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2005年07月06日

【期刊论文】Schwarz algorithm for the solution of variational inequalities with nonlinear source terms

曾金平， Jinping Zeng， Shuzi Zhou *

Applied Mathematics and Computation 97(1998)23-35，-0001，（）：

-1年11月30日

Numerical solution of variational inequalities of obstacle type associated with some free boundary problems with nonlinear source terms is considered. Iterative methods based on the combination of the domain decomposition technique and the Newton-like approach are proposed for solving discrete obstacle problems arising from the continu-ous, piecewise linear finite element approximation of the problems. The calculation pro-cesses are easily to be parallelized. The convergence and specially the convergent rate of the algorithms are obtained.

Domain decomposition， Nonlinear source term， Variational inequality， Convergence， Convergent rate

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2005年07月06日

【期刊论文】WEIGHTED MAX-NORM ESTIMATE OF ADDITIVE SCHWARZ METHODS FOR SOLVING NONLINEAR COMPLEMENTARITY PROBLEMS

曾金平， YING-JUN JIANG， DONG-HUI LI and JIN-PING ZENG.

，-0001，（）：

-1年11月30日

摘要

In this paper, we consider some additive Schwarz methods for solving the finite-dimensional nonlinear complementarity problem. The methods considered contain some existing algorithms as special cases. We establish monotone convergence of the methods. Moreover, by applying the concept of weak regular splitting to one of the proposed methods, we obtain the weighted max-norm bound for iteration errors, and show that the sequence generated by the method converges to the unique solution of the problem.

Additive Schwarz method， Nonlinear complementarity problem， Monotone convergence， Weighted max-norm

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2005年07月06日

【期刊论文】On the Convergence Rate of a Space Decomposition Method

曾金平， Shu-zi Zhou， Jinping Zeng， Gui-hua Shan

Acta Mathematicae Applicatae Sinica, English Series Vol. 18, No.3 (2002) 455-460，-0001，（）：

-1年11月30日

摘要

Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.

Nonlinear problem,， space decomposition method,， Schwarz algorithm,， geometrical convergence 2000 MR Subject Classification 65M55,， 65N55,， 65M60,， 65N60

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2005年07月06日

【期刊论文】ON MONOTONE AND GEOMETRIC CONVERGENCE OF SCHWARZ METHODS FOR TWO-SIDED OBSTACLE PROBLEMS*

曾金平， JINPING ZENG† AND SHUZI ZHOU †

SIAM J. NUMER. ANAL. Vol. 35, No.2, pp. 600-616, April 1998，-0001，（）：

-1年11月30日

摘要

Convergence of Schwarz methods is discussed for certain discretizations of twosided obstacle problems. Monotone and especially geometrical convergence are established if the sti_ness matrix is a kind of M-matrix, and an h-independent convergence rate is proved for uniformly overlapping decomposition.

variational inequalities,， obstacle problems,， Schwarz algorithms,， monotone convergence,， geometrical convergence,， h-independent convergence rate.，

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