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The dimensional splitting iteration methods for solving saddle point problems arising from time-harmonic eddy current models

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  • Ke, Yi-Fen
  • Ma, Chang-Feng

Abstract

A dimensional splitting iteration method is proposed for solving the saddle point problems arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current models, which is by making use of the special positive semidefinite splittings of the saddle point matrix. It is proved that the proposed iteration method is unconditionally convergent for both cases of simple topology and general topology. Numerical results show that the corresponding preconditioner is superior to the existing preconditioners, when those preconditioners are used to accelerate the convergence rate of Krylov subspace methods.

Suggested Citation

  • Ke, Yi-Fen & Ma, Chang-Feng, 2017. "The dimensional splitting iteration methods for solving saddle point problems arising from time-harmonic eddy current models," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 146-164.
    • Handle: RePEc:eee:apmaco:v:303:y:2017:i:c:p:146-164
    DOI: 10.1016/j.amc.2017.01.037
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    References listed on IDEAS

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    1. Huang, Na & Ma, Chang-Feng, 2015. "The nonlinear inexact Uzawa hybrid algorithms based on one-step Newton method for solving nonlinear saddle-point problems," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 291-311.
    2. Shao, Xin-Hui & Li, Chen, 2015. "A generalization of preconditioned parameterized inexact Uzawa method for indefinite saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 691-698.
    3. Chen, Cai-Rong & Ma, Chang-Feng, 2015. "A generalized shift-splitting preconditioner for singular saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 947-955.
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