Research on Two-point Aggregated Algebraic Multigrid Preconditioning Methods

DOI

10.2991/ceis-16.2016.15How to use a DOI?

Keywords

sparse linear algebraic equations; aggregation based algebraic multigrid; smoothing process; preconditioner; Krylov subspace method

Abstract

Among the methods to solve sparse linear systems, the aggregation based algebraic multigrid is widely focused on, due to the potential of approximately optimal convergence and the cheap cost to setup. And it is often used as the preconditioner to Krylov subspace methods. But the actual efficiency is restricted to the extent of compliment of two processes, the smoothing and the correction. In the aggregation based algebraic multigrid methods, it is one of the critical steps to aggregate the finer-grid points to construct coarser grids. In this paper, several two-point aggregations are given first, and then for model problems, three characteristics are compared and analyzed, including the spectral radius of the related iterative matrix, the similarity between the spectra of the coefficient matrix on the coarser grid and that on the finer grid, the number of preconditioned conjugate gradient iterations with algebraic multigrid as the preconditioner. The results show that the spectral radius and the similarity of spectra have potentials to direct the design of highly efficient algebraic multigrid methods. Meanwhile, during the aggregation, it is better to match the fine points with heavy edge weights than with weak ones. When Jacobi iteration is used as smoothing, it is difficult to determine the best strategy to aggregate. But if Gauss-Seidel iteration is used as smoothing, the number of iterations is significantly reduced, and the optimal aggregation strategy is more certain, that is, the optimal is always among the three ones with matching priority for edges with heave weights, and the number of iterations with the other two is very close to that with the optimal.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Jian-Ping Wu
AU  - Fu-Kang Yin
AU  - Jun Peng
AU  - Jin-Hui Yang
PY  - 2016/11
DA  - 2016/11
TI  - Research on Two-point Aggregated Algebraic Multigrid Preconditioning Methods
BT  - Proceedings of the 2016 International Conference on Computer Engineering and Information Systems
PB  - Atlantis Press
SP  - 73
EP  - 78
SN  - 2352-538X
UR  - https://doi.org/10.2991/ceis-16.2016.15
DO  - 10.2991/ceis-16.2016.15
ID  - Wu2016/11
ER  -