非线性AMLI循环多重网格的比较收敛性分析
Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid
AI总结：
针对对称正定问题，基于逼近和平滑性质假设，证明非线性AMLI循环多重网格方法一致收敛，并证明其性能不劣于V循环方法，数值实验验证理论结果。
摘要：
本文的主要目的是对对称正定问题的非线性AMLI循环多重网格方法进行全面的收敛性分析。基于逼近和平滑性质的经典假设，我们证明了非线性AMLI循环多重网格方法是一致收敛的。此外，仅在平滑器收敛的假设下，我们证明了非线性AMLI循环方法总是优于（或不劣于）相应的V循环多重网格方法。最后，通过数值实验说明了理论结果。
英文摘要：
The main purpose of this paper is to provide a comprehensive convergence analysis of 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 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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