New algebraic multigrid preconditioning for iterative solvers in electromagnetic finite edge-element analyses
New algebraic multigrid preconditioning for iterative solvers in electromagnetic finite edge-element analyses
复制标题
电磁有限边缘元分析中迭代求解器的新代数多重网格预处理
DOI：
10.1109/tmag.2003.810350
复制
发表时间：
2003
影响因子：
2.1
通讯作者：
M. Shimasaki
中科院分区：
文献类型：
--
作者：
T. Mifune;T. Iwashita;M. Shimasaki
代数多重网格 (AMG) 方法是线性方程组的代数多级求解器，源于偏微分方程的离散化。本文开发了一种高效的 AMG 求解器，用于解决使用边缘单元进行电磁有限元 (FE) 分析时产生的奇异线性方程组。所提出的求解器可以使用类似于移位不完全 Cholesky 共轭梯度法的技术来求解奇异方程。利用移位的全局系数矩阵来构造 AMG 预处理器。数值结果表明，所提出的AMG共轭梯度（AMGCG）求解器可以在大范围的“移位”下收敛。
The algebraic multigrid (AMG) method is an algebraic multilevel solver for linear systems of equations, which stem from the discretization of partial differential equations. This paper develops an efficient AMG solver for singular linear systems of equations arising from electromagnetic finite element (FE) analyses using edge elements. The presented solver can solve singular equations using a technique similar to the shifted incomplete Cholesky conjugate gradient method. Shifted global coefficient matrices are utilized to construct the AMG preconditioner. The numerical results show that the proposed AMG conjugate gradient (AMGCG) solver can converge with a wide range of "shift".