Frontiers of Mathematics in China

, Volume 13, Issue 2, pp 313–340 | Cite as

A new alternating positive semidefinite splitting preconditioner for saddle point problems from time-harmonic eddy current models

  • Yifen Ke
  • Changfeng Ma
  • Zhiru Ren
Research Article


Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new alternating positive semidefinite splitting (APSS) iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.


Time-harmonic eddy current problem saddle point problem alternating positive semidefinite splitting (APSS) convergence analysis preconditioner iteration method 


65F08 65F10 65F50 


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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11301521, 11771467, 11071041), the Natural Science Foundation of Fujian Province (Nos. 2016J01005, 2015J01578), and the National Post-doctoral Program for Innovative Talents (No. BX201700234).


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Computational Geodynamics of Chinese Academy of SciencesUniversity of Chinese Academy of SciencesBeijingChina
  2. 2.College of Mathematics and Informatics & FJKLMAAFujian Normal UniversityFuzhouChina
  3. 3.School of Statistics and MathematicsCentral University of Finance and EconomicsBeijingChina

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