Strictly Analytic Calculation to the Renormalized Finite Quantity of the Photon Loop(Chain) Propagator

In the minimum electromagnetism coupling model of interaction between photon and electron(antielectron),Feynman convergence integral method is often used to deal with the finite quantity of one-loop correction scheme.After analyzing,discussing and researching the method,a new method is found.That is the great moment integral limitation method.Through the method,the relative result is obtained.     

Effective Method Calculating the Renormalized Finite Quantity of the Meson Loop Propagator (II)

In the Lorentz Invariable Coupling Model of interaction between pion and nucleon (antinucleon), by applying the complex function integral method, the authors have strictly calculated the one-dimensional integral, which is derived from the great momentum integral limit, of the renormalized finite quantity of one-loop propagator and chain propagator in the momentum renormalization scheme and gained the finally strict analysis result. At the last, they have detailed these numerical results of the renormalized finite quantity, and also done the relevant discussion about these minute radiation corrections.     

Effective Expressions for Momenta Normalization and Renormalization to e-(e) Loop propagator

In the electromagnetic minimum coupling model, the authors study the expansion of the finite quantity function in the momenta renormalization e - e loop propagator function, and find that if they use the matrix function expansion they can approach the separation of the finite quantity function, but also can get a strictly analytic solution for one dimension integral calculation method of it. This will give an effective new way to study the question about the exact solving to the renormalization finite quantity function.     

A Non-overlapping Domain Decomposition Method for Scattering Problems

In this paper, a domain decomposition method for the exterior Helmholtz problem is investigated. The unboundary domain is divided into some non overlapping subdomains. The natural integral operator is used as the artificial boundary conditions on the exterior boundary of the computational domains. The convergence of the algorithm is given in the sense of energy norm. Finally, the discrete problem is discussed and some numerical examples are presented.     

A BOUNDARY ELEMENT METHOD FOR THE NEUMANN PROBLEM OF HELMHOLTZ EQUATION BY USE OF A DOUBLE LAYER POTENTIAL IN R~3

This paper presents a new numerical solution for Neumann problem of Helmholtz equation in R~3. The expression of the solution for this problem is obtained by use of a double layer potential and it leads to a Fredholm boundary integral equation of the first kind. Then, the existence and unicity of the integral equation which is equivalent to the boundary value problem are obtained in a suitable Sobolev space. Finally, a variational form which is equivalent to the integral equation is applied to the construction of a finite element method and the error estimate is given.     

Complex Variable Function Solution of Stress and Displacement of Surrounding Rock Buried Deep Horseshoe-Shaped Tunnel Excavation

An analytical solution was presented for the stresses and displacements around horseshoe-shaped tunnel using Cauchy integral method and Optimization theory in an elastic half-plane. Since the depth of a tunnel was larger than the size of the tunnel, gravity loads were simplified as uniform normal loads along far-field boundary. Finite element model was used to verify the accuracy of analytical solutions. Comparison between the results of numerical analysis by finite element method and those from the closed solutions indicates that the closed solution is reliable and applicable for the stress and displacement field around horseshoe-shaped tunnel tunnels at great depth.     

A BOUNDARY ELEMENT METHOD FOR SOLVING DIRICHLET PROBLEM OF THE HELMHOLTZ EQUATION IN R~2

This paper presents a boundary element method for solving Dirichlet bou-ndary value problem of the Helmholtz equation in R~2.First,the existence andthe uniqueness of an extended solution for the problem are obtained.Then,thesolution is expressed in terms of simple layer potentials,and this expression,which is suitable to the interior as well as the exterior problem,leads to aboundary integral equation of the first kind.Finally,a finite element approachis applied to solve a variational form which is equivalent to the boundaryintegral equation.     

Exact Integration of Constant Element of Elastomer in Boundary Element Method

The boundary integral in Boundary Element Method affects the precision and the speed of the method. If the boundary integral with constant element, the nonsingular integrals are popularly calculated by the Gauss numerical integral, and the singular integrals are popularly calculated by the analytical integral. This paper presents an alternative way with Gauss formula to transform the double integral in elastic problem on 3-d into the linear integrals on the boundary of each subdomains, so that all the singular integrals and nonsingular integrals are calculated by analytical method. The example indicates that this method makes the precision and the speed of BEM improve.     

Exact Integration of Biharmonic Equation In Boundary Element Method

The boundary integral in Boundary Element Method effects the precision and the speed of the method. The boundary integrals are composed of the normal integrals and singular integrals. The normal integrals are popularly calculated by exact integral, and the singular integrals by the Gauss numerical integral. The singular integrals are low in precision when the source points approach the element. This paper presents an alternative way to transform the double integral in Biharmonic Equation on 3-d into the linear integrals on the boundary of each subdomain, so that all the singular integrals and nonsingular integrals are calculated by analytical method. It makes the precision and the speed of BEM improve.     

Galerkin Boundary Element Method for Direct Boundary Integral Eqution for Dirichlet Problem of 2-D Laplace Eqation

The direct boundary integral equation of two-dimensional Laplace equation for Dirichlet problem is(con-sidered).It is deduced by Green's formula and the fundamental solution.The most-used numerical method for solving(direct) boundary integral equation is collocation method,and seldom have been used the Galerkin scheme in this case.The direct boundary integral eqution is changed into the variational eqution.Using linear element,it is solved by Galerkin boundary method.In the variational eqution double integrations shall be carried out.The paper presents the analytical formula to calculate the inner integration and the Gaussian quadrature is used for the outer integration. The numerical experimentation proved thefaesibility and the efficiency.     

A Method for Online Measurement of Dielectric Loss of HV Capacitive Equipment Insulation

It is still a major problem for research on online monitor dielectric dissipation factor of high voltage equipment insulation. In the field, new methods are paid attention by researchers especially. At present, there are no methods achieving the satisfactory measurement results. Based on the voltage and current at their respective zero crossed points, this paper proposes the integral measurement method which can be used to measure the dielectric dissipation factor of high voltage capacitive apparatus. The formula for dielectric dissipation factor angle computation is deduced by theoretical analysis and the computation results are achieved by digital simulation. Meanwhile, this paper explains the effect to measurements by system frequency, content of harmonic and zero-drift and draws the relevant error curves. It also proposes the measures to reduce the integral measurement method presented in this paper,which can convert measurement of small signal into that of big signal and accurately measure dielectric loss of capacitive apparatus. It also possesses great anti jamming ability under strong electromagnetic interference environment. The online measurement system can detect the dielectric dissipation factor of high voltage equipment by the integral measurement method.     

Finite Element Reliability Analysis of the Stability of a Slope

The whole reliability index of a slope is derived through using the strength reduction method in the finite element analysis, which can make use of the former finite element program and can be used to both linear and nonlinear finite element analysis. The affection of the evaluation of derivative and the selection of reliability analysis methods is discussed, which shows that it is very important to select the type of limit state function of the slope stability. A new iterafive formula, which can consider the correlation of fundamental parameters, is proposed for FORM, and the convergence is very well.     

Apply the Hybrid Method of FDTD/MoM to Calculate the Radiation from the Aperture

This paper presents a hybrid method of the Finite-Difference Time-Domain(FDTD) and the method of moment(MoM) to compute the radiation from the aperture.The FDTD is a commonly used electromagnetic simulation way.It can solve the question with complex dielectric,but it is difficult(even cannot) for FDTD to calculate the far field because of large compute time and computer memory.So the authors can make use of the FDTD to get a large number of near electric field intensity,and then use the MoM,which based on electric field integral equation to compute the far field.Using this procedure,the authors solve the radiation of the box with apertures on one or more sides and reduced the compute time and the computer memory.     

A NEW BOUNDARY INTEGRAL EQUATION METHOD FOR SOLVING EXTERIOR BOUNDARY VALUE PROBLEMS OF THREE-DIMENSIONAL HELMHOLTZ EQUATION

This paper pressnts a new boundary integral equation method for solving exteri-or boundary value problems of three-dimensional Heimheltz equation by using the multiple reciproc-ity method.Firstly,integral representations of the solution in an exterior domain as well as on itsboundary,which have the peculiarity that integral kernels are infin ite seriesea developed from thenormal fundamental solution of Laplace equation and independent of the wavenumber,are given andproved under the Dirichlet condition.Then,based on the representation of the solution on the bound-ary,boundary integral equations for solving the Dirichlet and the Neumann boundary value prob-lems are obtained,and remarks for some problems concerned with solving these integral equationsnumerically are made.Finally, the advantages of the proposed method,as compared with the conven-tional boundary element methods,are summarized.     

APPLICATION OF INTEGRAL EQUATION TO THE STABILITY OF COMPRESSION BARS

This paper proposes integral equation to find the criticalbuckling load of compression bars in mechanics of materials,thus theresearch method of this problem has been improved.     

THE APPLICATION OF THE INTEGRAL EQUATION OF RING SHELLS IN INITIAL PARAMETER FORM TO THE PROBLEMS OF S-TYPE CORRUGATED TUBES

By means of the method of integral equation of ring shells ininitial parameter form,the problems of S-type corrugated tubes are studied inthis paper.Two calculating examples are given,and compared with the exactsolutions.     

Improvement Methods of Fuzzy Control with Intelligent Integration

Fuzzy controller can achieve satisfactory dynamic performance even for complicated process without mathematical model of the process.Its main imperfection is the existence of steady state error and ultimate oscillatory in the process output. This limits its application area. How to eliminate the steady state error while keep its good dynamic performance has been paid much attention. The strategy to introduce integral function to the conventional fuzzy control system is put forward in this paper to overcome the above problem. After expound two key factors on introducing integral action,an intelligent integral algorithm has been employed,and two methods on introduction of the intelligent integral to the fuzzy control system are proposed. Their characteristics and applied situations are summarized.     

Galerkin Boundary Element Method for Two-dimension Laplace Equation of Neumman Condition

The authors apply the Galenkin variational equation to solve the integral equation with hyper singularity, which can be deduced from the double layer solution for Neumann problem of Laplace equation. The scheme of partial integration in the sense of distributions is introduced to reduce the hyper singularity integral into a weak one with the boundary rotation of unknown function. The numerical implementation with linear boundary elements is presented. The numerical examples illustrate the feasibility and efficiency of the method.     

Quadrature Methods and Their Extrapolations for Solving Boundary Integral Equations of Steady Navier-Stokes Problems

This paper presents an iteration method of solving non linear boundary integral equations (BIE) of the plane Navier Stokes problem,which each step of the iteration is to solve a linear BIE of nonhomogeneous Stokes problem. Using the quadrature methods of [1],we give a new algorithm with a high order accuracy.The algorithm not only saves work,but also the accuracy can be improved by Richardson extrapolation.