Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid

Details Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid

2012-02-09

arxiv.org/abs/1202.1987v1

Mathematics

Numerical Analysis

19 pages

Scientific paper

The main purpose of this paper is to provide a comprehensive convergence analysis of a nonlinear AMLI-cycle multigrid method for symmetric positive definite problems. Based on classical assumptions for approximation and smoothing properties, we show that the nonlinear AMLI-cycle MG is uniformly convergent. Furthermore, under the only assumption that the smoother is convergent, we show that the nonlinear AMLI-cycle is always better (or not worse) than the respective V-cycle MG. Finally, numerical experiments are presented to support the theoretical results.

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