The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG). To date, however, no parallel AMG algorithms exist. We introduce a parallel algorithm for the selection of coarse-grid points, a crucial component of AMG, based on modifica- tions of certain parallel independent set algorithms and the application of heuristics designed to insure the quality of the coarse grids. A prototype serial version of the Mgorithm is implemented, and tests are conducted to determine its effect on multigrid convergence, and AMG complexity.
Cleary, A. J., Falgout, R. D., Henson, V. E., & Jones, J. E. (1998). Coarse-grid selection for parallel algebraic multigrid. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1457 LNCS, pp. 104–115). Springer Verlag. https://doi.org/10.1007/bfb0018531