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.
%0 Journal Article
%1 falgout2004generalizing
%A Falgout, Robert D.
%A Vassilevski, Panayot S.
%D 2004
%I Society for Industrial & Applied Mathematics (SIAM)
%J SIAM Journal on Numerical Analysis
%K 65f10-iterative-methods-for-linear-systems 65n30-pdes-bvps-finite-elements 65n55-pdes-bvps-multigrid-methods-domain-decomposition
%N 4
%P 1669--1693
%R 10.1137/s0036142903429742
%T On Generalizing the Algebraic Multigrid Framework
%U https://doi.org/10.1137%2Fs0036142903429742
%V 42
%X 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.
@article{falgout2004generalizing,
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.},
added-at = {2020-05-11T08:00:59.000+0200},
author = {Falgout, Robert D. and Vassilevski, Panayot S.},
biburl = {https://www.bibsonomy.org/bibtex/20374da1acaa91baa954db169df93f4db/gdmcbain},
doi = {10.1137/s0036142903429742},
interhash = {1b626f4c183e6eb51cc7d2f2067f9172},
intrahash = {0374da1acaa91baa954db169df93f4db},
journal = {{SIAM} Journal on Numerical Analysis},
keywords = {65f10-iterative-methods-for-linear-systems 65n30-pdes-bvps-finite-elements 65n55-pdes-bvps-multigrid-methods-domain-decomposition},
month = jan,
number = 4,
pages = {1669--1693},
publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
timestamp = {2020-05-11T08:00:59.000+0200},
title = {On Generalizing the Algebraic Multigrid Framework},
url = {https://doi.org/10.1137%2Fs0036142903429742},
volume = 42,
year = 2004
}