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Volume 12, Issue 2
Efficient Preconditioned Iterative Linear Solvers for 3-D Magnetostatic Problems Using Edge Elements

Xian-Ming Gu, Yanpu Zhao, Tingzhu Huang & Ran Zhao

Adv. Appl. Math. Mech., 12 (2020), pp. 301-318.

Published online: 2020-01

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  • Abstract

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 Coulomb-gauged 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 Headings

65F08, 65N30, 78A30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

guxianming@live.cn (Xian-Ming Gu)

yanpu.zhao@whu.edu.cn (Yanpu Zhao)

tingzhuhuang@126.com (Tingzhu Huang)

rzhao@ahu.edu.cn (Ran Zhao)

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@Article{AAMM-12-301, author = {Gu , Xian-MingZhao , YanpuHuang , Tingzhu and Zhao , Ran}, title = {Efficient Preconditioned Iterative Linear Solvers for 3-D Magnetostatic Problems Using Edge Elements}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {2}, pages = {301--318}, abstract = {

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 Coulomb-gauged 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0207}, url = {http://global-sci.org/intro/article_detail/aamm/13623.html} }
TY - JOUR T1 - Efficient Preconditioned Iterative Linear Solvers for 3-D Magnetostatic Problems Using Edge Elements AU - Gu , Xian-Ming AU - Zhao , Yanpu AU - Huang , Tingzhu AU - Zhao , Ran JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 301 EP - 318 PY - 2020 DA - 2020/01 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2018-0207 UR - https://global-sci.org/intro/article_detail/aamm/13623.html KW - Coulomb gauge, edge element, iterative linear solver, magnetostatics, block preconditioner. AB -

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 Coulomb-gauged 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.

Xian-Ming Gu, Yanpu Zhao, Tingzhu Huang & Ran Zhao. (2020). Efficient Preconditioned Iterative Linear Solvers for 3-D Magnetostatic Problems Using Edge Elements. Advances in Applied Mathematics and Mechanics. 12 (2). 301-318. doi:10.4208/aamm.OA-2018-0207
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