Scalable adaptive mantle convection simulation on petascale supercomputers
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Graph partitioning and disturbed diffusion
Parallel Computing
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
Multilevel space-time aggregation for bright field cell microscopy segmentation and tracking
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
Algebraic Multigrid for Markov Chains
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Compatible Relaxation and Coarsening in Algebraic Multigrid
SIAM Journal on Scientific Computing
Efficient Parallel AMG Methods for Approximate Solutions of Linear Systems in CFD Applications
SIAM Journal on Scientific Computing
On the performance of an algebraic multigrid solver on multicore clusters
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
Modeling the performance of an algebraic multigrid cycle on HPC platforms
Proceedings of the international conference on Supercomputing
Scalable parallel AMG on ccNUMA machines with OpenMP
Computer Science - Research and Development
Multigrid Smoothers for Ultraparallel Computing
SIAM Journal on Scientific Computing
On-the-Fly Adaptive Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
Parallel geometric-algebraic multigrid on unstructured forests of octrees
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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Algebraic multigrid (AMG) is a very efficient iterative solver and preconditioner for large unstructured sparse linear systems. Traditional coarsening schemes for AMG can, however, lead to computational complexity growth as problem size increases, resulting in increased memory use and execution time, and diminished scalability. Two new parallel AMG coarsening schemes are proposed that are based solely on enforcing a maximum independent set property, resulting in sparser coarse grids. The new coarsening techniques remedy memory and execution time complexity growth for various large three-dimensional (3D) problems. If used within AMG as a preconditioner for Krylov subspace methods, the resulting iterative methods tend to converge fast. This paper discusses complexity issues that can arise in AMG, describes the new coarsening schemes, and examines the performance of the new preconditioners for various large 3D problems.