Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid

Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao

doi:10.1137/110850049

Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid

Journal Article · 30 April 2013 · SIAM Journal on Numerical Analysis

DOI:https://doi.org/10.1137/110850049· OSTI ID:1226999

Hu, Xiaozhe ^[1]; Vassilevski, Panayot S. ^[2]; Xu, Jinchao ^[1]

Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

The purpose of our paper is to provide a comprehensive convergence analysis of the nonlinear algebraic multilevel iteration (AMLI)-cycle multigrid (MG) method for symmetric positive definite problems. We show that the nonlinear AMLI-cycle MG method is uniformly convergent, based on classical assumptions for approximation and smoothing properties. 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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Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

DOE Contract Number:: AC52-07NA27344

OSTI ID:: 1226999

Report Number(s):: LLNL-JRNL--498993

Journal Information:: SIAM Journal on Numerical Analysis, Journal Name: SIAM Journal on Numerical Analysis Journal Issue: 2 Vol. 51; ISSN 0036-1429

Publisher:: Society for Industrial and Applied Mathematics

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
multigrid
non-linear AMLI-cycle multigrid
nonlinear preconditioned conjugate gradient method

Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid

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