An improved interpolating element-free Galerkin method with a nonsingular weight function for two-dimensional potential problems

In this paper, an improved interpolating moving least-square （IIMLS） method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker 5 function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. The number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square （MLS） approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin （IIEFG） method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin （EFG） method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.

An improved boundary element-free method (IBEFM) for two-dimensional potential problems

The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （BEFM）, combining the boundary integral equation （BIE） method with the IMLS method, the improved boundary element-free method （IBEFM） for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker ~ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.

A moving Kriging interpolation-based boundary node method for two-dimensional potential problems

In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.

A new complex variable element-free Galerkin method for two-dimensional potential problems

In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-free Galerkin （ICVEFG） method for two-dimensional potential problems, is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square （CVMLS） approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.

The dimension split element-free Galerkin method for three-dimensional potential problems

This paper presents the dimension split element-free Galerkin （DSEFG） method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares （IMLS） approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

ANALYTICAL TREATMENT OF BOUNDARY INTEGRALS IN DIRECT BOUNDARY ELEMENT ANALYSIS OF PLAN POTENTIAL AND ELASTICITY PROBLEMS

An analytical scheme, which avoids using the standard Gaussian approximate quadrature to treat the boundary integrals in direct boundary element method (DBEM) of two-dimensional potential and elastic problems, is established. With some numerical results, it is shown that the better precision and high computational efficiency, especially in the band of the domain near boundary, can be derived by the present scheme.

NOVEL REGULARIZED BOUNDARY INTEGRAL EQUATIONS FOR POTENTIAL PLANE PROBLEMS

The universal practices have been centralizing on the research of regularization to the direct boundary integal equations （DBIEs）. The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value （CPV） and Hadamard-finite-part （HFP） integrals are established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system.

The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems

Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.

The Solution to Current Psychosocial Problems and the “Unfulfilled Enlightenment” of Modernity in the New Era

The transition period of Chinese society has spawned many psychosocial problems in China,which are characterized by high incidence,universality and growth. Compared with social and economic development,the devel-opment of social psychology has been relatively slow for a long time,which has led to the prevalence of psychosocial problems and the lack of modernity cultivation in China's modernization. Xi Jinping theory on socialism with Chi-nese characteristics(SCC) in the new era is a scientific plan for the all - round development and modernization of SCC,and it contains rich ideas of modernity. It is also the ideological inheritance and innovation of Marx's "full and free development of human beings",and the basic strategy of cultivating the modernity of the new era. Therefore,it is an important way to solve the current psychosocial problems in China through the Marxist theory and the "unfulfilled enlightenment" of the theory of the new era.

Estimation on wetland loss and its restoration potential in Modern Yellow River Delta,Shandong Province of China

Wetland is one of the most important ecosystems with varied functions and structures,and its loss has been a major issue.Wetland loss in Modem Yellow River Delta(MYRD) becomes a serious environmental problem,so its restoration attracts a great deal of attention from academia and governments.This article proposes a GIS-based multi-criteria comprehensive evaluation methodology for potential estimation of wetland restoration,using MYRD as an example.The model uses four kinds of data(hydrology,terrain,soil,and land use) and could be adapted by planners for use in identifying the suitability of locations as wetland mitigation sites at any site or region.In the application of the model in the MYRD,the research developed a lost wetland distributed map taking the better wetland situation of 1995 as the reference,and elevated the overall distribution trends of wetland restoration potential based on wetland polygon.The results indicated that the total area of wetland loss from 1995 to 2014 was 568.12 km^2,which includes 188.83 km^2 natural wetland and 21.80 km^2 artificial wetland,respectively.The areas of lost wetland with low,middle,and high resilience ability are 126.82 km^2,259.92 km^2,and 119.59 km^2,occupying 25.05%,51.33%,and 23.62%,respectively.The high-restoration-potential wetland included98.47 km^2 of natural wetland and 21.12 km^2 of artificial wetland,which are mainly bush,reed,and ponds.The highrestoration-potential wetland is mainly distributed in the vicinity of Gudong oil field,the Yellow River Delta protected areas,and the eastern sides of Kenli county and Dongying city.

Potential theory method for 3D crack and contact problemsof multi-field coupled media： A survey

This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media. This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy, from which, however, the results for the isotropic case can be readily obtained.

A Potential-Reduction Algorithm for Linear Complementarity Problems

Feasible-interior-point algorithms start from a strictly feasible interior point, but infeassible-interior-point algorithms just need to start from an arbitrary positive point, we give a potential reduction algorithm from an infeasible-starting-point for a class of non-monotone linear complementarity problem. Its polynomial complexity is analyzed. After finite iterations the algorithm produces an approximate solution of the problem or shows that there is no feasible optimal solution in a large region. Key words linear complementarity problems - infeasible-starting-point - P-matrix - potential function CLC number O 221 Foundation item: Supported by the National Natural Science Foundation of China (70371032) and the Doctoral Educational Foundation of China of the Ministry of Education (20020486035)Biography: Wang Yan-jin (1976-), male, Ph. D candidate, research direction: optimal theory and method.

REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS

A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The factor leading to the singularity was transformed out of the integral representations with integration by parts, so non-singular regularized formulas were presented for the two forms of integrals. Furthermore, quadratic elements are used in addition to linear ones. The quadratic element very close to the internal point can be divided into two linear ones, so that the algorithm is still valid. Numerical examples demonstrate the effectiveness and accuracy of this algorithm. Especially for problems with curved boundaries, the combination of quadratic elements and linear elements can give more accurate results.

Study on Potential Problems of Shandong Economic Forest Construction and Standardization Construction Scheme

Shandong is a culturally powerful province with excellent natural geographical condition and the warm temperate monsoon climate creates abundant benefits to the agricultural development there.In 2009,Shandong administration bureau of Yellow River economic development held the forum on related issues of national new countryside industry office planning to build economic forest base around the Yellow River in Shandong.The primary intention was settled and the construction of Shandong Economic Forest was formally started.Although impressive progress has been achieved in recent years,there also exists potential problems in the construction of economic forest,among which heavy metal pollution and soil acidification are the worst,causing huge damage to the physiological health of the consumers of economic forest.The writer proposes the countermeasures against standardization construction of economic forest.Scientific management is to be adopted to improve the professional skills of the employees in economic forest and brand innovation should be emphasized to quicken the quality certification of the products of economic forest.Besides,standard production demonstration is to be created and promoted in order to boost scale development.Furthermore,mechanism innovation is also to be stressed and forestry specialized cooperation organizations should be largely supported.

Four Nontrivial Solutions for Kirchhoff Problems with Critical Potential, Critical Exponent and a Concave Term

In this paper, we consider the existence of multiple solutions to the Kirchhoff problems with critical potential, critical exponent and a concave term. Our main tools are the Nehari manifold and mountain pass theorem.

Element Free Gelerkin Method for 2-D Potential Problems

A meshfree method namely, element free Gelerkin (EFG) method, is presented in this paper for the solution of governing equations of 2-D potential problems. The EFG method is a numerical method which uses nodal points in order to discretize the computational domain, but where the use of connectivity is absent. The unknowns in the problems are approximated by means of connectivity-free technique known as moving least squares (MLS) approximation. The effect of irregular distribution of nodal points on the accuracy of the EFG method is the main goal of this paper as a complement to the precedent researches investigated by proposing an irregularity index (II) in order to analyze some 2-D benchmark examples and the results of sensitivity analysis on the parameters of the method are presented.

Exact Solutions of Klein-Gordon Equation with Scalar and Vector Rosen-Morse-Type Potentials

We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.

Mathematical model and numerical method for spontaneous potential log in heterogeneous formations

This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has beer/ shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method.

Problems and Countermeasures for the Development of Modern Agriculture in Henan Province,China

Current status of agricultural development in Henan Province of China is analyzed,showing that the agricultural production condition is increasingly improved;food production reaches to a new level;characteristic agriculture and green agricultural production begin to take shape;the level of agricultural mechanization is significantly improved;and the agricultural standardization and opening degree are enhanced.Problems in the development of modern agriculture in Henan Province are pointed out,such as the prominent pressure on the increase in grain production,the great risks in food safety,the tough employment situation,and the weak ecological environment.Countermeasures for developing the modern agriculture in Henan Province are put forward,including stabilizing cultivation area,optimizing structure,relying on science and technology,doing everything possible to ensure the increase in grain production,strengthening the supervision on food safety,actively exploring the employment space of modern agriculture,and protecting ecological environment by modern agriculture.

Higher-Order Line Element Analysis of Potential Field with Slender Heterogeneities

Potential field due to line sources residing on slender heterogeneities is involved in various areas,such as heat conduction,potential flow,and electrostatics.Often dipolar line sources are either prescribed or induced due to close interaction with other objects.Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect.In the present work,we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities.In a benchmark example of two parallel rods,we compare the line element solution with the boundary element solution to show the accuracy as a function in terms of rods distance.Furthermore,we use more complicated examples to demonstrate the capability of the line element technique.