Susanne C. Brenner
Department of Mathematics, University of South Carolina
Additive Multigrid Theory
Abstract
The convergence of the V-cycle multigrid algorithm is usually handled by
a multiplicative theory where the iteration operator (matrix) is expressed
as a product of operators measuring the effect of the multigrid algorithm
on different grid levels.
In this talk an additive convergence theory for the V-cycle algorithm will
be presented. This theory is effective for establishing the asymptotic
behavior of the contraction number of the V-cycle algorithm as the number
of smoothing steps is increased.
The following applications of the additive theory will be discussed:
(1) a complete generalization of the classical V-cycle convergence theorem
of Braess and Hackbusch to the case of less than full elliptic regularity,
(2) convergence of V-cycle and F-cycle algorithms for nonconforming methods
with a sufficiently large number of smoothing steps.
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