MULTIGRID ALGORITHM FOR THE COUPLING SYSTEM OF NATURAL BOUNDARY ELEMENT METHOD AND FINITE ELEMENT METHOD FOR UNBOUNDED DOMAIN PROBLEMS

In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.     

NATURAL BOUNDARY ELEMENT METHOD FOR THREE DIMENSIONAL EXTERIOR HARMONIC PROBLEM WITH AN INNER PROLATE SPHEROID BOUNDARY

In this paper, we study natural boundary reduction for Laplace equation with Dirichletor Neumann boundary condition in a three-dimensional unbounded domain, which is theoutside domain of a prolate spheroid. We express the Poisson integral formula and naturalintegral operator in a series form explicitly. Thus the original problem is reduced to aboundary integral equation on a prolate spheroid. The variational formula for the reducedproblem and its well-posedness are discussed. Boundary element approximation for thevariational problem and its error estimates, which have relation to the mesh size andthe terms after the series is truncated, are also presented. Two numerical examples arepresented to demonstrate the effectiveness and error estimates of this method.     

解一类半线性外边值问题的自然边界元与有限元耦合法

In this paper, we combine a finite element approach with the natural boundary element method to stduy the weak solvability and Galerkin approximations of a class of semilinear exterior boundary value problems. Our analysis is mainly based on the variational formulation with constraints. We discuss the error estimate of the finite element solution and obtain the asymptotic rate of convergence O（h^n) Finally, we also give two numerical examples.     

A PRECONDITIONER FOR COUPLING SYSTEM OF NATURAL BOUNDARY ELEMENT AND COMPOSITE GRID FINITE ELEMENT

1. IntroductionThe coupling of boundary elemellts and finite elements is of great imPortance for the nu-mercal treatment of boundary value problems posed on unbounded domains. It permits us tocombine the advanages of boundary elements for treating domains extended to infinity withthose of finite elemenis in treating the comP1icated bounded domains.The standard procedure of coupling the boundary elemeni and finite elemeni methods isdescribed as follows. First, the (unbounded) domain is divided…     

关于二维双曲型初边值问题的自然积分方程

本文将自然边界元方法应用于求解一类双曲型初边值问题。给出自然积分方程及Poisson积分公式,研究了自然积分算子的性质,并详细讨论了自然积分方程的数值解法,最后给出数值例子。     

INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

1. IntroductionThe infinite element method has been successfully applied to some boundary valueproblems of partial differential equations, where the solutions possess corner singularpoints or the domains are exterior ones. If the equations are invariant under similaritytransformation the approaches have been given in [11] [131 for singular solutions, and in[12][15][181119] for the exterior problems. If the equations do not admit the above invariant property? one approach has been given in [14]…     

边界元的分区解法

边界元法是一种比‘区域’型解法(如有限单元法,有限差分法)有着更多优点的方法。由于它能使所考虑的问题在维数上降阶,只需要对结构的边界进行离散,离散误差仅来自边界[1],因而具有输入量小,精度高等优点,在工程界受到广泛的重视.随着边界元网格的增加,其非对称满值的系数矩阵呈自由度平方级的增大,系数矩阵的总量可高达几千上万个。如此巨大的数组空间,一次送入计算机内存进行整体计算显然是办不到的,本文所提出的分区解法,使用了静力凝聚的概念,将一个整体的定解问题转化为若干个彼此有联系的分区定解问题,这样不仅解决了容量问题,而且提高了计算效率。     

非线性双曲型方程的混合元方法

1　引　　言考虑下述非线性双曲型方程的混合问题:c(x,u)utt-.(a(x,u)u)=f(x,u,t),　　x∈Ω,t∈J,(1.1)u(x,0)=u0(x),　　x∈Ω,(1.2)ut(x,0)=u1(x),　　x∈Ω,(1.3)u(x,t)=-g(x,t),　　(x,t)∈Ω×J,(1.4)其中ΩR2是一具有Lipschitz边界Ω的有界区域,J=[0,T],0相似文献   

双曲型方程的质量集中有限元法

用有限元法求解波动方程有许多工作,在此不多加阐述,本文针对线性双曲型方程采用质量集中有限元法,该方法产生于用特定的数值积分公式计算普通有限元法中的内积积分,这种方法具有较好的数值稳定性。     

THE ELLIPSOID ARTIFICIAL BOUNDARY METHOD FOR THREE-DIMENSIONAL UNBOUNDED DOMAINS

The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.     

非线性双曲型积分微分方程有限元逼近的误差分析

考虑非线性双曲型积分微分方程半离散有限元格式,得到H^1超收敛和最优阶L^∞和W^1,∞模误差估计,结果丰富了有限元方法的理论。     

一类具有吸收边界条件的二阶非线性双曲方程的混合元法分析

1　引　　言关于二阶双曲型方程的有限元解的收敛性问题 ,目前已经有不少结果 .Dupont[1 ] 给出了一类线性双曲方程 Galerkin解的 L2 误差估计 ,Baker[2 ] 对此作了改进 ,用的是一种所谓“非标准的能量方法”.这一方法为 Cowsar,Dupont,Wheeler[3] 所采用 ,分析了一类具有吸收边界条件的线性双曲方程的混合元格式的 L2收敛性 .对于非线性双曲型问题 ,袁益让 ,王宏[4,5] 等给出了标准有限元方法的 H1 与 L2 误差估计 .本文试图把 [3]的工作更进一步研究 ,我们考虑如下非线性双曲问题 :φ(x) utt= mi,j=1 xi(aij(x) p(x,u) u xj) + mi=1…     

COUPLING OF FINITE ELEMENT AND BOUNDARY ELEMENT METHODS FOR THE SCATTERING BY PERIODIC CHIRAL STRUCTURES

Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R^3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedness of the continuous and discretized problems is established. Uniform convergence for the coupling variational approximations of the model problem is obtained.     

椭圆外区域上的自然边界元法

１．引言 二十年来,自然边界元法已在椭圆问题求解方面取得了许多研究成果。它可以直接用来解决圆内（外）区域、扇形区域、球内（外）区域及半平面区域等特殊区域上的椭圆边值问题［１,２,５］,也可以结合有限元法求解一般区域上的椭圆边值问题,例如基于自然边界归化的耦合算法及区域分解算法就是处理断裂区域问题及外问题的一种有效手段［２－４,６］。 人们在设计求解外问题的耦合算法或者区域分解算法时,通常选取圆周或球面作人工边界。但对具有长条型内边界的外问题,以圆周或球面作人工边界显然并非最佳选择,它将会导致大量的…     

二维双曲型方程动边界问题有限元逼近格式和数值分析

1 引言 物理实际中,许多振动的传播过程,如弦振动、弹性杆纵向振动过程中的位移,理想高频传输线上的电压和电流,声波传播中的声压速度势以及电磁波等,都满足双曲型方程。关于     

THE FINITE ELEMENT METHOD FOR SEMILINEAR PARABOLIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

1.IntroductionLetxbepointsonplaneR',andfibeapolygonaldomain,wedenotetheboundaryoffibyOff.Thereinfiarefinitemanybrokelineswhichdivideitilltofinitepolygonalsubdomainsall,I=1,''jL.Thefunctionp(x)EL'(fl)isassumedtohaveboundedfirstderivativesinallsubdomainsall,whilepisallowedtobediscontinuousontheinterfacesoflinOflj.AndthereexistsapositiveconstantTsuchthatp(x)2T)Vxefi.WeadopttheusualnotationsoftheSobolevspacesinthispaper,thatis,denotebyH'(fl)andHI(fl)thespacesand11'11.thenorms,l'1.theseminor…     

THE OPTIMAL ORDER ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS TO HYPERBOLIC PROBLEMS

In this paper, the linear finite element approximation to the positive and symmetric,linear hyperbolic systems is analyzed and an O(h^2) order error estimate is established under the conditions of strongly regular triangulation and the H^3-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Our method and result here are also applicable to general hyperbolic problems.Finally, we discuss the linearized shallow water system of equations.     

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｉｎｉｔｅｖｏｌｕｍｅｅｌｅｍｅｎｔｍｅｔｈｏｄｏｒＦＶＥＭｕｓｅｓａｖｏｌｕｍｅｉｎｔｅｇｒａｌｆｏｒｍｕｌａｔｉｏｎｏｆｔｈｅｄｉｆ ｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｗｉｔｈａｆｉｎｉｔｅｐａｒｔｉｔｉｏｎｉｎｇｓｅｔｏｆｖｏｌｕｍｅｔｏｄｉｓｃｒｅｔｉｚｅｔｈｅｅｑｕａｔｉｏｎ ,ｔｈｅｎｒｅ ｓｔｒｉｃｔｓｔｈｅａｄｍｉｓｓｉｂｌｅｆｕｎｃｔｉｏｎｓｔｏａｌｉｎｅａｒｆｉｎｉｔｅｅｌｅｍｅｎｔｓｐａｃｅｔｏｄｉｓｃｒｅｔｉｚｅｔｈｅｓｏｌｕｔｉｏｎ ([1 -4 ] ) .…     

抛物型初边值问题的自然积分方程及其数值解法

１．引言数值求解无界区域的偏微分方程,自然的处理方式是削去区域的无界部分,即引入一条适当的人工边界ｒ。,将原问题的求解限制在一个适当的有界区域Ｄ内,这样必须在人工边界上引入适当边界的条件．于是很自然地导致这样一个问题：'是否存在一个人工边界条件,使得在这边界条件下,原问题在区域Ｄ内所求得的数值解与原无界区域的解在Ｄ上的限制是完全一致的？"这里我们的着眼点是寻求与原无界区域问题等价的数学形式,以便于数值求解．因为边界元方法可以将区域内的问题转化到区域的边界上去处理,经典的边界元方法常被应用．七十年代…     

抛物型初边值问题的有限元与边界积分耦合的离散化及其误差分析

1．引言边界元方法是近二十几年来迅速发展起来的一类新的偏微分方程的数值方法．它的独特之处是将空间的维数降低一维,从而倍受工程技术人员的青睐,并在工程技术与计算数学领域得到越来越广泛的重视和研究．对椭圆型问题,边界元方法的理论与应用研究已取得丰硕成果;对发展型问题,近年来在理论方面的研究也已取得重要进展［6－11］．但边界元方法难以处理非均质问题,而有限元对各类问题及各种区域具有较好的适应性,将两者结合起来可充分发挥各自的优点．文山提出了一种抛物方程初边值问题的有限元与边界积分的耦合方法,其主要思想是…