Reducing Complexity in Parallel Algebraic Multigrid Preconditioners
Algebraic multigrid (AMG) is a very efficient iterative solver and preconditioner for large unstructured 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 on solely 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.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 883821
- Report Number(s):
- UCRL-JRNL-206780; TRN: US200615%%271
- Journal Information:
- SIAM (Society for Industrial and Applied Mathematics) Journal on Matrix Analysis and Applications, Vol. 27, Issue 4
- Country of Publication:
- United States
- Language:
- English
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