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.     

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.     

Galerkin Boundary Element Method for Laplace Equation

Galerkin method based on the variation principle is used to solve differential and integral equations. The boundary problem of Laplace equation is changed into the variational equation which is equivalent to the boundary integral equation. Using linear element, it is solved by Galerkin boundary element method. In computation of stiffness matrix, the exactly integral formula is used in the first order integral expression, The numerical integral formula is used in the second order integral expression. Thus the problem of calculation of double singular integral is carried out. The numerical experiments also prove this method is reliable. The error of Galerkin boundary element is tested with numerical experimentation.     

Analyzing the StiffnesS of Foundation Plate By BEM

This.paper derives the basic solution of elastic half-space foundation plate byHankel transform,Then its boundary integral equation of distortion is estabished,The paper discuss-es bou ndary integral equation on plate of fixxing and/or simple support boundary.Then a systemof algebraic equations for the boundary values are established.A numerical example is given , its re-sult shows that this Method is correct.     

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.     

Boundary Element Methods with Overlapping Domain Decomposition for Parabolic Problem

Boundary element method is a numerical method for solving partial differential equations. There are several formulations of boundary element method (BEM) applied to solve a parabolic differential equation.The approach,which employs time- dependent fundamental solution,allows longer time steps in time integration than other approaches,and this can cut down on time for computer implementation with high precision.Domain decomposition method,which decompose the domain that a given problem is to be solved into subdomains,has the advantages of reducing the large problem into smaller ones and reducing the complex problem into simpler ones,and allows parallel computing.An overlapping domain decomposition method is applied combining a boundary element formulation with time-dependent fundamental solution to solve a diffusion equation. Firstly, by domain decomposition, the problem divided into two problems on subdomains, and then the initial-Boundary problems are solved by boundry element method on each subdomain.Some numerical examples are presented to illustrate feasibility and efficiency of the method. The numerical experiments show that the convergence rate of the method is dependent with the overlapping degree of the subdomains.     

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.     

Finite Element Method of 3D Stable Heat Conduction of Steel Fluid in Continuous Casting Moulds

The heat transfer of steel fluid in continuous casting mould is a stable process and can be depicted with three-dimensional stable heat conduction equation depending on tension speed. The corresponding finite element equation, including the first, second and third boundary conditions, is deduced out with Galerkin residual method. The coded FEM program is used to analyze the temperature distribution of Q235 steel in continuous billet casting mould. The method proposed is a foundation of thermo-mechanical coupled analysis for the formation of solidified shells and stress in the shells in continuous casting.     

Remarks for Various Boundary IntegralEquations Reduced from the ExteriorNeumann Problem of Helmholtz Equation

This paper presents a discussion on various boundary integral equations reduced from the exterior Neumann problem of Helmholtz equation.The author analyses how the famous difficulty that some equations have no unique solution when the wave number k is an eigenvalue of an interior problem is arised in the course of reducing these equations from Helmholtz representations,and proposes a method of overcoming the difficulty,that is,introducing a direct boundary integral equation which has unique solution for all wave numbers k and is equivalent to the original boundary value problem.Besides,advantages and shortcomings for these integral equations are estimated respectively.     

Study on the Nonlinear Vibration System with Slow-changing Parameters

In this paper a posteriori error estimates for Galerkin approximation of general operator equations is firstly presented in the framework of Sobolev spaces. Then a practical posteriori error estimates formula for the adaptive boundary element method solving the acoustic scattering problem with a finite plane screen is obtained by triangulations. The mathematical model of this problem is the three dimensional Neumann boundary value problem of Helmholtz equation with finite plane boundary.     

BEM of Two-dimension Multiharmonic Equation and Its Applications

The paper discusses BEM of 2_dimension non_homogeneous multiharmonic equation.Under supposing non_homogeneous term is m_degree homonic,the integral in domain is transformed boundary integrals,and boundary integral equations are obtained correspondly.     

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.     

Positive Solutions of a Kind of Special Nonlinear Neumann Boundary Value Problems

The purpose of this paper is to consider a kind of special nonlinear Neumann boundary value problems. The kind of boundary value problems has not Green function. Using suitable transformation,we can change these problems to general Neumann boundary value problems. By applying integral equation and degree theory on cone,the existence of n positive solutions is proved for the kind of problems,where n is an arbitrary natural number.     

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.     

A Numerical Method for Transmission Line Equations

Transient analysis of transmission line has recently been received more attention because operating speeds in high-speed digital electronics are increasing. Transmission line equations are hyperbolic partial differential equations, firstly this paper deduces how to change transmission line equations into quasilinear differential equations , thus the transmission line equation numerical result is gotten by computing the differential formation of quasilinear differential equations. The constraint of voltage and current is be considered and lumped equivalent circuit mode at boundary network collaborated at the same time in finding boundary conditions. Finally the paper computes transient response of transmission line with two typical boundary conditions. Numerical result shows that this approach is an effective way. It is explicit algorithm with less CPU consumption which can get time field response directly. The agree-upon effective way does be frequency field method, however it could not get time response unless the numerical inverse laplace transformation (NILT) be introduced. Thus this approach is more effective than FFT algorithm.     

THE THREE-DIMENSIONAL CALCULATING MODEL OF INVERSE PROBLEM IN ECG AND A SPECIAL BOUNDRYVALUE PROBTEM

In this paper, the mathematical model and the three-dimensional finite clement formulation of inverse problem in electrocardiography (ECG) under a general inhomogcneous and anisotropic configuration of the torso conductor is focused on. The following points are especially considered: 1. The mathamatical model is described by a differential equation instead of the Fredholm integral equation. 2. A kind of special boundary value problem is defined as ill-posed boundary value problem. 3. A group of finite element formulation, in which the method that treats anisotropic medium, is built up. 4. The calculating method of ill-posed boundary value problem is discussed.     

INCREMENTAL FORM OF ENDOCHRONIC CONSTITUTIVE EQUATION AND ITS APPLICATIONS

An incremental formula is derived from integral form of endochronic plastic constitutive equation, which greatly reduces the error caused by the one which was directly obtained from differential form of the constitutive equation. An elastoplastic matrix is then proposed, based on which a stiffness finite element approach is developed. The analysis of the residual stress at the inner skin of an autofrettaged thick-walled cylinder agrees well with the experimental result. The calculated stress-strain fields of a double - edge - notched plate subjected to cyclic zero-to-tension loading are also quite reasonable. The numerical process is steady and quickly convergent, and the developed approach can easily be applied to practical engineering analysis.     

Application of Symmetric Galerkin Boundary Element Method in Limit Analysis of Plane Problems

Based on Melan's theorem, the symmetric Galerkin boundary element method (SGBEM) is used to discretize two dimensional structures and a computational formulation of structural limit analysis is established. The self equilibrium stress field is constructed by linear combination of several basic vectors, which are the stress differences between different iteration steps at the same increment using the traditional elastoplastic incremental method. Then the complex method is used to solve the nonlinear programming directly, so that the lower bound load multiplier of two dimensional structures is obtained. The validation of the present method has been confirmed by some numerical examples.     

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.     

Service Life Prediction of Concrete Structures under Chloride Environment

The problems rendered from the conventional time marching, referring to stepwise time marching scheme (STMS) adopted in boundary element method (BEM) for chloride diffusion in concrete structures, were investigated, and a new time marching, referring to initial time marching scheme (ITMS) in BEM, was developed for evaluation of service life of the concrete structures under chloride environment. Results of the numerical examples show that the ITMS-BEM proposed can eliminate domain integral and simplify the computational model, so that the stability in iteration process can be improved, resulting in better efficiency and accuracy, compared with the STMS-BEM. It can also be concluded that the dimensions of the diffusion of chloride can affect the service life of the concrete structure significantly, which should be taken into account in structural design.