An application of multigrid methods for a discrete elastic model for epitaxial systems
Journal of Computational Physics
Towards Adaptive Smoothed Aggregation ($\alpha$SA) for Nonsymmetric Problems
SIAM Journal on Scientific Computing
General Constrained Energy Minimization Interpolation Mappings for AMG
SIAM Journal on Scientific Computing
Least-Squares Finite Element Methods for Quantum Electrodynamics
SIAM Journal on Scientific Computing
Compatible Relaxation and Coarsening in Algebraic Multigrid
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
Algebraic multilevel methods with aggregations: an overview
LSSC'05 Proceedings of the 5th 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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Substantial effort has been focused over the last two decades on developing multilevel iterative methods capable of solving the large linear systems encountered in engineering practice. These systems often arise from discretizing partial differential equations over unstructured meshes, and the particular parameters or geometry of the physical problem being discretized may be unavailable to the solver. Algebraic multigrid (AMG) and multilevel domain decomposition methods of algebraic type have been of particular interest in this context because of their promises of optimal performance without the need for explicit knowledge of the problem geometry. These methods construct a hierarchy of coarse problems based on the linear system itself and on certain assumptions about the smooth components of the error. For smoothed aggregation (SA) methods applied to discretizations of elliptic problems, these assumptions typically consist of knowledge of the near-nullspace of the weak form. This paper introduces an extension of the SA method in which good convergence properties are achieved in situations where explicit knowledge of the near-nullspace components is unavailable. This extension is accomplished by using the method itself to determine near-nullspace components and adjusting the coarsening processes accordingly.