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应用数学学报  1994, Vol. 17 Issue (3): 334-346    DOI:
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求解一般椭圆型方程的可加型多层网格Schwarz方法
储德林, 胡显承
清华大学应用数学系, 北京100084
AN ADDITIVE MULTILEVEL SCHWARZ METHOD FOR GENERAL ELLIPTIC PROBLEMS
CHU DELIN, HU XIANCHENG
Department of Applied Mathematics, Tsinghua University, Beijing 100084
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摘要 区域分解方法是求解椭圆型方程的最有效的方法,近年来,已受到数值计算工作者高度的重视,并取得了丰硕的成果[1,2]. 对于自共扼椭圆型方程,基于Lions[3]的针对Schwarz交替法的误差分析,Widlund等提出并深入地研究了可加型Schwarz算法,该方法易于并行实现且当子区域剖分满足一定条件时,代数方程的条件数与子区域的直径和有限元参数无关,进而适于采用共扼梯度法求解,理论与数值试验均表明这类方法是非常有效的.本文将研究可加形多层网格Schwarz算法,相应地得到了近乎最佳收敛速度的结论.
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储德林
胡显承
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Abstract: In this paper, we present an additive mullevel Schwarz method for second order elliptic problems in two dimensions, which shows great promise for parallel computers. An alternative linear system, which has the same solution as the finite element equation, is derived. For symmetric, positive elliptic problems, the alternative linear system is solved by using conjugate gradient algorithm with a quite rapid convergent rate. For nonsymmetric or indefinite elliptic problmes, the alternative linear system is solved by using GMRES. and we show that the convergent rate is independent of the number of degrees of freedom and the number of local problems if the subdomains are fine enough. The performance of the our method is illustrated by results of several numerical experiments.
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收稿日期: 1990-12-08;
引用本文:   
储德林,胡显承. 求解一般椭圆型方程的可加型多层网格Schwarz方法[J]. 应用数学学报, 1994, 17(3): 334-346.
CHU DELIN,HU XIANCHENG. AN ADDITIVE MULTILEVEL SCHWARZ METHOD FOR GENERAL ELLIPTIC PROBLEMS[J]. Acta Mathematicae Applicatae Sinica, 1994, 17(3): 334-346.
 
[1] Powell,M.J.D.,Some Global Convergence Properties of a Variable Metric Algorithm for Minimization without Exact Line Searches,in NonlinearProgramming,SIAM-AMS proceedings,R.W.Cottle and C.E.Lemke,eds.,1976,9: 53-72.
[2] M.Dry;jia and O. Widlund, Some Domain Decomposition Algorithms for Elliptic Problems, In Iterative Methods for Large Systems, L. Hayea and D. Kinosid eda, 1989.
[3] A.van der Sluis.Gerschgorin Domains for Partitioned Matrices.Linear Algebra and Appl.,1979,26:355-280.
[4] Sawaragi,B.Y.and Yoshikawa,T.,Discrete-time Markovian Decision Processes with Incomplete State Observation,Ann.Math.Statist.,41:1(1970),78-86.
[5] R.G.Newton.Inversion of Reflection Date for Layered Media,A Review of Exact Methods.Geophys J.R.Astr.Soci.,1981,65: 191-215.
[6] Werner,J.,Uber die globale konvergenze von variablemetric verfahrea mit nichtexakter schrittweitenbestimmung,Numer.Math.,1978,31: 321-334.
[7] 栗文贵.地球物理中的反问题.科学出版社,1989年.
[8] Strauch,R.E.,Negative Dynamic Programming,Ann.Math.Statiat.,37:4(1966),871-890
[9] J.H. Bramble, J.E. Pasciak and Jinchao Xu. Parallel Multilevel Preconditioners,Technical Report,Cornell University, Ithaca, NY, 1990.
[10] 张关泉.一维波动方程的反间题.中国科学,(A辑),7 (1988),707-721.
[11] Cohn,A.L.,Stepsize Analysis for Descont Methods,JOTA,1981,33 (2): 187-205.
[12] Barnes E.R.Circular Discs Containing Eigenvalues of Normal Matrices.Linear Algebrn Appl.,1989,114/115:501-521.
[13] H.Yserentant, On the Multi-level Splitting of Finite Element Spaces, Numer Math., 1986, 49:379-412.
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