On Generalizing the Algebraic Multigrid Framework

Authors:
Robert D. Falgout;Panayot S. Vassilevski
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2004

Citing 0
Cited 12

Algebraic Multigrid Based on Computational Molecules, 1: Scalar Elliptic Problems

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An Introduction to Algebraic Multigrid

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Compatible coarsening in the multigraph algorithm

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Convergence analysis of multigrid methods with residual scaling techniques

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Compatible Relaxation and Coarsening in Algebraic Multigrid

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Bootstrap AMG

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A General Interpolation Strategy for Algebraic Multigrid Using Energy Minimization

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Multigrid Smoothers for Ultraparallel Computing

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Energy based performance tuning for large scale high performance computing systems

Proceedings of the 2012 Symposium on High Performance Computing
An Algebraic Multigrid Method with Guaranteed Convergence Rate

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A Bootstrap Algebraic Multilevel Method for Markov Chains

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Further comparison of additive and multiplicative coarse grid correction

Applied Numerical Mathematics

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Abstract

We present a theory for algebraic multigrid (AMG) methods that allows for general smoothing processes and general coarsening approaches. The goal of the theory is to provide guidance in the development of new, more robust, AMG algorithms. In particular, we introduce several compatible relaxation methods and give theoretical justification for their use as tools for measuring the quality of coarse grids.