On the Application of the Adomian’s Decomposition Method to a Generalized Thermoelastic Infinite Medium with a Spherical Cavity in the Framework Three Different Models

A mathematical model is elaborated for a thermoelastic infinite body with a spherical cavity.A generalized set of governing equations is formulated in the context of three different models of thermoelasticity:the Biot model,also known as“coupled thermoelasticity”model;the Lord-Shulman model,also referred to as“generalized thermoelasticity with one-relaxation time”approach;and the Green-Lindsay model,also called“generalized thermoelasticity with two-relaxation times”approach.The Adomian’s decomposition method is used to solve the related mathematical problem.The bounding plane of the cavity is subjected to harmonic thermal loading with zero heat flux and strain.Numerical results for the temperature,radial stress,strain,and displacement are represented graphically.It is shown that the angular thermal load and the relaxation times have significant effects on all the studied fields.

A CLASS OF DECOMPOSITION METHODS FOR LARGE-SCALE SYSTEMS OF NONLINEAR EQUATIONS

This paper presents a new decomposition method for solving large-scale systems of nonlinear equations. The new method is of superlinear convergence speed and has rather less computa tional complexity than the Newton-type decomposition method as well as other known numerical methods, Primal numerical experiments show the superiority of the new method to the others.

DOMAIN DECOMPOSITION METHODS FOR SOLVING PDE's ON MULTI-PROCESSORS

In this paper, we discuss the parallel domain decomposition method(DDM)for solving PDE's on parallel computers. Three types of DDM: DDM with overlapping, DDM without overlapping and DDM with fictitious component are discussed in a uniform framework. The eonvergence of the asynchronous parallel algorithms based on DDM are discussed.

Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems

In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.

Restarted Adomian Decomposition Method for Solving Volterra’s Population Model

In this paper, we used an efficient algorithm to obtain an analytic approximation for Volterra’s model for population growth of a species within a closed system, called the Restarted Adomian decomposition method (RADM) to solve the model. The numerical results illustrate that RADM has the good accuracy.

Analytical Solution of Two Extended Model Equations for Shallow Water Waves By Adomian’S Decomposition Method

In this paper, we consider two extended model equations for shallow water waves. We use Adomian’s decomposition method (ADM) to solve them. It is proved that this method is a very good tool for shallow water wave equations and the obtained solutions are shown graphically.

Application of Adomian’s Decomposition Method for the Analytical Solution of Space Fractional Diffusion Equation

Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by Adomian’s decomposition method (ADM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present techniques. The present method performs extremely well in terms of efficiency and simplicity.

Adomian Decomposition Method for Solving Goursat's Problems

In this paper, Goursat’s problems for: linear and nonlinear hyperbolic equations of second-order, systems of nonlinear hyperbolic equations and fourth-order linear hyperbolic equations in which the attached conditions are given on the characteristics curves are transformed in such a manner that the Adomian decomposition method (ADM) can be applied. Some examples with closed-form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient.

An Efficient Decomposition Method for Solving Bratu’s Boundary Value Problem

The purpose of this paper is to employ the Adomian Decomposition Method (ADM) and Restarted Adomian Decomposition Method (RADM) with new useful techniques to resolve Bratu’s boundary value problem by using a new integral operator. The solutions obtained in this way require the use of the boundary conditions directly. The obtained results indicate that the new techniques give more suitable and accurate solutions for the Bratu-type problem, compared with those for the ADM and its modification.

基于S-R和分解定理的二维几何非线性问题的虚单元法求解

应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。

Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion

Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.

中国人均CO_2排放水平地区差异的成因分析——基于GINI系数和回归的Shapley Value分解方法

根据2000-2011年中国省际面板数据,以GINI系数为衡量指标,测算了人均CO2排放水平的地区差异,分析了人均CO2排放水平随时间的演变趋势,在此基础上采用基于回归的Shapley Value分解方法,对中国人均CO2排放水平地区差异形成原因进行了考察,探究各影响因素对差异程度的影响水平,从而为有效缩小地区差异和制定CO2减排政策提供有益的参考。结果表明：人均能源消费量因素的影响程度最大,平均贡献率为72.80%,各省份的经济发展水平和产业结构是人均CO2排放水平省际差异的第二大贡献因素,其平均贡献率依次为8.01%与10.20%,且在不同的时间段其结果有所不同。排在第四位和第五位的因素分别是城镇化水平和对外开放水平,二者都是影响人均CO2排放水平省际差异的重要因素,平均贡献率分别达到5.17%与3.81%。

中国寿险业区域发展均衡性研究——基于shapley值分解法

运用2003—2012年的省际面板数据,建立了中国寿险业区域发展差异的回归方程。研究发现,教育水平和社会保障覆盖率的省际差异对于中国寿险业的区域发展差异不存在显著影响,中国寿险业区域发展的差距呈现缩小趋势。基于回归方程,对中国寿险业区域发展差异进行了不平等分解,结果显示,各地区经济发展水平和城镇化水平是其寿险业发展差异的关键因素;区域金融业的发展差异对区域寿险业的影响,随着各地寿险业的不断发展而愈发明显。最后针对研究结论提出了相应的对策建议。

A Comparative Study of Adomain Decompostion Method and He-Laplace Method

In this paper, we present a comparative study between the He-Laplace and Adomain decomposition method. The study outlines the significant features of two methods. We use the two methods to solve the nonlinear Ordinary and Partial differential equations. Laplace transformation with the homotopy method is called He-Laplace method. A comparison is made among Adomain decomposition method and He-Laplace. It is shown that, in He-Laplace method, the nonlinear terms of differential equation can be easy handled by the use He’s polynomials and provides better results.

Calculation of Combustion Products by the New Iteration Method of Non-linear Equations

For a specific combustion problem involving calculations of several species at the equilibrium state, it is simpler to write a general computer program and calculate the combustion concentration. Original work describes, an adaptation of Newton-Raphson method was used for solving the highly nonlinear system of equations describing the formation of equilibrium products in reacting of fuel-additive-air mixtures. This study also shows what possible of the results. In this paper, to be present the efficient numerical algorithms for. solving the combustion problem, to be used nonlinear equations based on the iteration method and high order of the Taylor series. The modified Adomian decomposition method was applied to construct the numerical algorithms. Some numerical illustrations are given to show the efficiency of algorithms. Comparisons of results by the new Matlab routines and previous routines, the result data indicate that the new Matlab routines are reliable, typical deviations from previous results are less than 0.05%.

带副翼的翼身组合体绕流的Euler和N-S方程解

将对接分区网格与分区求解算法结合 ,有效地求解了带副翼偏转的翼身组合体绕流的N S方程 .数值方法中选用VanLeer分裂格式离散无粘通量项 ,采用中心差分格式来离散粘性通量项 .分区交界面采用了一种满足通量守恒的内边界耦合条件 .数值算例表明该方法是求解带操纵面偏转的翼身组合体绕流的有效方法 .

带副翼三维机翼绕流的N-S方程解

提出了一种求解带副翼偏转三维机翼绕流的Ｎ－Ｓ方程计算方法。采用对接分区网格与分区求解算法的结合，有效地求解绕此外形的复杂流动。提出了一种满足通量守恒的内边界耦合条件。数值方法中选用ｖａｎＬｅｅｒ分裂格式离散无粘通量项，并构造了一种Ｌｉｍｉｔｅｒ函数以保证ＴＶＤ性质，采用中心差分格式来离散粘性通量项。数值算例表明该方法是求解带操纵面偏转的机翼绕流的有效方法。

应用广义S变换频谱分解技术识别松辽盆地三肇凹陷泉头组三-四段的河道砂体

松辽盆地三肇凹陷东部地区泉头组三-四段储层以河道砂岩为主,具有单层厚度薄、横向变化快等特点。本文将基于广义S变换的频谱分解技术应用于厚度为1～5 m的河道砂体的识别,取得了良好的效果。据此编制了研究区的河道砂体预测图,经钻井验证,证明它是对薄层河道砂体有较强识别能力的有效技术。

基于广义S变换模时频矩阵的局部放电特高频信号去噪方法

为有效抑制局部放电特高频信号中的噪声干扰,提出一种基于广义S变换模时频矩阵的去噪方法。基于二维模时频矩阵,采用区域最大能量法提取周期性窄带干扰的特征量,并通过矩阵逆向分离将其去除;采用奇异值分解去噪方法抑制信号中的高斯白噪声。使用该方法对仿真信号和实验室实测信号进行去噪处理,并与传统方法去噪结果进行对比。结果表明,所提方法能有效抑制局部放电信号特高频信号中的噪声,同时更好地保留了原始局部放电信号特征。对现场实测信号进行去噪处理,与传统方法相比,该方法具有较高的噪声抑制比和较低的幅值衰减比,可以有效提取局部放电超高频信号。

基于S-R和分解定理的三维几何非线性无网格法

S-R(strain-rotation)和分解定理克服了经典有限变形理论的一些缺点,使其可以为几何非线性数值分析提供可靠的理论基础.对于大变形问题,由于无网格法(element-free method)避免了对单元网格的依赖,从而从根本上避免了有限单元法(finite element method,FEM)的单元畸变问题,保证了求解精度.因此,将无网格法和S-R和分解定理结合起来势必能建立一套更加合理可靠的几何非线性数值计算方法.目前基于S-R定理的无网格数值方法研究较少并且只能用于二维平面问题的求解,但实际上绝大多数问题都必须以三维模型来进行处理,因此建立适用于三维情况的S-R无网格法是非常有必要的.本文给出了适用于三维情况的S-R无网格法:采用由更新拖带坐标法和势能率原理推导出来的增量变分方程,利用基于全局弱式的无网格Galerkin法(EFG)得到了用于求解三维空间问题的离散格式.利用MATLAB编制三维S-R无网格法程序,对受均布载荷的三维悬臂梁和四边简支矩形板结构的非线性弯曲问题进行了计算.最后将所得的数值结果与已有文献进行了比较,验证了本文的三维S-R无网格数值算法的合理性、有效性和准确性.本文的三维S-R无网格数值算法可以作为一种可靠的三维几何非线性数值分析方法.