VBEM Analysis for Signorini Problem

the virtual boundary element method is applied for the numerical solution of a Signorini problem, which is conduced by an electro-paint process. The present method base on a switching algorithm, which can be applied to the problem defined in a non-regular domain, and it can reach good accuracy with less elements.     

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.     

BEM for Simulation of 2D Elastic Body with Randomly Distributed Identical Circular Inclusions

Based on the 2D BEM software THBEM2 developed by the authors' group, which can be applied to simulate the elastic body with randomly distributed circular holes. A scheme of BEM for the simulation of elastic bodies with randomly distributed identical circular inclusions is presented. The workload of the computation is nearly the same as for the corresponding case of circular holes, the numerical examples given show that the scheme is applicable and effective.     

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.     

An Analysis of Thick Plates underIn-plane and Transversal Loadings by the BEM

In accordance with the behaviours of thick plates under the in-plane and transversal loadings,and introducing the concept of equivalent load, the coupled equations for the problem have been deduced with the theory of BEM in this paper.Thus a new method is presented for solving the problems of interaction of superstructure and foundation and subsoil,as well as for the problems of the thick plates under the complicated loadings.     

A New Spline Boundary Element Method

This paper introduces a New Spline Boundary Element Method, which neither has corner problems and singular integrals nor involves extreme-conditions of spline function. Three numerical examples are given to show the validity of the method.     

The Multiple Solutions for a Class of Quasilinear Elliptic Equations

A three critical point theorem is proved. As its applications, Dirichlet problem for a class of quasilinear elliptic equations cf second order is considered.     

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.     

Research on Shoelast CAD/CAM Technology

Some new developments of boundary contour method have been presented in this paper. The developments include the boundary contour method based on equivalent boundary integral equations, the traction boundary contour method as well as the application of the boundary contour method to crack problems and elastic thin plate bending problems.     

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.     

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.     

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.     

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.     

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.     

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.     

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.