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## Non-overlapping Domain Decomposition Method Based on the Natural Boundary Reduction

LIU Jing-gang (Department of Applied Mathematics and Physics, North China Electric Power University, Baoding 071003)
Based on the theory of natural boundary reduction, a non-overlapping domain decomposition method is applied to elliptic boundary value problems on a kind of unbounded half plane with a cave. It is proved that the convergence rate of the algorithm is independent of the finite element mesh size. With proper selection of the relaxation factor, it is shown that the convergence rate of the algorithm is geometrical. Furthermore, the general values of the relaxation factor are given. The numerical example shows that the algorithm is effective.
【Fund】： 华北电力大学青年教师科研基金(200511015)
【CateGory Index】： O241.82
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 【Citations】
 Chinese Journal Full-text Database 4 Hits
 1 Yu De-hao Computing Center,Academia Sinica;The Coupling of Natural BEM and FEM for Stokes Problem on Unbounded Domain[J];Mathematica Numerica Sinica;1992-03 2 Yu De-hao (Computing Canter, Academia Sinica);A DOMAIN DECOMPOSITION METHOD BASED ON THE NATURAL BOUNDARY REDUCTION OVER UNBOUNDED DOMAIN[J];MATHEMATICA NUMERICA SINICA;1994-04 3 Yu De-hao (Institute of Computational Mathematics and Scientifi/Engineering Computing, Chinese Academy of Sciences);DISCRETIZATION OF NON-OVERLAPPING DOMAIN DECOMPOSITION METHOD FOR UNBOUNDED DOMAINS AND ITS COVERCENCE[J];MATHEMATICA NUMERICA SINICA;1996-03 4 Yu Dehao(State Key Laboratory of Scientific and Engineering ComputingInstitute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences, Beijing 100080);SELECTION OF RELAXATION FACTOR AND CONVERGENCE RATE FOR DN DOMAIN DECOMPOSITION METHOD OVER UNBOUNDED DOMAIN[J];CHINESE JOURNAL OF COMPUTATION PHYSICS;1998-01
 【Co-citations】
 Chinese Journal Full-text Database 10 Hits
 1 LIU Jing-gang (Department of Applied Mathematics and Physics,North China Electric Power University,Baoding 071003,China);Non-overlapping Domain Decomposition Method Based on the Natural Boundary Reduction Over Unbounded Half Plane[J];Journal of Baoding University;2008-02 2 KANG Tong,WU Zheng-peng,YU De-hao (Department of Applied Mathmatics, College of Sciences, Beijing Broadcasting Institute, Beijing, China;Academy of Mathematics and System Science, Chinese Academy of Sciences Beijing, China);An H-based Nonoverlapping Domain Decomposition Method for Eddy Current Problem in the Unbounded Domain[J];Journal of Beijing Broadcasting Institute;2004-04 3 YuDehao (Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080).;Natural Boundary Integral Equations and Related Computational Methods[J];Journal of Yanshan University;2004-02 4 Yang Minzhi,Xu Fang (Shanghai Jiaotong University, Shanghai, 200030);Numerical Thermal Analysis of Cryogenic Component Parts[J];CRYOGENICS AND SUPER CONDUCTIVITY;1998-04 5 ZHANG Tai ping, ZHU Jia lin (Institute of Mathematics and Physics,Chongqing University,Chongqing 400044,China);Boundary Element Methods with Overlapping Domain Decomposition for Parabolic Problem[J];Journal of Chongqing University(Natural Science Edition);2002-02 6 ZHANG Jie1, ZHU Jialin2, ZHANG Kai2 (1. Department of Foundation studies, Logistical Engineering University, Chongqing 400016,China; 2.College of Mathematics and Physics,Chongqing University,Chongqing 400044,China);Galerkin Boundary Element Method for Laplace Equation[J];Journal of Chongqing University(Natural Science Edition);2003-10 7 YUAN Zheng-qiang~(1), YUAN Fei~(1), ZHU Jia-lin~(2)(1.College of Civil Engineering; 2.College of Mathematical and Physical Science, Chongqing University, Chongqing 400030,China);Exact Integration of Constant Element of Elastomer in Boundary Element Method[J];Journal of Chongqing University(Natural Science Edition);2005-08 8 XIANG Rui-yin,ZHU Jia-lin(1.College of Mathematics and Physics,Chongqing University,Chongqing 400030,China;2.Department of Computer Science,Chongqing Three Gorges College,Wanzhou Chongqing 404000,China);Galerkin Boundary Element Method for Plane Stationary Stokes Equation[J];Journal of Chongqing University(Natural Science Edition);2006-02 9 ZHANG Shou-gui~(1),ZHU Jia-lin~(2),DONG Hai-yun~(2)(1.College of Mathematics and Computer Science,Chongqing Normal University,Chongqing 400047,China;2.College of Mathematics and Physics,Chongqing University,Chongqing 400030,China);Galerkin Boundary Element Method for Two-dimension Laplace Equation of Neumman Condition[J];Journal of Chongqing University(Natural Science Edition);2006-03 10 Zhu Changjie; Du Qikui(Huaibei Coal Mining Teachers College);The Well-posedness of Coupled Variational Formulation for a Nonlinear Parabolic Equation[J];JOURNAL OF HUAIBEI INDUSTRY TEACHERS COLLEGE (NATURAL SCIENCES EDITION);1998-02
 【Secondary Citations】
 Chinese Journal Full-text Database 2 Hits
 1 Zhu Jia-lin Chongqing Institute of Architecture and Engineering;A BOUNDARY INTEGRAL EQUATION METHOD FOR SOLVING STATIONARY STOKES PROBLEM[J];Mathematica Numerica Sinica;1986-03 2 Yu De-hao Computing Center,Academia Sinica;The Coupling of Natural BEM and FEM for Stokes Problem on Unbounded Domain[J];Mathematica Numerica Sinica;1992-03
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