Preconditioned iterative solver on the coarsest level of a multi-grid method for high frequency time harmonic electromagnetic field analyses
Preconditioned iterative solver on the coarsest level of a multi-grid method for high frequency time harmonic electromagnetic field analyses
复制标题
用于高频时间谐波电磁场分析的多重网格方法最粗层次的预处理迭代求解器
DOI：
10.1007/s00791-007-0063-z
复制
发表时间：
2008
影响因子：
--
通讯作者：
S. Abe
中科院分区：
文献类型：
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作者：
T. Iwashita;K. Yosui;M. Mori;E. Kobayashi;S. Abe
多重网格法是电磁场有限元分析中最强大的线性求解器之一。然而，随着离散化模型最近被扩大，在最粗糙级别上产生的线性系统的求解过程在完整的多网格求解过程中往往会出现问题。而在粗层次上的线性系统通常是通过直接求解器来求解的，我们在这里通过迭代求解器来解决它，以减少内存需求。由于传统的预处理技术是不有效的，这样一个线性系统，我们介绍的预处理技术的基础上阿诺德，福尔克，温瑟和希特梅尔的平滑。数值试验表明，新的预处理技术大大提高了收敛速度。
A multi-grid method is one of the most powerful linear solvers for finite element electromagnetic field analysis. However, as the discretized model has recently been enlarged, a solution process for a linear system arising on the coarsest level tends to be problematic in a complete multi-grid solution process. Whereas a linear system on the coarsest level is generally solved by a direct solver, we solve it here by means of an iterative solver to reduce the memory requirements. Since a conventional preconditioning technique is not effective for such a linear system, we introduce preconditioning techniques based on Arnold, Falk, and Winther’s and on Hiptmair’s smoothers. Numerical tests show that the newly installed preconditioning technique greatly improves the convergence rate.
DOI：
10.1137/1.9780898718003
发表时间：
2003-05
期刊：
--
影响因子：
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作者：
Y. Saad
通讯作者：
Y. Saad