Acceleration and stabilization properties of minimal residual smoothing technique in multigrid
The present paper extends results in previous work by the author on a new minimal residual smoothing technique. Such techniques are proven to be a good remedy for the difficulties that arise when the multigrid method is applied to solve non-elliptic problems. They have some important drawbacks though, as the fact that they are often problem-dependent. The author has modified a minimal residual smoothing (MRS) method proposed by \textit{W. Schönauer} [Scientific computing on vector computers, North-Holland, Amsterdam (1987)], in order to overcome some of those drawbacks. The method is easily described when applying a two-level multigrid (TLM) method.; Schönauer's procedure is applied after having computed the fine-level residuals and this is followed by projecting to the coarser level both the smoothed residual and the corresponding modified iterate. It is proven in the paper that under proper conditions, this MRS not only accelerates convergence, but it also stabilizes TLM when it would otherwise diverge. An interesting heuristic related point, based on numerical experiments, is that in case of slow convergence of TLM, the acceleration thus provided is significant, while also the reciprocal seems to hold. This and other related points are demonstrated in work published elsewhere by the same author. [Two-grid analysis of minimal residual smoothing as a multigrid acceleration technique, Appl. Math. Comput. 96, No.~1, 27-45 (1998)].
scientific article; zbMATH DE number 1311088
scientific article