CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2013, Vol. 30 ›› Issue (4): 483-490.

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Preconditioned Jacobian-free Newton-Krylov Methods for Nonequilibrium Radiation Diffusion Equations

FENG Tao1,2, YU Xijun3, AN Hengbin3, ZHANG Rongpei2   

  1. 1. School of Mathmatical Sciences, University of Science and Technology of China, Hefei 230052, China;
    2. Graduate School of China Academy Engineering Physics, Beijing 100088, China;
    3. National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
  • Received:2012-10-10 Revised:2013-01-24 Online:2013-07-25 Published:2013-07-25
  • Supported by:
    Supported by National Natural Science Foundation of China(11171039,11171038,11271054);National Basic Research Program of China(2011CB309702,2011CB309703);Science Foundation of CAEP(2012B0202026,2010A0202010);Foundation of National Key Laborotory of Science and Technology on Computation Physics and Defence Industrial Technology Development Program(B1520110011)

Abstract: Four semi-implicit discretization schemes are used to construct preconditioners.And preconditioned Jacobian-free Newton-Krylov (JFNK) are presented to solve one-dimensional problems.Numerical results show that the preconditioning methods improve the convergence behavior of JFNK method dramatically.

Key words: nonequilibrium radiation diffusion, Newton-Krylov method, linearization, preconditioning

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