The Cascadic Multigrid Method of the Weak Galerkin Method for Second-Order Elliptic Equation

Sun Shi; Huang Ziping; Wang Cheng; Guo Liming

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The Cascadic Multigrid Method of the Weak Galerkin Method for Second-Order Elliptic Equation

机译：二阶椭圆方程的弱Galerkin方法的级联多重网格方法

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This paper is devoted to the analysis of the cascadic multigrid algorithm for solving the linear system arising from the weak Galerkin finite element method. The proposed cascadic multigrid method is optimal for conjugate gradient iteration and quasi-optimal for Jacobi, Gauss-Seidel, and Richardson iterations. Numerical results are also provided to validate our theoretical analysis.

机译：本文致力于分析由弱伽勒金有限元方法产生的线性系统的级联多重网格算法。所提出的级联多重网格方法对于共轭梯度迭代是最优的，对于Jacobi，Gauss-Seidel和Richardson迭代是准最优的。还提供了数值结果以验证我们的理论分析。

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《Mathematical Problems in Engineering》 |2017年第10期|7912845.1-7912845.8|共8页
作者
Sun Shi; Huang Ziping; Wang Cheng; Guo Liming;
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作者单位

Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China;

Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China;

Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China;

Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Peoples R China;

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2. A computational study of the weak Galerkin method for second-order elliptic equations [J] . Mu L., Wang J., Wang Y., Numerical algorithms . 2013,第4期

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3. A Two-Level Additive Schwarz Preconditioning Algorithm for the Weak Galerkin Method for the Second-Order Elliptic Equation [J] . Qin Fangfang, Zha Min, Wang Feng Mathematical Problems in Engineering . 2016,第pta3期

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4. Kernel-Based Collocation Methods Versus Galerkin Finite Element Methods for Approximating Elliptic Stochastic Partial Differential Equations [C] . Gregory E. Fasshauer, Qi Ye International workshop on meshfree methods for partial differential equations . 2013

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5. Discontinuous Galerkin methods and cascading multigrid methods for integro-differential equations. [D] . Ma, Jingtang. 2004

机译：积分微分方程的间断Galerkin方法和级联多重网格方法。
6. WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS [O] . LIN MU, JUNPING WANG, GUOWEI WEI, -1

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7. A COMPUTATIONAL STUDY OF THE WEAK GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC EQUATIONS [O] . Lin Mu, Junping Wang, Yanqiu Wang, 2016

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8. BLOCK ITERATIVE METHODS FOR TWO-CYCLIC MATRIX EQUATIONS WITH SPECIAL APPLICATION TO THE NUMERICAL SOLUTION OF THE SECOND-ORDER SELF-ADJOINT ELLIPTIC PARTIAL DIFFERENTIAL EQUATION IN TWO DIMENSIONS [R] . Louis A. Hageman 1962

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The Cascadic Multigrid Method of the Weak Galerkin Method for Second-Order Elliptic Equation

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