一类各向异性外问题的重叠型区域分解算法

本文以椭圆外调和问题的自然边界归化为基础，提出了求解各向异性常系数椭圆方程的一种重叠型区域分解算法，并分析了算法的收敛性及收敛速度．理论分析及数值实验表明，该方法对于求解各向异性外问题非常有效．     

一类各向异性外问题的非重叠型区域分解算法

In this paper, based on the natural integral operator on elliptic boundary, a nonoverlapping domain decomposition method is presented for a kind of anisotropic elliptic problem with constant coefficients in an exterior domain, and the convergence of the method is analyzed. The choice of the relaxition factor is discussed.Some numerical examples are given. Theoretical analysis as well as numerical examples show that our method is performance.     

A NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR EXTERIOR 3-D PROBLEM

1. IntroductionIn recent y6ars, the elliptic boUndaly value problems ill unbounded domains have dlawnmore and more attention. TO solve an equation in an unbounded domain numerically, a basicidea is to licit the computation to a bounded domain by introducing an artWial boundary.Based on this idea, many numerical methods, such as the coupling of BEM and FEM, the FEMwith boundary conditions at atilicial boundary) the coupled finite-~ie elemellt ndhodthe DDM(domain decomposition method)(cf.,…     

无界区域上基于自然边界归化的一种区域分解算法

无界区域上基于自然边界归化的一种区域分解算法余德浩（中国科学院计算中心）ＡＤＯＭＡＩＮＤＥＣＯＭＰＯＳＩＴＩＯＮＭＥＴＨＯＤＢＡＳＥＤＯＮＴＨＥＮＡＴＵＲＡＬＢＯＵＮＤＡＲＹＲＥＤＵＣＴＩＯＮＯＶＥＲＵＮＢＯＵＮＤＥＤＤＯＭＡＩＮ￥ＹｕＤｅ－ｈａｏ（...     

无界区域Stokes 问题非重叠型区域分解算法及其收敛性

本文研究无界区域Stokes方程外问题的利用有限元法和自然边界归化的非蕈叠型区域分解算法,此方法对无界区域Stokes问题非常有效.给出连续和离散情形的D-N算法及其收敛性分析,得到算法收敛的充要条件及充分条件,并得到最优的松弛因子和压缩因子,最后给出数值算例予以验证.     

DOMAIN DECOMPOSITION WITH NONMATCHING GRIDS FOR EXTERIOR TRANSMISSION PROBLEMS VIA FEM AND DTN MAPPING

In this paper, we are concerned with a non-overlapping domain decomposition method （DDM） for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Dirichlet-to-Neumann （DtN） mapping and provide the numerical analysis with nonmatching grids. The weak continuity of the approximation solutions on the interface is imposed by a dual basis multiplier. We show that this multiplier space can generate optimal error estimate and obtain the corresponding rate of convergence. Finally, several numerical examples confirm the theoretical results.     

A NON-OVERLAPPING DOMAIN DECOMPOSITION ALGORITHM BASED ON THE NATURAL BOUNDARY REDUCTION FOR WAVE EQUATIONS IN AN UNBOUNDED DOMAIN

In this paper, a new domain decomposition method based on the natural boundary reduction, which solves wave problems over an unbounded domain, is suggestted. An circular artificial boundary is introduced. The original unbounded domain is divided into two subdomains, an internal bounded region and external unbounded region outside the artificial boundary. A Dirichlet-Neumann(D-N) alternating iteration algorithm is constructed. We prove that the algorithm is equavilent to preconditional Richardson iteration method. Numerical studies are performed by finite element method. The numerical results show that the convergence rate of the discrete D-N iteration is independent of the finite element mesh size.     

二维Helmholtz方程外问题基于自然边界归化的非重叠型区域分解算法

１．引言 设是平面光滑闭曲线,是以为边界的外部区域,考虑二维Ｈｅｌｍｈｏｌｔｚ方程外Ｎｅｕｍａｎｎ问题并在无穷远处满足Ｓｏｍｍｅｒｆｅｌｄ辐射条件其中 ｉ＝是区域的边界 的外法线方向,即指向由 包围的内部区域． ｋ在许多情况下（例如约化波动方程）是实数,在另一些情况下则是纯虚数,本文仅讨论ｋ为纯虚数的情况,且不失一般性,可设Ｉｍ（ｋ）＞０． 用某些数值方法求解线性抛物型方程或线性双曲型方程的初边值问题时,可能间接地导致求解Ｈｅｌｍｈｏｌｔ。方程的外问题［１０,１１;１２;１３］．例如,用自然边界无法求…     

SCHWARZ DOMAIN DECOMPOSITION ALGORITHMS FOR BOUNDARY ELEMENT METHOD

In this paper, we introduce two Schwarz type domain decomposition algorithms for solving boundary element equations, which decompose the original problem defined on global boundary surface into several ones defined on sub-domains so that they may be solved ileratively or parallelly. The convergence of these methods are also proved.     

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.     

Dirichlet-Neumann alternating algorithm for an exterior anisotropic quasilinear elliptic problem

In this paper, by the Kirchhoff transformation, a Dirichlet-Neumann (D-N) alternating algorithm which is a non-overlapping domain decomposition method based on natural boundary reduction is discussed for solving exterior anisotropic quasilinear problems with circular artificial boundary. By the principle of the natural boundary reduction, we obtain natural integral equation for the anisotropic quasilinear problems on circular artificial boundaries and construct the algorithm and analyze its convergence. Moreover, the convergence rate is obtained in detail for a typical domain. Finally, some numerical examples are presented to illustrate the feasibility of the method.     

波动方程外区域问题基于自然边界归化的区域分解算法(英文)

本文以二维波动方程为例 ,研究基于自然边界归化的一种区域分解算法 .首先将控制方程对时间进行离散化 ,得到关于时间步长离散化格式 ,对每一时间步长求解一椭圆型外问题 ;然后引入两条人工边界 ,提出了 Schwarz交替算法 ,给出了算法的收敛性 ,并对圆外区域研究了压缩因子     

基于非协调元的区域分解法

基于非协调元的区域分解法戴培良，沈树民（常熟高专）（苏州大学）ＡＤＯＭＡＩＮＤＥＣＯＭＰＯＳＩＴＩＯＮＭＥＴＨＯＤＢＡＳＥＤＯＮＮＯＮＣＯＮＦＯＲＭＩＮＧＦＩＮＩＴＥＥＬＥＭＥＮＴＳ￥ＤａｉＰｅｉ－ｈａｎｇ；ＳｈｅｎＳｈｕ－ｍｉｎ（ＣｈａｎｇｓｈｕＣ...     

NUMERICAL SOLUTIONS OF PARABOLIC PROBLEMS ON UNBOUNDED 3-D SPATIAL DOMAIN

In this paper,the numerical solutions of heat equation on 3-D unbounded spatial do-main are considered. n artificial boundary Γ is introduced to finite the computationaldomain.On the artificial boundary Γ,the exact boundary condition and a series of approx-imating boundary conditions are derived,which are called artificial boundary conditions.By the exact or approximating boundary condition on the artificial boundary,the originalproblem is reduced to an initial-boundary value problem on the bounded computationaldomain,which is equivalent or approximating to the original problem.The finite differencemethod and finite element method are used to solve the reduced problems on the finitecomputational domain.The numerical results demonstrate that the method given in thispaper is effective and feasible.     

The coupling of boundary integral and finite element methods for the bidimensional exterior steady stokes problem

In this paper, we represent a new numerical method for solving the steady-state Stokes equations in an unbounded plane domain. The technique consists in coupling the boundary integral and the finite element methods. An artificial smooth boundary is introduced separating an interior inhomogeneous region from an exterior one. The solution in the exterior domain is represented by an integral equation over the artificial boundary. This integral equation is incorporated into a velocitypressure formulation for the interior region, and a finite element method is used to approximate the resulting variational problem. This is studied by means of an abstract framework, well adapted to the model problem, in which convergence results and optimal error estimates are derived. Computer results will be discussed in a forthcoming paper.     

空间半无界区域的非重叠区域分解算法

主要研究了空间一种半无界凹球区域上的区域分解算法.在三维空间自然边界规划的基础上,以三维Dirichlet外边值问题为例,进行的D-N交替算法.并提出了该算法与Richardson迭代法的等价性,并分析其收敛性及其收敛速度与网格参数h无关.同时给出了松弛因子的取值范围.     

Interface problem in holonomic elastoplasticity

The three-dimensional interface problem with the homogeneous Lamé system in an unbounded exterior domain and holonomic material behaviour in a bounded interior Lipschitz domain is considered. Existence and uniqueness of solutions of the interface problem are obtained rewriting the exterior problem in terms of boundary integral operators following the symmetric coupling procedure. The numerical approximation of the solutions consists in coupling of the boundary element method (BEM) and the finite element method (FEM). A Céa-like error estimate is presented for the discrete solutions of the numerical procedure proving its convergence.     

A finite-element capacitance matrix method for exterior Helmholtz problems

Summary. We introduce an algorithm for the efficient numerical solution of exterior boundary value problems for the Helmholtz equation. The problem is reformulated as an equivalent one on a bounded domain using an exact non-local boundary condition on a circular artificial boundary. An FFT-based fast Helmholtz solver is then derived for a finite-element discretization on an annular domain. The exterior problem for domains of general shape are treated using an imbedding or capacitance matrix method. The imbedding is achieved in such a way that the resulting capacitance matrix has a favorable spectral distribution leading to mesh independent convergence rates when Krylov subspace methods are used to solve the capacitance matrix equation. Received May 2, 1995     

Analysis of a FEM/BEM coupling method for transonic flow computations

A sensitive issue in numerical calculations for exterior flow problems, e.g.around airfoils, is the treatment of the far field boundary conditions on a computational domain which is bounded. In this paper we investigate this problem for two-dimensional transonic potential flows with subsonic far field flow around airfoil profiles. We take the artificial far field boundary in the subsonic flow region. In the far field we approximate the subsonic potential flow by the Prandtl-Glauert linearization. The latter leads via the Green representation theorem to a boundary integral equation on the far field boundary. This defines a nonlocal boundary condition for the interior ring domain. Our approach leads naturally to a coupled finite element/boundary element method for numerical calculations. It is compared with local boundary conditions. The error analysis for the method is given and we prove convergence provided the solution to the analytic transonic flow problem around the profile exists.

     

The h-p version of the coupling of finite element and boundary element methods for transmission problems in polyhedral domains

Summary. This paper analyzes the rate of convergence of the h-p version of the coupling of the finite element and boundary element method for transmission problems with a linear differential operator with variable coefficients in a bounded polyhedral domain and with constant coefficients in the exterior domain . This procedure uses the variational formulation of the differential equation in and involves integral operators on the interface between and . The finite elements are used to obtain approximate solutions of the differential equation in and the boundary elements are used to obtain approximate solutions of the integral equations. For given piecewise analytic data we show that the Galerkin solution of this coupling procedure converges exponentially fast in the energy norm if the h-p version is used both for finite elements and boundary elements. Received February 10, 1996 / Revised version received April 4, 1997