Electronic Resource
Springer
Numerische Mathematik
63 (1992), S. 521-539
ISSN:
0945-3245
Keywords:
65F10
;
65N30
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary We consider the solution of the algebraic system of equations which result from the discretization of second order elliptic equations. A class of multilevel algorithms are studied using the additive Schwarz framework. We establish that the condition number of the iteration operators are bounded independent of mesh sizes and the number of levels. This is an improvement on Dryja and Widlund's result on a multilevel additive Schwarz algorithm, as well as Bramble, Pasciak and Xu's result on the BPX algorithm. Some multiplicative variants of the multilevel methods are also considered. We establish that the energy norms of the corresponding iteration operators are bounded by a constant less than one, which is independent of the number of levels. For a proper ordering, the iteration operators correspond to the error propagation operators of certain V-cycle multigrid methods, using Gauss-Seidel and damped Jacobi methods as smoothers, respectively.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01385873
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