共查询到20条相似文献，搜索用时 15 毫秒
1.
Jin Chaosong 《保鲜与加工》1988,(3)
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. 相似文献
2.
Jin Chaosong 《保鲜与加工》1990,(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. 相似文献
3.
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. 相似文献
4.
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. 相似文献
5.
《保鲜与加工》1998,(2):35
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. 相似文献
6.
Cao Shuxiao 《保鲜与加工》1990,(4)
Two-dimensional incompressible laminar boundary layer equation can be changed into Blasius equation by means of similarity transformation. In this paper, Blasius equation 2f" '+ff"=0 is transferred into a nonlinear and autonomous system of second order by variable transforming. Taking the advantage of its approximation to linear system, the stability near zero solution can be discussed. 相似文献
7.
Gan Jianxue Jiang Zejia Yu Jihui 《保鲜与加工》1991,(3):1-8
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. 相似文献
8.
When having similar flow,a two-dimensional equationfor incompressible laminar boundary layer can be transformed into aFalkner-Skan equation.This paper has made transformation of F-Sequation into two-order non-autonomous system by variable permutationwith its stability around zero solution discussed and explained physi-cally. 相似文献
9.
Zhang Shide 《保鲜与加工》1993,(4)
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. 相似文献
10.
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. 相似文献
11.
Jin Chaosong 《保鲜与加工》1990,(4)
This paper presents boundary element methods for the solution of elliptic partial differential equation with Neumann boundary problem in R~2. Total details of error analysis are given for general condition, and optimal estimates are obtained. For simplicity Laplace's equation is discussed in illustration. 相似文献
12.
YAO Qing-liu 《保鲜与加工》2007,(9):93
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. 相似文献
13.
Li RonglinJiang ZejiaYu Jihui 《保鲜与加工》1992,(3):24-30
A B-spline finite etement method for solving general 2-D electromagnetic field problems is established. The B-spline bases for a general field region are constructed using the Bspline interpolation functions defined on a rectangle which contains the region. The Dirichlet boundary condition is dealt with by means of the generalized variational principle. Two numerical examples are given that show the characteristics and practical value of the method. 相似文献
14.
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. 相似文献
15.
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. 相似文献
16.
《保鲜与加工》2003,(10):39-41
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. 相似文献
17.
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. 相似文献
18.
Li Zhengliang 《保鲜与加工》1995,(1)
In this paper,the boundary element methods are applied to analyse the plates ontwo-parameter elastic foundation according to two boundary integral equations.The bending mo-ment,torsion and shear force at any point of plates are discussed by means of the theory of elasticitymechanics.An example and a plate in practital engineering are analysed.The resulta show that thereare high efficiency,good accuracy and little storage with this method. 相似文献
19.
The singular perturbation problem of 2-order quasilinear elliptic is discussed, the outer solution and N-order successive equation of boundary layer term is given,and the remaind term is estimated. Hence,the asymptotic expantion of solution and the existence and uniqueness of the solution of the perturbation problem are derived. 相似文献
20.
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. 相似文献