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Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid

2013; Society for Industrial and Applied Mathematics; Volume: 51; Issue: 2 Linguagem: Inglês

10.1137/110850049

ISSN

1095-7170

Autores

Xiaozhe Hu, Panayot S. Vassilevski, Jinchao Xu,

Tópico(s)

Numerical methods for differential equations

Resumo

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

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