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1.
本文对于一类具非光滑核第二类Fredholm方程的Collocation解提出一种迭代一校正方法,使得在计算量增加很少的前提下,成倍提高逼近解精度,并将此方法用于平面角域上边界积分方程,从而给出了其相应微分方程逼近解的高精度算法,此方法还是一种自适应方法。 相似文献
2.
一个扩散问题的自然边界元法与有限元法组合 总被引:7,自引:0,他引:7
李瑞遐 《高校应用数学学报(A辑)》1998,13(3):333-341
本文讨论由Helmholtz方程描述的扩散问题的自然边界元法与有限元法的组合.取一个圆作为公共边界,用Fourier展开建立边界积分方程,将无界区域上的问题化为有界区域上的非局部边值问题.在变分方程中公共边界上的未知量只包含函数本身而不包含其法向导数,从而减少了未知数的数目,并且边界元剐度矩阵只有极少量不同的元素,有利于数值计算.这种组台方法优越于建立在直接边界元法基础上的组合方法.文中证明了变分解的唯一性,数值解的收敛性和误差估计.最后讨论了数值技术并给出一个算倒. 相似文献
3.
本文考虑了二维Helmholtz方程的Dirichlet问题.首先利用单层位势将问题归结为第一类边界积分方程,然后利用有限元方法求解该边界积分方程的近似解,给出近似解的收敛性、一致收敛性以及最优收敛速度定理,并进行解的稳定性分析. 相似文献
4.
逆热传导问题是严重不适定问题,它的解如果存在,其解将不连续依赖于定解数据,使得数值计算和理论分析都非常困难。但目前关于逆热传导问题的已有文 献大都主要集中于讨论由标准热传导方程所描述的问题。该文给出了一种适用于由一般一维抛物方程所描述的逆热传导问题且具有Holder连续性的Fourier正则化新方法。 相似文献
5.
本文利用拉普拉斯方程的基本解作为权函数,给出求解交系数非齐次亥姆霍茨方程的迭代格式,进而得到求解这类方程的边界元迭代法.文中给出了算例.最后,把本文给出的边界元迭代法与作者早些时候提出的边界元耦合法进行了比较. 相似文献
6.
逆热传导问题是严重不适定问题,它的解如果存在,其解将不连续依赖于定解数据,使得数值计算和理论分析都非常困难.但目前关于逆热传导问题的已有文献大都主要集中于讨论由标准热传导方程所描述的问题.该文给出了一种适用于由一般一维抛物方程所描述的逆热传导问题且具有Ho。lder连续性的Fourier正则化新方法. 相似文献
7.
考虑热传导方程的初边值问题的解。当初值与边值“不相容”时。由于热传导方程的特性这个解可以在很短时间内变得光滑。并形成一个边界层,本文将通过上、下解的控制给出解在边界附近变化的渐进行为. 相似文献
8.
9.
完备Brouwerian格上Fuzzy关系方程有极小解的条件 总被引:22,自引:0,他引:22
本文在有限论域上对完备Brouwerian格上Fuzzy关系方程极小的存在问题作了探讨,首先构造了Fuzzy关系方程有解但无极小解的一个例子,然后在解集非空时给出了对Fuzzy关系方程的每一个解都存在一个小于等于它的极小解的一个充分条件及一个充要条件,特别地,在充分条件下给出了一类Fuzzy关系方程所有极小解的个数的公式。 相似文献
10.
11.
Abdeljalil Nachaoui 《Numerical Algorithms》2003,33(1-4):381-398
In this paper, an inverse problem of determining geometric shape of a part of the boundary of a bounded domain is considered. Based on a conjugate gradient method, employing the adjoint equation to obtain the descent direction, an identification scheme is developed. The implementation of the method based on the boundary element method (BEM) is also discussed. This method solves the inverse boundary problem accurately without a priori information about the unknown shape to be estimated. 相似文献
12.
This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise. 相似文献
13.
In this paper, we consider an inverse problem of determining the corrosion occurring in an inaccessible interior part of a pipe from the measurements on the outer boundary. The problem is modelled by Laplace's equation with an unknowm term γ in the boundary condition on the inner boundary. Based on the Maz'ya iterative algorithm, a regularized BEM method is proposed for obtaining approximate solutions for this inverse problem. The numerical results show that our method can be easily realized and is quite effective. 相似文献
14.
George C. Hsiao 《Journal of Computational and Applied Mathematics》2011,235(17):5213-5221
The interior transmission problem (ITP) is a boundary value problem arising in inverse scattering theory, and it has important applications in qualitative methods. In this paper, we propose a coupled boundary element method (BEM) and a finite element method (FEM) for the ITP in two dimensions. The coupling procedure is realized by applying the direct boundary integral equation method to define the so-called Dirichlet-to-Neumann (DtN) mappings. We show the existence of the solution to the ITP for the anisotropic medium. Numerical results are provided to illustrate the accuracy of the coupling method. 相似文献
15.
In this paper we propose a numerical scheme for treating the problem of sJow viscous flow past an obstacle in the plane. This scheme is a combination of boundary element and finite element methods. By introducing an auxiliary boundary curve, we divide the region under consideration into two subregions, an inner and an outer region. In the inner region, we employ a finite element method (FEM) for solving a system of simplified field equations with proper natural boundary conditions. In the outer region, the solution is expressed in the form of a simple-layer potential with density function satisfying a system of modified integral equations of the first kind. The latter are solved by a boundary element method (BEM). Both solutions are matched on the common auxiliary boundary curve. Error estimates in suitable function spaces are derived in terms of the mesh widths as well as the small parameters, the Reynolds numbers 相似文献
16.
In this paper,the authors discuss an inverse boundary problem for the axi- symmetric steady-state heat equation,which arises in monitoring the boundary corrosion for the blast-furnace.Measure temperature at some locations are used to identify the shape of the corrosion boundary. The numerical inversion is complicated and consuming since the wear-line varies during the process and the boundary in the heat problem is not fixed.The authors suggest a method that the unknown boundary can be represented by a given curve plus a small perturbation,then the equation can be solved with fixed boundary,and a lot of computing time will be saved. A method is given to solve the inverse problem by minimizing the sum of the squared residual at the measuring locations,in which the direct problems are solved by axi- symmetric fundamental solution method. The numerical results are in good agreement with test model data as well as industrial data,even in severe corrosion case. 相似文献
17.
This paper is presented as a way to model transient heat conduction in a 3-D axisymmetric case where large rates of heat fluxes are applied on the surfaces as done in the case of laser processing. This would result in large temperature gradients in a small area irradiated by the laser on the incident surface that could also reach melting and subsequent vaporization. BEM can handle large fluxes very easily and it also can be formulated if needed to incorporate the moving boundary problem in a unique manner while on the other hand FDM is a fast and efficient method. For these reasons a coupled BEM–FDM method is formulated to simulate the heat conduction process. In the BEM method linear elements for the boundary and quadratic elements for the domain were used. The integrals in BEM were integrated in time using the asymptotic expansion for the modified Bessel functions in the Green’s function. To further improve the accuracy, special techniques were employed in the spatial integration. As for the FDM formulation, a flux conservation scheme with a 4th order formula for the fluxes was used. The FDM and BEM were coupled at the interface by the temperature from the FDM formulation being imposed on the BEM and the flux from the BEM being utilized by the FDM elements near to the interface. To advance in time, the Crank–Nicholson scheme was used on the FDM directly and due to coupling indirectly on the BEM. The relative errors for the simulation of constant and variable flux cases demonstrate the successful nature of the numerical model. 相似文献
18.
《Numerical Methods for Partial Differential Equations》2018,34(2):575-601
The article is devoted to extension of boundary element method (BEM) for solving coupled equations in velocity and induced magnetic field for time dependent magnetohydrodynamic (MHD) flows through a rectangular pipe. The BEM is equipped with finite difference approach to solve MHD problem at high Hartmann numbers up to 106. In fact, the finite difference approach is used to approximate partial derivatives of unknown functions at boundary points respect to outward normal vector. It yields a numerical method with no singular boundary integrals. Besides, a new approach is suggested in this article where transforms 2D singular BEM's integrals to 1D nonsingular ones. The new approach reduces computational cost, significantly. Note that the stability of the numerical scheme is proved mathematically when computational domain is discretized uniformly and Hartmann number is 40 times bigger than length of boundary elements. Numerical examples show behavior of velocity and induced magnetic field across the sections. 相似文献
19.
Masato Kimura 《Numerische Mathematik》1996,73(2):209-233
Summary.
We apply the boundary element methods (BEM) to the interior Dirichlet problem of the
two dimensional Laplace equation, and its discretization is carried out
with the collocation method using piecewise linear elements. In this paper,
some precise asymptotic estimations for the discretization matrix
(where denotes
the division number) are investigated. We show that the maximum norm of
and the condition number of
have the forms:
and , respectively, as
, where the constants
and are explicitly given in
the proof. Although these estimates
indicate illconditionedness of this numerical computation,
the -convergence
of this scheme with maximum norm is
proved as an application of the main
results.
Received
January 25, 1993 / Revised version received March 13,
1995 相似文献
20.
Consider an inverse problem for the time-fractional diffusion equation in one dimensional spatial space. The aim is to determine the initial status and heat flux on the boundary simultaneously from heat measurement data given on the other boundary. Using the Laplace transform and the unique extension technique, the uniqueness for this inverse problem is proven. Then we construct a regularizing scheme for the reconstruction of boundary flux for known initial status. The convergence rate of the regularizing solution is established under some a priori information about the exact solution. Moreover, the initial distribution can also be recovered approximately from our regularizing scheme. Finally we present some numerical examples, which show the validity of the proposed reconstruction scheme. 相似文献