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Volume 39, Issue 5
Modified Alternating Positive Semidefinite Splitting Preconditioner for Time-Harmonic Eddy Current Models

Yifen Ke & Changfeng Ma

DOI: 10.4208/jcm.2006-m2020-0037

J. Comp. Math., 39 (2021), pp. 733-754.

Published online: 2021-08

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  • Abstract

In this paper, we consider a modified alternating positive semidefinite splitting preconditioner for solving the saddle point problems arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current model. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are studied for both simple and general topology. Numerical results demonstrate the effectiveness of the proposed preconditioner when it is used to accelerate the convergence rate of Krylov subspace methods such as GMRES.

  • Keywords

Time-harmonic eddy current model, Saddle point problem, Eigenvalue distribution, Preconditioner.

  • AMS Subject Headings

65F08, 65F10, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

keyifen@fjnu.edu.cn (Yifen Ke)

macf@fjnu.edu.cn (Changfeng Ma)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-733, author = {Ke , Yifen and Ma , Changfeng}, title = {Modified Alternating Positive Semidefinite Splitting Preconditioner for Time-Harmonic Eddy Current Models}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {39}, number = {5}, pages = {733--754}, abstract = {

In this paper, we consider a modified alternating positive semidefinite splitting preconditioner for solving the saddle point problems arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current model. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are studied for both simple and general topology. Numerical results demonstrate the effectiveness of the proposed preconditioner when it is used to accelerate the convergence rate of Krylov subspace methods such as GMRES.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2006-m2020-0037}, url = {http://global-sci.org/intro/article_detail/jcm/19379.html} }
TY - JOUR T1 - Modified Alternating Positive Semidefinite Splitting Preconditioner for Time-Harmonic Eddy Current Models AU - Ke , Yifen AU - Ma , Changfeng JO - Journal of Computational Mathematics VL - 5 SP - 733 EP - 754 PY - 2021 DA - 2021/08 SN - 39 DO - http://doi.org/10.4208/jcm.2006-m2020-0037 UR - https://global-sci.org/intro/article_detail/jcm/19379.html KW - Time-harmonic eddy current model, Saddle point problem, Eigenvalue distribution, Preconditioner. AB -

In this paper, we consider a modified alternating positive semidefinite splitting preconditioner for solving the saddle point problems arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current model. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are studied for both simple and general topology. Numerical results demonstrate the effectiveness of the proposed preconditioner when it is used to accelerate the convergence rate of Krylov subspace methods such as GMRES.

Ke , Yifen and Ma , Changfeng. (2021). Modified Alternating Positive Semidefinite Splitting Preconditioner for Time-Harmonic Eddy Current Models. Journal of Computational Mathematics. 39 (5). 733-754. doi:10.4208/jcm.2006-m2020-0037
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