An Introduction to Algebraic Multigrid
Computing in Science and Engineering
Relaxed RS0 or CLJP coarsening strategy for parallel AMG
Parallel Computing
Convergence analysis of multigrid methods with residual scaling techniques
Journal of Computational and Applied Mathematics
General Constrained Energy Minimization Interpolation Mappings for AMG
SIAM Journal on Scientific Computing
Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
Algebraic Multigrid for Markov Chains
SIAM Journal on Scientific Computing
Compatible Relaxation and Coarsening in Algebraic Multigrid
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Recursively Accelerated Multilevel Aggregation for Markov Chains
SIAM Journal on Scientific Computing
Advances in Computational Mathematics
SIAM Journal on Matrix Analysis and Applications
Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
On-the-Fly Adaptive Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Modification and Compensation Strategies for Threshold-based Incomplete Factorizations
SIAM Journal on Scientific Computing
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Efficient numerical simulation of physical processes is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to unsatisfied assumptions made on the near null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. Emphasis is on the principles that guide the adaptivity and their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.