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.     

Mix Domain Decomposition Method with Boundary Element Method For Stokes Equations and Application

As the BEM was used in the knaggy domain,its approach error was big.Domain Decomposition Method change the problem in the knaggy domain to the problem in several convex domains which do not wrap.The whole solution is gained by alternating boundary conditions between Dirichlet condition and Neumann condition on the common boundary.Domain Decomposition Method for Stokes equations in the anomalistic knaggy domain is presented,the example of Domain Decomposition Method in the flow of the lake in GuiYang City is given.     

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 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.     

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.     

Improvements on the Boundary Element Method( I )

This paper presents an improved BEM, which is free of singular integrals and corner problems. The numerical accuracy is also efficiently improved by this 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.     

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.     

A Boundary Element Method for the Electrostatic Field with Anisotropic Media

The boundary-value problem for the electrostatic field with anisotropic media is formulated on the basis of introducing the medium property coefficient tensor. The boundary integral equations for this problem are deduced by the weighted residual method. The elementary solutions to the two-and three-dimensional anisotropic problems are derived. A two dimensional example with anisotropic media is given.     

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.     

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.     

Spline Boundary Element Method for Calculating Three-Dimensional Electrostatic Fields

Based on [l].this paper presents a new spline-BEM for calculating 3-D electrostatic fields,in which bi-cubic B-splines are used as basis functions. The corner problem in BEM and the extreme conditions for splines are circumvented. The numerical results presented show that the global approximation .convergence and stability of the method are satisfactory.     

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.     

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.     

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.     

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.     

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.     

Boundary Element Method for Time-dependent Chloride Diffusion and the Chloride Distribution in Concrete

The process of chloride diffusion in concrete is time-dependent.The boundary element method (BEM) with a time-dependent diffusion coefficient is presented for chloride diffusion in concrete based on the suitable transformation of variables.The fundamental solution of the partial differential equation for time-dependent chloride diffusion in concrete is developed,and the compensation length of the diffusion field is defined as well as the compensation coefficient.The scheme of BEM with a time-dependent diffusion coefficient is developed.Two examples are given to demonstrate the accuracy and efficiency of the presented method and the rationality and the importance of the compensation length for the method.     

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.