Sparse approximate inverse smoothers for geometric and algebraic multigrid
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- 作者：Brö ; ker ; Oliver ; Grote ; Marcus J.
- 关键词：Approximate inverses ; Robust smoothing ; Algebraic multigrid ; Parallel multigrid
- 刊名：Applied Numerical Mathematics
- 出版年：2002
- 出版时间：April, 2002
- 年：2002
- 卷：41
- 期：1
- 页码：61-80
- 全文大小：255 K
文摘
Sparse approximate inverses are considered as smoothers for geometric and algebraic multigrid methods. They are based on the SPAI-Algorithm [M.J. Grote, T. Huckle, SIAM J. Sci. Comput. 18 (1997) 838–853], which constructs a sparse approximate inverse M of a matrix A, by minimizing I−MA in the Frobenius norm. This leads to a new hierarchy of inherently parallel smoothers: SPAI-0, SPAI-1, and SPAI(?). For geometric multigrid, the performance of SPAI-1 is usually comparable to that of Gauss–Seidel smoothing. In more difficult situations, where neither Gauss–Seidel nor the simpler SPAI-0 or SPAI-1 smoothers are adequate, further reduction of ? automatically improves the SPAI(?) smoother where needed. When combined with an algebraic coarsening strategy [J.W. Ruge, K. Stüben, in: S.F. McCormick (Ed.), Multigrid Methods, SIAM, 1987, pp. 73–130] the resulting method yields a robust, parallel, and algebraic multigrid iteration, easily adjusted even by the non-expert. Numerical examples demonstrate the usefulness of SPAI smoothers, both in a sequential and a parallel environment.