Deflation Techniques for Computational Electromagnetism: Theoretical Considerations
Deflation Techniques for Computational Electromagnetism: Theoretical Considerations
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计算电磁学的紧缩技术：理论考虑
DOI：
10.1109/tmag.2010.2094998
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发表时间：
2010
影响因子：
2.1
通讯作者：
Kota Watanabe
中科院分区：
文献类型：
--
作者：
Hajime Igarashi;Kota Watanabe
本文描述了电磁场有限元矩阵的压缩问题。通过用零点代替小特征值的矩阵收缩，改善了有限元矩阵的条件。众所周知，用AV方法以及从多重网格法衍生出来的显式和隐式误差修正(EC)方法可以改善有限元方程线性求解器的收敛。这些数值结果是建立在矩阵收缩的理论基础上的。特别是，在AV和隐式EC方法中出现的增广矩阵在预处理后具有良好的条件性。这些结果表明，上述方法是基于一个共同的数学原理。
This paper describes deflation of finite element (FE) matrices for electromagnetic fields. The condition of the FE matrices is improved by the matrix deflation which replaces small eigenvalues with zeros. It is known that convergence of linear solvers for FE equations can be improved by using the AV method as well as explicit and implicit error correction (EC) methods which have been derived from the multigrid method. These numerical results are theorized on the basis of the matrix deflation. In particular, augmented matrices appeared in the AV and implicit EC methods are shown to have good conditioning after preconditioning. These results suggest that the above methods are based on a common mathematical principle.
隐式修正多重网格法的概念
DOI：
--
发表时间：
2007
期刊：
影响因子：
--
作者：
岩下武史;美舩健;島崎眞昭;高橋康人;石田智之;廣谷迪;増子拓也;美舩健;高橋康人;高橋康人;岩下武史;岩下武史;高橋康人;高橋康人;守口聡一;荒井宗範;岩下武史;美舩健;荒井宗範;Takeshi Iwashita;美舩健;Takeshi Iwashita
通讯作者：
Takeshi Iwashita