Parallel Smoothers Using Sparse Approximate Inverse

Sparse approximate inverses ' usefulness in a parallel environment has motivated much interest in recent years. However, the superior capability of an approximate inverse in eliminating the local error has not yet been fully exploited in multi-grid algorithms. We propose a new class of sparse approximate inverse smoothers in this paper and present their analytic smoothing factors for constant coe cient PDEs. In particular, by adjusting the quality of the approximate inverse, the smoothing factor can be improved accordingly. For hard problems, this a useful feature. Our theoretical and numerical results have demonstrated the e ectiveness of this new technique.