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.     

Boundary Element Methods with Non-overlapping Doma in Decomposition for Elastodynamics

This paper presents the numerical implementation of boundary element method incorporated into a non overlapping domain decomposition method for solving the Navier equations of linear elastodynamics problems by Fourier transformation. Several examples are presented.     

Some Notes on the Variational Principles of Mechanics and Their Applications

This paper discusses the limitations of extension of classical Hamiltonian Principle to continuous systems, then reviews the new developments of operational theory in functional analysis and variational principles in non equilibrium thermodynamics based on field variation. Complementary dual variational principles including adjoined variational methods and generalized Green function method are bases of finite element analysis and boundary element analysis as well. From the point of view of physics, variational principles of macroscopic non equilibrium thermodynamic can be applied to all continuous mechanical systems. However, they have some limitations in application scope and remain to be developed.     

AN EXTENDED TRANSFER MATRIX AND BOUNDARY ELEMENT METHOD

A combination of extended transfer matrix and boundary element method is proposed for solving two dimentional statics problems of complicated nonhomogeneous structure. It is explained with the theory and the example. The method can get greater numerical accuray and shorten computation time in small amount of computer storage without getting involved with large matrices.     

AN OPTIMIZATION METHOD FOR SOLVING THE BOUNDARY WALUE QUESTION OF DIFFERENTIAL EQUATIONS

This paper presents an optimization method for solving the boundary value question of a differential equation on the basis of the trial-and-error method and the optimization method. As compared with the differential method, this method has some advantages such as quiker velocity at count, higher precision(especially at the boundary points) and can be widely used.     

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.     

A Boundary Element Separation Solution to the Elastic Contact Problems and the Optimal Penalty Factor

In this paper the boundary element separation to the elastic contact problems proposed by Kamiya is improved. It gives another optimal penalty factor to accelerate the iteratively saluting procedure, which makes a theoretical foundation for the application of computers' parallel processing method to reduce the calculation time and memory. A practical example is given to confirm the validity of the present method in comparison with Kamiya method.     

Boundary Element Method of Material Parameter Identification in 3-D Infinite Problem

A 3 D boundary element method and dual boundary control technique of material parameter identification were proposed in this paper. The infinite boundary element was used for infinite problem in geomechanics.The computational result shows the validity of the proposed method.     

The Taylor series multipole boundary element method (TSM BEM)and its applications in rolling engineering

Rainfall is the main input for probabilistic analysis and prediction of rainfall-triggered landslide. The joint probabilistic structure of daily rainfall (DR) and cumulative rainfall (CR), which are dominant parameters of rainfall related on landslide in Chongqing region, was analyzed. Following the traditional technology, daily rainfall was translated into discrete variable by rainfall grade and cumulative rainfall became continuous variable if records with very small cumulative rainfall were ignored. Then joint probabilistic model of discrete variable and continuous one was derived, and transiting solution of conditional density function was put forward, together with its approximation via a family of Dirac δ sequences. Naturally, the proposed method was used to analyze conditional density function of cumulative rainfall in Chongqing region, and the numerical results were verified by comparison. However, most of the conditional density functions were irregular and not modeled by simple probability density function, thus the finite mixture distribution was introduced, which is of uncomplicated format and relatively high precision. At last, the joint probabilistic model of daily rainfall and cumulative rainfall was built up by combining frequency function of grade of daily rainfall with conditional density model of cumulative rainfall.     

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.     

Similar Boundary Element Method in Elastodynamics

For the boundary element method of elastodynamics, some properties of matrices are discussed in case of similar boundary elements and the similar boundary element method is presented. In a series of similar boundary elements, when the corresponding matrices of a boundary element are obtained, the ones of other boundary elements in the series can be obtained by proportion. Then the coefficient matrix of the last system of linear algebraic equations can be obtained by the method of superposition. Compared with the general boundary element method, the computing speed can be raised by the similar boundary element method given in this paper.     

Dynamic Imaging for 3 - D Brain Hematoma

Based on disturbance method of electrical current field, numerical calculation about dynamic imaging for brain hematomas have been studied on a 3 - D sphere model. With current injected, we have found the law of the brain boundary potentials'change while the volume of brain hematoma changed. Some studies about the effect of brain skull with poor electrical conductivity to the brain boundary potentials. The results show that we can know the change of brain hematomas in terms of the measurement for the change of boundary potentials. The injected current can penetrate through the skull. These results are valuable to help doctor to accurately diagnose the brain hematoma and realize the noninvasive monitoring the brain hematoma.     

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.     

对偶性与特大增量步算法在复杂平面框架中的应用

特大增量步算法（LIM）是一种基于力法和广义逆矩阵理论的迭代算法,在简单桁架和刚架非线性初步应用中,达到相同计算精度下有同等甚至超过位移有限元的计算效率。针对工程中的复杂杆系结构,利用平衡与协调的对偶性,探讨LIM在复杂平面框架结构中的应用,建立了平面框架结构的LIM基本方程,提出了针对典型支座约束以及组合结点的处理方法。该处理方法的线弹性问题算例表明,与位移有限元相比具有至少同等的精度和相当的计算效率。在支座本身不考虑塑性的情况下,该处理方法同样适用于弹塑性问题,为LIM在复杂杆系结构的弹塑性分析中奠定了基础。     

Boundaty Element Method for Analysis of Thick Plates on Two- Parameter Elastic Foundations

This paper discusses the Reissner's plates on elastic foundation.The elastic foundation is considered as two- paramerer and its effect to thick plates are taken into account by a set of govering differential equations. According to the foundamental solutions for bending problem on two- parameter foundation derived, three boundary integral equations denoted by generalized displacement functions are established. This method is suitable to solve the bending problem of thin or thick plates on two- parameter foundation with arbitary boundary condition, arbitary shape and arbitary load conditions     

SINGULARITIES IN BOUNDARY ELEMENT METHODS

This paper presents an all round review of recent deve-lopments in treating the singularities in boundary element methods bothfor numerical computing and for mathematical analysing.Approachesfor numerical treatment of singular and hyper-singular integrations arelisted.Singular behaviour of solution on non-smooth boundary are discus-sed and the mathematical tools for describing it,such as the Sobolevspaces defined on a part of boundary,the pseudo-differential operatorsare presented.In order to incorporate the singular behaviour into theboundary element approximation,the technique of introducing singularboundary element is suggested.     

THE SPLINE BOUNDARY ELEMENT METHOD FOR CALCULATION OF ELECTROMAGNETIC FIELD PROBLEMS

The spline boundary element method is presented for electromagnetic field problems. Based on B-spline function interpolation, the formulation of calculation of two dimensional statical electromagnetic field problems is obtained. Boundary corner and singular integration problems are efficiently handled. Furthermore,the Method is used for solving two calculation examples.     

Garlerkin Boundary Element Method with Hyper Singular integral kernel

A Galerkin Boundary Elements was applied to solve the first kind of integral equation with hyper-singularity, which can be deduced from the direct boundary integral formula for the Neumann problem of Laplace equation. The concept of integration by parts in the sense of distributions was used. When boundary rotation is introduced, the two order derivatives of singular kernel are shifted to the boundary rotation of unknown function in the Galerkin variational formulation. While linear boundary elements are used for 2-dimensional problems, the boundary rotation on each element can be discretized into a constant vector, so that the integration can be performed in a simple way and the difficulty of numerical calculation for hyper-singularity is overcome. The results of numerical examples demonstrate that the scheme presented is practical and effective.     

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.     

The BEM for Elliptic Unilateral Problems

Unilateral problems is a kind of important partial differential problems. It can be solved by treating it as a complementary problem. As the complementary conditions lie in the boundary of the region,it is suitable for BEM. This paper is based on the switching algorithm,which is first used by J. M. Aitchison for the Signorini Problems of Laplace operator,then extends it to the elliptic operator,and conjunct it with the BEM. At last the detail of the algorithm is given. The new algorithm is easy to be implied effectively and quickly. It only needs the minimal change of the BEM programming. The numerical tests show the algorithm is effective and conventional.