BIT Numerical Mathematics

, Volume 53, Issue 4, pp 987–1012 | Cite as

Convergence analysis of HSS-multigrid methods for second-order nonselfadjoint elliptic problems

  • Shishun Li
  • Zhengda Huang


In this paper, the multigrid methods using Hermitian/skew-Hermitian splitting (HSS) iteration as smoothers are investigated. These smoothers also include the modified additive and multiplicative smoothers which result from subspace decomposition. Without full elliptic regularity assumption, it is shown that the multigrid methods with these smoothers converge uniformly for second-order nonselfadjoint elliptic boundary value problems if the mesh size of the coarsest grid is sufficiently small (but independent of the number of the multigrid levels). Numerical results are reported to confirm the theoretical analysis.


Multigrid methods HSS iteration method Additive smoother Multiplicative smoother 

Mathematics Subject Classification (2000)

65N55 65N30 



We would like to thank the referees for their insightful and valuable suggestions, which greatly improved the original manuscript of this paper.


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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceHenan Polytechnic UniversityJiaozuoP.R. China
  2. 2.Department of MathematicsZhejiang UniversityHangzhouP.R. China

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