Some Remarks on A Multigrid Preconditioner (Xu and Qin)

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SIAM Journal on Scientific Computing
Volume 15-1, January 1994, pp.  172-184
(C) 1994 by Society for Industrial and Applied Mathematics
All rights reserved


Title:            Some Remarks on A Multigrid Preconditioner

Author:           Jinchao Xu and Jinshui Qin 

AMS Subject
Classifications:  65F10, 65F35, 65M60, 65N30

Key words:        finite element, hierarchical basis, multigrid, 
                  preconditioner

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ABSTRACT

This paper is devoted to a class of multilevel preconditioners
developed in [{\it Math Comp}., 55 (1990), pp.\ 1--22] by Bramble, 
Pasciak, and Xu and in the  Ph.D.\ thesis of Xu at Cornell University, 
Ithaca, NY, 1989.  A simple proof is given for optimal estimation of 
the conditioning. A derivation of matrix representations and a 
description of efficient implementation techniques are also given. 
Some modified preconditioners are proposed  combining the hierarchical
basis method.  Numerical examples are also given that compare
various preconditioners discussed in this paper.


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