The analysis of PMHSS-multigrid methods for elliptic problems with smooth complex coefficients
The analysis of PMHSS-multigrid methods for elliptic problems with smooth complex coefficients
复制标题
光滑复系数椭圆问题的PMHSS-多重网格方法分析
DOI：
10.1016/j.amc.2015.05.024
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发表时间：
2015
影响因子：
4
通讯作者：
Wenqiang Li
中科院分区：
文献类型：
--
作者：
Shishun Li;Wenqiang Li
本文研究了一类带HSS光滑子的多重网格法应用于主导系数为复值的二阶椭圆型问题。这些光滑器基于Hermitian/Skew-Hermitian分裂(HSS)、修正HSS(MHSS)和预条件MHSS(PMHSS)迭代。结果表明，多重网格法的抽象理论可以推广到复系数椭圆型问题。在一定的假设条件下，证明了采用PMHSS光滑器的多重网格法是收敛的和最优的。数值结果证实了理论分析的正确性。
In this paper, we investigate a class of multigrid methods with HSS smoothers applied to second order elliptic problems whose dominant coefficient is complex valued. These smoothers are based on Hermitian/skew-Hermitian splitting (HSS), modified HSS (MHSS) and preconditioned MHSS (PMHSS) iterations. It is shown that the abstract theory for multigrid method can be extended and applied to elliptic problems with complex coefficient. Under some assumption conditions, we prove that multigrid method with PMHSS smoother is convergent and optimal. Numerical results are reported to confirm the theoretical analysis.