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
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
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
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
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
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
This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid.The layer densities are approximated b...This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid.The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid.With the proposed technique,the computation cost of collocation matrix entries is reduced from O(M2N4)to O(MN4),where N2 is the number of spherical harmonics(i.e.,size of the matrix)and M is the number of one-dimensional integration quadrature points.Numerical results demonstrate the spectral accuracy of the method.展开更多
A multi-variable non-singular boundary element method (MNBEM) is presented for 2-D potential problems. This method is based on the coincident collocation of non-singular boundary integral equations (BIEs) of the pot...A multi-variable non-singular boundary element method (MNBEM) is presented for 2-D potential problems. This method is based on the coincident collocation of non-singular boundary integral equations (BIEs) of the potential and its derivatives, where the nodal potential derivatives are considered independent of the nodal potential and flux. The system equation is solved to determine the unknown boundary potentials and fluxes, with high accuracy boundary nodal potential derivatives obtained from the solution at the same time. A modified Gaussian elimination algorithm was developed to improve the solution efficiency of the final system equation. Numerical examples verify the validity of the proposed algorithm.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
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
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 induce...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.展开更多
In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficie...In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.展开更多
This paper gives a detailed annlysis of the learner-based teaching in EFL （English as a Foreign Language）. It deals with how we arrive at learner-based teaching, what is the role of teachers and the textbooks, and t...This paper gives a detailed annlysis of the learner-based teaching in EFL （English as a Foreign Language）. It deals with how we arrive at learner-based teaching, what is the role of teachers and the textbooks, and the advantages and potential problems of learner-based teaching in EFL. The main principle in learner-based teaching is that all class activities can be done in using information that the learners themselves bring into the class. What is novel about learner-based teaching is the idea that all activities can be based on that wealth of experience, their grammar exercises, or translations, etc.. In learner-based teaching, we should know how to help students to teach themselves in learning English. In using a learner-based approach, the learners themselves are responsible for the information input, thereby ensuring its relevance and topicality for each particular group. The basic procedure has two stages First, learners prepare materials which are designed to practice. Second, these materials are passed to other learners in the class who carry out the activities. In this way, students obtain valuable language practice, not only while they are using the materials, but also while they are preparing them as well.展开更多
In China there are such middle school English language teachers who are not qualified enough in listening and speaking to fulfill the requirements in their work due to lack of formal pre-service training. Therefore an...In China there are such middle school English language teachers who are not qualified enough in listening and speaking to fulfill the requirements in their work due to lack of formal pre-service training. Therefore an EOP （English for Occupational Purposes） course is needed to improve their related skills. In the design of the course, factors, such as the course takers, overall aims, needs, length, content, materials, training modes and assessment, are taken into consideration to make the course a systematic one. Besides, the background theory and the supporting syllabus for the course are presented and the potential problems are also analyzed in the course outline.展开更多
A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding tim...A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding time-space boundary integral equation: is obtained. Then, a set of time domain boundary element equations with recurrence form is immediately formulated through discretization in both time and boundary. After having carried out the numerical calculation two solutions are found in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impact on the surface of a half-space fluid. The results show that the present method is more efficient than the previous ones.展开更多
In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann op...In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.展开更多
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.
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.
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.
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Financial support for this work was provided by the National Institutes of Health(grant number:1R01GM083600-01)Z.Xu is also partially supported by the Charlotte Research Institute through a Duke Postdoctoral Fellowship.
文摘This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid.The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid.With the proposed technique,the computation cost of collocation matrix entries is reduced from O(M2N4)to O(MN4),where N2 is the number of spherical harmonics(i.e.,size of the matrix)and M is the number of one-dimensional integration quadrature points.Numerical results demonstrate the spectral accuracy of the method.
基金Supported by the National Natural Science Foundation of China(No. 10102019) the Special Fund for Returning Scholars in the Chinese Academy of Sciences (No. 20010826214905) and the Ministry of Education of China
文摘A multi-variable non-singular boundary element method (MNBEM) is presented for 2-D potential problems. This method is based on the coincident collocation of non-singular boundary integral equations (BIEs) of the potential and its derivatives, where the nodal potential derivatives are considered independent of the nodal potential and flux. The system equation is solved to determine the unknown boundary potentials and fluxes, with high accuracy boundary nodal potential derivatives obtained from the solution at the same time. A modified Gaussian elimination algorithm was developed to improve the solution efficiency of the final system equation. Numerical examples verify the validity of the proposed algorithm.
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.
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.
文摘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.
文摘In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.
文摘This paper gives a detailed annlysis of the learner-based teaching in EFL （English as a Foreign Language）. It deals with how we arrive at learner-based teaching, what is the role of teachers and the textbooks, and the advantages and potential problems of learner-based teaching in EFL. The main principle in learner-based teaching is that all class activities can be done in using information that the learners themselves bring into the class. What is novel about learner-based teaching is the idea that all activities can be based on that wealth of experience, their grammar exercises, or translations, etc.. In learner-based teaching, we should know how to help students to teach themselves in learning English. In using a learner-based approach, the learners themselves are responsible for the information input, thereby ensuring its relevance and topicality for each particular group. The basic procedure has two stages First, learners prepare materials which are designed to practice. Second, these materials are passed to other learners in the class who carry out the activities. In this way, students obtain valuable language practice, not only while they are using the materials, but also while they are preparing them as well.
文摘In China there are such middle school English language teachers who are not qualified enough in listening and speaking to fulfill the requirements in their work due to lack of formal pre-service training. Therefore an EOP （English for Occupational Purposes） course is needed to improve their related skills. In the design of the course, factors, such as the course takers, overall aims, needs, length, content, materials, training modes and assessment, are taken into consideration to make the course a systematic one. Besides, the background theory and the supporting syllabus for the course are presented and the potential problems are also analyzed in the course outline.
基金This project is financially supported by the National Education Foundation of China.
文摘A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding time-space boundary integral equation: is obtained. Then, a set of time domain boundary element equations with recurrence form is immediately formulated through discretization in both time and boundary. After having carried out the numerical calculation two solutions are found in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impact on the surface of a half-space fluid. The results show that the present method is more efficient than the previous ones.
文摘In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.
