基于自然边界元的一类拟线性问题的数值算法
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摘要
基于自然边界归化原理,利用非重叠型区域分解算法(即Dirichlet-Neumann交替算法)研究了长条形区域拟线性方程问题.在得到椭圆人工边界上的自然积分方程后,构造出相应的交替算法,并根据非线性算子的特性,证明了算法在连续和离散条件下的收敛性.数值实例的结果表明,算法是可行且有效的.
Based on the principle of natural boundary reduction,the non overlapping domain decomposition algorithm(Dirichlet-Neumannalternating algorithm)is used to study the quasi linear equations in the long strip region.First,the natural integral equation on the elliptical artificial boundary is obtained;and then,the corresponding iterative algorithm is constructed.According to the characteristics of nonlinear operators,the convergence of the algorithm in continuous and discrete cases is proved,and the corresponding numerical examples are given to illustrate the feasibility of the method.
Based on the principle of natural boundary reduction,the non overlapping domain decomposition algorithm(Dirichlet-Neumannalternating algorithm)is used to study the quasi linear equations in the long strip region.First,the natural integral equation on the elliptical artificial boundary is obtained;and then,the corresponding iterative algorithm is constructed.According to the characteristics of nonlinear operators,the convergence of the algorithm in continuous and discrete cases is proved,and the corresponding numerical examples are given to illustrate the feasibility of the method.
引文
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[5]HANH D,HUANGZ Y,YIND S.Exact Artificial Boundary Conditions for Quasilinear Elliptic Equations in Unbounded Domains[J].Communications Mathematical Science,2008,6(1):71-83.
[6]LIU Baoqing,DU Qikui.Dirichlet-Neumann Alternating Algorithm for an Exterior Anisotropic Quasilinear Elliptic Problem[J].Applications of Mathematics,2014,59(3):285-301.
[7]HIAVACEK IVAN.A Note on the Neumann Problem for a Quasilinear Elliptic Problem of a Nonmonotone Type[J].Journal of Mathematical Analysisand Applications,1997,211(1):365-369.
[8]INGHAMD B,KELMANSON MA.Boundary Integral Equation Analysis of Singular,Potential,and Biharmonic Problems[M]∥Lecture Notes in Engineer.Berlin:Springer Verlag,1984.
[9]YU Dehao.Natural Boundary Integral Method and Its Applications[M].Beijing:Science Press &Kluwer Academic Publishers,2002:507-519.
[2]余德浩.无界区域上Stokes问题的自然边界元与有限元耦合法[J].计算数学,1992,14(3):371-378.
[3]LIU Baoqing,DU Qikui.On the Coupled of NBEM and FEM for an Anisotropic Quasilinear Problem in Elongated Domains[J].American Journal of Computational Mathematics,2012,2:143-155.
[4]杜其奎,余德浩.凹角型区域椭圆边值问题的自然边界归化[J].计算数学,2003,25(1):85-98.
[5]HANH D,HUANGZ Y,YIND S.Exact Artificial Boundary Conditions for Quasilinear Elliptic Equations in Unbounded Domains[J].Communications Mathematical Science,2008,6(1):71-83.
[6]LIU Baoqing,DU Qikui.Dirichlet-Neumann Alternating Algorithm for an Exterior Anisotropic Quasilinear Elliptic Problem[J].Applications of Mathematics,2014,59(3):285-301.
[7]HIAVACEK IVAN.A Note on the Neumann Problem for a Quasilinear Elliptic Problem of a Nonmonotone Type[J].Journal of Mathematical Analysisand Applications,1997,211(1):365-369.
[8]INGHAMD B,KELMANSON MA.Boundary Integral Equation Analysis of Singular,Potential,and Biharmonic Problems[M]∥Lecture Notes in Engineer.Berlin:Springer Verlag,1984.
[9]YU Dehao.Natural Boundary Integral Method and Its Applications[M].Beijing:Science Press &Kluwer Academic Publishers,2002:507-519.