisy subdomains

The interpolation method by radial basis functions is used widely for solving scattered data approximation. However, sometimes it makes more sense to approximate the solution by least squares fit. This is especially true when the data are contaminated with noise. A meshfree method namely, meshless dynamic weighted least squares (MDWLS) method, is presented in this paper to solve least squares problems with noise. The MDWLS method by Gaussian radial basis function is proposed to fit scattered data with some noisy areas in the problem’s domain. Existence and uniqueness of a solution is proved. This method has one parameter which can adjusts the accuracy according to the size of noises. Another advantage of the developed method is that it can be applied to problems with nonregular geometrical domains. The new approach is applied for some problems in two dimensions and the obtained results confirm the accuracy and efficiency of the proposed method. The numerical experiments illustrate that our MDWLS method has better performance than the traditional least squares method in case of noisy data.     

基于分段损失分布法和Copula的银行操作风险集成度量

多个风险单元的集成度量是银行操作风险管理的关键步骤之一。立足于操作风险的“厚尾”、“截断”性,从分段损失分布法的视角出发,探讨操作风险集成度量的模式和数值方法。首先,引入两阶段损失分布法来拟合单个风险单元边际损失分布,用双截尾分布代替传统的完整分布来刻画“高频低损”损失数据的双截断特性,利用POT模型捕获“低频高损”事件的厚尾特性。再次,基于分段建模思路,对传统度量过程中边际分布为单一、完整分布的Copula模型进行了扩展,研究边际分布为分段分布、截尾分布条件下使用Copula函数集成度量操作风险的框架和步骤,并设计了Monte Carlo模拟算法。最后,以实证分析的形式验证所构建模型。通过对中国商业银行416个操作风险损失数据的实证分析,结果表明分段分布、截尾分布能对单个风险单元边际分布有更好的拟合效果,能减小由于分布选择不当而引发的模型风险。分段度量视角下Copula函数的引入能灵活处理多个操作风险单元间的相依结构,使风险度量结果更为合理。     

A conservative extension of the method of characteristics for 1-D shallow flows

The method of characteristics (MOC) has been used for a long time in open channels and pipes flows. It is based on non-conservative equations, and hence it cannot be used directly for solving discontinuous shallow flows. In this paper we develop a conservative version of the MOC scheme for 1-D shallow flows by imposing the conservation law at the interpolation step. The conservation property of the scheme ensures the production of an accurate shock modeling and enables the MOC scheme to simulate dam-break type flows. By using a proper interpolation function, the proposed method can also produce quite accurate low-oscillatory results. A number of challenging test cases show considerable improvement compared to the traditional non-conservative MOC scheme in the case of dam-break type and trans-critical flow simulations.     

A finite element modified method of characteristics for convective heat transport

We propose a finite element modified method of characteristics for numerical solution of convective heat transport. The flow equations are the incompressible Navier‐Stokes equations including density variation through the Boussinesq approximation. The solution procedure consists of combining an essentially non‐oscillatory modified method of characteristics for time discretization with finite element method for space discretization. These numerical techniques associate the geometrical flexibility of the finite elements with the ability offered by modified method of characteristics to solve convection‐dominated flows using time steps larger than its Eulerian counterparts. Numerical results are shown for natural convection in a squared cavity and heat transport in the strait of Gibraltar. Performance and accuracy of the method are compared to other published data. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Determination of some dynamic characteristics of forming bone callus by the induced vibration method

Conclusions 1. Upon maturation, bone callus not only goes through a series of morphological chantes but also changes in mechanical properties. This is true primarily for an increase in the elasticity modulus.2. The specific energy of dispersion and loss modulus have maxima which occur after 25 to 30 days. This behavior is apparently related to the fact that bone callus at this period has the nature of spongy bone tissue. For compact bone tissue, on the other hand, these values are equal to zero.3. The area of the hysteresis loop is almost completely independent of the frequency upon cyclic stressing.4. The elasticity modulus is proportional to the x-ray density of the samples, which thus may serve as an objective criterion of the degree of maturity of callus.Smolensk State Medical Institute. Translated from Mekhanika Polimerov, No. 5, pp. 896–900, September–October, 1977.     

New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values

New variants of the generalized level method for minimization of convex Lipschitz functions on a compact set with a nonempty interior are proposed. These variants include the well-known generalized and classical level methods. For the new variants, an estimate of the convergence rate is found, including the variants in which the auxiliary problems are solved approximately.     

介质与结构三维动力相互作用分析的半解析边界元—半解析有限元结合法

本文将半解析边界元一半解析有限无结合法用于介质与结构的动力相互作用研究:用半解析边界元法分析具有复杂地表面的半无限介质,用半解析有限元法分析具有任意截面形状的柱体结构,利用介质与结构交界面上的位移相容条件和力平衡条件,将介质与结构联系起来。联立京解上述半解析边界元方程和半解析有限元方程,对应每一时间步进,可同时求出介质与结构交界面上的位移、速度、加速度和相互作用力以及地表面的运动情况.与目前广泛研究的边界元—有限元结合法相比,本方法在介质与结构二个个区域各降低了一维空间,因而离散单元数和计算工作量大幅度减少,人工输入数据非常简单.文中还考虑了地下结构的长跨比效应、厚度效应和介质效应.     

Numerical-experimental investigation of resonance characteristics of a sounding board

The paper presents results of numerical and experimental investigations into the vibrations of thin-walled structures, considering such their features as the complexity of geometry, the laminated structure of walls, the anisotropy of materials, the presence of stiffeners, and the initial stresses. The object of the study is the sounding board of an acoustic guitar, the main structural material of which is a three-layer birch veneer. Based on the finite-element method, a corresponding calculation model is created, and the steady-state regimes of forced vibrations of the sounding board are investigated. A good correspondence between calculation results and experimental data is found to exist. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 399–410, May–June, 2007.