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Cascadic multigrid methods for parabolic problems

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Science China Mathematics 2008年第8期51卷 1415-1439页

作者： DU Qiang MING PingBing Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesBeijing 100190China

In this paper,we consider the cascadic multigrid method for a parabolic type *** Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the *** new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular *** error bound sare derived for both smooth and non-smooth *** strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.

关键词： cascadic multigrid method parabolic problem finite element methods backward Euler scheme smoother stability optimal error order optimal complexity 65N30 65N55 65f10

Several splittings for non-Hermitian linear systems

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Science China Mathematics 2008年第8期51卷 1339-1348页

作者： BAI Zhong-Zhi State Key Laboratory of Scientific/Engineering Computing,Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,P.O.Box 2719,Beijing 100080,China 1. State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

for large sparse non-Hermitian positive definite system of linear equations, we present several variants of the Hermitian and skew-Hermitian splitting (HSS) about the coefficient matrix and establish correspondingly several HSS-based iterative schemes. Theoretical analyses show that these methods are convergent unconditionally to the exact solution of the referred system of linear equations, and they may show advantages on problems that the HSS method is ineffective.

关键词： Hermitian and skew-Hermitian splitting non-Hermitian linear system splitting iterative scheme convergence 65f10 65f15 65f50 65N22

ASYNCHRONOUS MULTISPLITTING NONLINEAR GAUSS-SEIDEL TYPE METHOD

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Applied Mathematics(A Journal of Chinese Universities) 1994年第2期9卷 189-194页

作者：白中治王德人 1. Department of Mathematics Shanghai University of Science and Technology 201800 Shanghai

In this paper, we propose a parallel Gauss-Seidel type iterative method for solving the large-scale system of nonlinear algebraic equations Aφ(x)+Bψ(x)=b, which is an asynchronous variant of the synchronous parallel nonlinear Gauus-Seidel type method given by R. E. White. With almost the same but somewhat more relaxed constrainte on the multiple splittings, we prove the convergence and estimate the convergence rate of the new method.

关键词： 65f10 65H20 Matrix multisplitting asynchronous iteration M-matrix convergence Gauss-Seidel type

CONVERGENCE Of ALGEBRAIC MULTIGRID METHODS fOR SYMMETRIC AND POSITIVE DEfINITE MATRICES WITH WEAK DIAGONAL DOMINANCE

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Chinese Science Bulletin 1991年第15期36卷 1241-1242页

作者：黄维章 Institute of Applied Mathematics Academia Sinica Beijing 100080 PRC

Consider an AMG for the linear system Au=f. Up to now, only the uniform convergence of two-level AMG is proved for symmetric and positive definite L-matrices with weak diagonal dominance. Using the new form (1), we extend the results in [1] to the case that A is a general symmetric and positive definite matrix with weak diagonal dominance. In the following, we shall use the same notations as in [1].

关键词： algebraic multigrid (AMG) method weak diagonal dominance convergence AMS 1980 subject classification: 65f10 65N20.