Efficient Preconditioned Iterative Linear Solvers for 3-D Magnetostatic Problems Using Edge Elements
Efficient Preconditioned Iterative Linear Solvers for 3-D Magnetostatic Problems Using Edge Elements
复制标题
使用边缘单元求解 3D 静磁问题的高效预处理迭代线性求解器
DOI：
10.4208/aamm.oa-2018-0207
复制
发表时间：
2020-04-01
影响因子：
1.4
通讯作者：
Zhao, Ran
中科院分区：
文献类型：
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作者：
Gu, Xianming;Zhao, Yanpu;Zhao, Ran
对于三维大规模静磁问题的数值计算，迭代求解器是优选的，因为在使用稀疏直接求解器的情况下需要大量的存储器。在本文中，最近提出的库仑规范磁矢量位（MVP）制定的静磁问题的有限元离散使用边缘元素，其中所得的线性系统是对称的，但病态的。为了有效地解决这样的线性系统，我们利用迭代Krylov子空间求解器，通过构造三个新的块预条件，这是来自传统的块雅可比，高斯-赛德尔和约束预条件。频谱特性和实际的实施细节的建议预条件进行了讨论。最后，通过数值算例验证了所提方法的有效性和准确性。AMS科目分类：65 F08、65 N30、78 A30
For numerical computation of three-dimensional (3-D) large-scale magnetostatic problems, iterative solver is preferable since a huge amount of memory is needed in case of using sparse direct solvers. In this paper, a recently proposed Coulombgauged magnetic vector potential (MVP) formulation for magnetostatic problems is adopted for finite element discretization using edge elements, where the resultant linear system is symmetric but ill-conditioned. To solve such linear systems efficiently, we exploit iterative Krylov subspace solvers by constructing three novel block preconditioners, which are derived from conventional block Jacobi, Gauss-Seidel and constraint preconditioners. Spectral properties and practical implementation details of the proposed preconditioners are also discussed. Then, numerical examples of practical simulations are presented to illustrate the efficiency and accuracy of the proposed methods. AMS subject classifications: 65F08, 65N30, 78A30