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 II...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.展开更多
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 （B...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.展开更多
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 st...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.展开更多
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-f...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.展开更多
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 proble...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.展开更多
This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara...This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.展开更多
An adaptive cell-based domain integration method（CDIM） is proposed for the treatment of domain integrals in 3D boundary element method（BEM）. The domain integrals are computed in background cells rather than volume...An adaptive cell-based domain integration method（CDIM） is proposed for the treatment of domain integrals in 3D boundary element method（BEM）. The domain integrals are computed in background cells rather than volume elements. The cells are created from the boundary elements based on an adaptive oct-tree structure and no other discretization is needed. Cells containing the boundary elements are subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements; and the sub-cells outside the domain are deleted to obtain the desired accuracy. The method is applied in the 3D potential and elasticity problems in this paper.展开更多
In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four s...In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.展开更多
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-d...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.展开更多
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 esta...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.展开更多
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...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.展开更多
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 couple...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.展开更多
This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe...This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.展开更多
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 ...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.展开更多
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 administ...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.展开更多
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.
Considering an elastically coupled Brownian motors system in a two-dimensional traveling-wave potential, we investigate the effects of the angular frequency of the traveling wave, wavelength, coupling strength, free l...Considering an elastically coupled Brownian motors system in a two-dimensional traveling-wave potential, we investigate the effects of the angular frequency of the traveling wave, wavelength, coupling strength, free length of the spring, and the noise intensity on the current of the system. It is found that the traveling wave is the essential condition of the directed transport. The current is dominated by the traveling wave and varies nonmonotonically with both the angular frequency and the wavelength. At an optimal angular frequency or wavelength, the current can be optimized. The coupling strength and the free length of the spring can locally modulate the current, especially at small angular frequencies. Moreover, the current decreases rapidly with the increase of the noise intensity, indicating the interference effect of noise on the directed transport.展开更多
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 fr...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.展开更多
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 ...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.展开更多
We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent devel...We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Shanghai Leading Academic Discipline Project, China (Grant No. S30106)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No 10871124)Innovation Program of Shanghai Municipal Education Commission (Grant No 09ZZ99)Shanghai Leading Academic Discipline Project (Grant No J50103)
文摘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.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.10902076)the Natural Science Foundation of Shanxi Province of China(Grant No.2007011009)+1 种基金the Scientific Research and Development Program of the Shanxi Higher Education Institutions(Grant No.20091131)the Doctoral Startup Foundation of Taiyuan University of Science and Technology(Grant No.200708)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Shanghai Leading Academic Discipline Project, China (Grant No. S30106)the Innovation Fund Project for Graduate Student of Shanghai University,China (Grant No. SHUCX112359)
文摘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.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11102125)
文摘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.
基金supported by the Tianjin Municipal Science and Technology Program of China(No.23JCZDJC00070)。
文摘This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.
基金Financial support for the project from the National Natural Science Foundation of China(No.51609181)
文摘An adaptive cell-based domain integration method（CDIM） is proposed for the treatment of domain integrals in 3D boundary element method（BEM）. The domain integrals are computed in background cells rather than volume elements. The cells are created from the boundary elements based on an adaptive oct-tree structure and no other discretization is needed. Cells containing the boundary elements are subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements; and the sub-cells outside the domain are deleted to obtain the desired accuracy. The method is applied in the 3D potential and elasticity problems in this paper.
基金supported by 973 Key program and the Key Program from Beijing Educational Commission with No. KZ200910028002Program for New Century Excellent Talents in University (NCET)+4 种基金Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR-IHLB)The research of Sheng partially supported by NSFC (10671120)Shanghai Leading Academic Discipline Project: J50101The research of Zhang partially supported by NSFC (10671120)The research of Zheng partially supported by NSF-DMS-0603859
文摘In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.
基金supported by the National Natural Science Foundation of China (Grants 11571223, 51404160)Shanxi Province Science Foundation for Youths (Grant 2014021025-1)
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China (No.10571110)the Natural Science Foundation of Shandong Province of China (No.2003ZX12)
文摘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.
基金Project (No. 10372088) supported by the National Natural Science Foundation of China
文摘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.
基金Project supported by the National Natural Science Foundation of China (No. 10962004)the Special-ized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)+1 种基金the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)the Natural Science Foundation of Inner Mongolia (No. 2009BS0101)
文摘This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.
文摘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.
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.11875135)Quanzhou Scientific and Technological Foundation,China(Grant No.2018C085R)+1 种基金the Key Project of Beijing Institute of Graphic Communication,China(Grant No.Ea201702)the International Ability Improvement Project of Teaching Staff of Beijing Institute of Graphic Communication,China(Grant No.12000400001).
文摘Considering an elastically coupled Brownian motors system in a two-dimensional traveling-wave potential, we investigate the effects of the angular frequency of the traveling wave, wavelength, coupling strength, free length of the spring, and the noise intensity on the current of the system. It is found that the traveling wave is the essential condition of the directed transport. The current is dominated by the traveling wave and varies nonmonotonically with both the angular frequency and the wavelength. At an optimal angular frequency or wavelength, the current can be optimized. The coupling strength and the free length of the spring can locally modulate the current, especially at small angular frequencies. Moreover, the current decreases rapidly with the increase of the noise intensity, indicating the interference effect of noise on the directed transport.
基金Supported by the National Natural Science Foun dation of China(70371032)the Doctoral Educational Foundation 0f China of the Ministry of Education(20020486035)
文摘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.
文摘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.
基金The research of Gui-Qiang G.Chen was supported in part by the UK Engineering and Physical Sciences Research Council Awards EP/L015811/1,EP/V008854/1,EP/V051121/1the Royal Society-Wolfson Research Merit Award WM090014.
文摘We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.
