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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
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Year:    2020

Author:    Xian-Ming Gu, Yanpu Zhao, Tingzhu Huang, Ran Zhao

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0207

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 2 : pp. 301–318

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Coulomb gauge edge element iterative linear solver magnetostatics block preconditioner.

Author Details

Xian-Ming Gu

Yanpu Zhao

Tingzhu Huang

Ran Zhao

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