Volume 10, Issue 1
A Local Positive (Semi)Definite Shift-Splitting Preconditioner for Saddle Point Problems with Applications to Time-Harmonic Eddy Current Models

Yang Cao & Zhi-Ru Ren

East Asian J. Appl. Math., 10 (2020), pp. 135-157.

Published online: 2020-01

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  • Abstract

A local positive (semi)defifinite shift-splitting preconditioner for non-Hermitian saddle point problems arising in fifinite element discretisations of hybrid formulations of time-harmonic eddy current models is constructed. The convergence of the corresponding iteration methods is proved and the spectral properties of the associated preconditioned saddle point matrices are studied. Numerical experiments show the effificiency of the proposed preconditioner for Krylov subspace methods.

  • Keywords

Saddle point problem, splitting iteration, preconditioning, convergence, time-harmonic eddy current model.

  • AMS Subject Headings

65F10, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

caoyangnt@ntu.edu.cn (Yang Cao)

renzr@ufe.edu.cn (Zhi-Ru Ren)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-10-135, author = {Cao , Yang and Ren , Zhi-Ru }, title = {A Local Positive (Semi)Definite Shift-Splitting Preconditioner for Saddle Point Problems with Applications to Time-Harmonic Eddy Current Models}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {1}, pages = {135--157}, abstract = {

A local positive (semi)defifinite shift-splitting preconditioner for non-Hermitian saddle point problems arising in fifinite element discretisations of hybrid formulations of time-harmonic eddy current models is constructed. The convergence of the corresponding iteration methods is proved and the spectral properties of the associated preconditioned saddle point matrices are studied. Numerical experiments show the effificiency of the proposed preconditioner for Krylov subspace methods.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150319.200619}, url = {http://global-sci.org/intro/article_detail/eajam/13607.html} }
TY - JOUR T1 - A Local Positive (Semi)Definite Shift-Splitting Preconditioner for Saddle Point Problems with Applications to Time-Harmonic Eddy Current Models AU - Cao , Yang AU - Ren , Zhi-Ru JO - East Asian Journal on Applied Mathematics VL - 1 SP - 135 EP - 157 PY - 2020 DA - 2020/01 SN - 10 DO - http://dor.org/10.4208/eajam.150319.200619 UR - https://global-sci.org/intro/article_detail/eajam/13607.html KW - Saddle point problem, splitting iteration, preconditioning, convergence, time-harmonic eddy current model. AB -

A local positive (semi)defifinite shift-splitting preconditioner for non-Hermitian saddle point problems arising in fifinite element discretisations of hybrid formulations of time-harmonic eddy current models is constructed. The convergence of the corresponding iteration methods is proved and the spectral properties of the associated preconditioned saddle point matrices are studied. Numerical experiments show the effificiency of the proposed preconditioner for Krylov subspace methods.

Yang Cao & Zhi-Ru Ren. (2020). A Local Positive (Semi)Definite Shift-Splitting Preconditioner for Saddle Point Problems with Applications to Time-Harmonic Eddy Current Models. East Asian Journal on Applied Mathematics. 10 (1). 135-157. doi:10.4208/eajam.150319.200619
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