SIAM Journal on Scientific Computing
Multigrid Smoothers for Ultraparallel Computing
SIAM Journal on Scientific Computing
A Bootstrap Algebraic Multilevel Method for Markov Chains
SIAM Journal on Scientific Computing
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We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Finally, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.