Close Search Advanced
Journals
Resources
About Us
Open Access

Picard-Newton Iterative Method with Time Step Control for Multimaterial Non-Equilibrium Radiation Diffusion Problem

Picard-Newton Iterative Method with Time Step Control for Multimaterial Non-Equilibrium Radiation Diffusion Problem
Preview
Add to basket

Year:    2011

Communications in Computational Physics, Vol. 10 (2011), Iss. 4 : pp. 844–866

Abstract

For a new nonlinear iterative method named as Picard-Newton (P-N) iterative method for the solution of the time-dependent reaction-diffusion systems, which arise in non-equilibrium radiation diffusion applications, two time step control methods are investigated and a study of temporal accuracy of a first order time integration is presented. The non-equilibrium radiation diffusion problems with flux limiter are considered, which appends pesky complexity and nonlinearity to the diffusion coefficient. Numerical results are presented to demonstrate that compared with Picard method, for a desired accuracy, significant increase in solution efficiency can be obtained by Picard-Newton method with the suitable time step size selection.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.310110.161010a

Communications in Computational Physics, Vol. 10 (2011), Iss. 4 : pp. 844–866

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:   

  1. Meshfree methods for nonlinear equilibrium radiation diffusion equation

    Wang, Rong | Xu, Qiuyan | Liu, Zhiyong

    Engineering Analysis with Boundary Elements, Vol. 144 (2022), Iss. P.311

    https://doi.org/10.1016/j.enganabound.2022.08.012 [Citations: 1]

  2. A second‐order space–time accurate scheme for nonlinear diffusion equation with general capacity term

    Zheng, Huan | Yuan, Guangwei | Cui, Xia

    Numerical Methods for Partial Differential Equations, Vol. 36 (2020), Iss. 6 P.1845

    https://doi.org/10.1002/num.22507 [Citations: 4]

  3. A moving mesh finite difference method for equilibrium radiation diffusion equations

    Yang, Xiaobo | Huang, Weizhang | Qiu, Jianxian

    Journal of Computational Physics, Vol. 298 (2015), Iss. P.661

    https://doi.org/10.1016/j.jcp.2015.06.014 [Citations: 12]

  4. An efficient acceleration technique of implicit schemes for quasi-linear parabolic problems

    Pan, Kejia | Xie, Jiajia | Fu, Kang | Hu, Hongling

    Numerical Algorithms, Vol. (2024), Iss.

    https://doi.org/10.1007/s11075-024-01973-y [Citations: 0]

  5. Numerical analysis and iteration acceleration of a fully implicit scheme for nonlinear diffusion problem with second‐order time evolution

    Cui, Xia | Yuan, Guang‐wei | Yue, Jing‐yan

    Numerical Methods for Partial Differential Equations, Vol. 32 (2016), Iss. 1 P.121

    https://doi.org/10.1002/num.21988 [Citations: 10]

  6. Weighted Interior Penalty Method with Semi-Implicit Integration Factor Method for Non-Equilibrium Radiation Diffusion Equation

    Zhang, Rongpei | Yu, Xijun | Zhu, Jiang | D. Loula, Abimael F. | Cui, Xia

    Communications in Computational Physics, Vol. 14 (2013), Iss. 5 P.1287

    https://doi.org/10.4208/cicp.190612.010313a [Citations: 3]

  7. An efficient iterative method for radiation heat conduction problems

    Yao, Yanzhong | Miao, Shuai | Lv, Guixia

    International Journal for Numerical Methods in Fluids, Vol. 93 (2021), Iss. 7 P.2362

    https://doi.org/10.1002/fld.4977 [Citations: 2]

  8. Iterative acceleration methods with second-order time accuracy for nonlinear diffusion equations

    Zhao, Fei | Cui, Xia | Yuan, Guangwei

    Advances in Computational Mathematics, Vol. 46 (2020), Iss. 1

    https://doi.org/10.1007/s10444-020-09756-4 [Citations: 2]

  9. Nonlinear iteration acceleration solution for equilibrium radiation diffusion equation

    Zhang, Yanmei | Cui, Xia | Yuan, Guangwei

    ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 54 (2020), Iss. 5 P.1465

    https://doi.org/10.1051/m2an/2019095 [Citations: 1]

  10. Moving mesh finite difference solution of non-equilibrium radiation diffusion equations

    Yang, Xiaobo | Huang, Weizhang | Qiu, Jianxian

    Numerical Algorithms, Vol. 82 (2019), Iss. 4 P.1409

    https://doi.org/10.1007/s11075-019-00662-5 [Citations: 1]

  11. Analysis on a high accuracy fully implicit solution for strong nonlinear diffusion problem - convergence, stability, and uniqueness

    Gong, Yujie | Yuan, Guangwei | Cui, Xia

    Applied Mathematics and Computation, Vol. 467 (2024), Iss. P.128499

    https://doi.org/10.1016/j.amc.2023.128499 [Citations: 0]

  12. Iteration acceleration methods for solving three‐temperature heat conduction equations on distorted meshes

    Yu, Yunlong | Chen, Xingding | Yao, Yanzhong

    Numerical Methods for Partial Differential Equations, Vol. 40 (2024), Iss. 4

    https://doi.org/10.1002/num.23085 [Citations: 0]

  13. New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

    Lipnikov, Konstantin | Moulton, David | Svyatskiy, Daniil

    Advances in Water Resources, Vol. 94 (2016), Iss. P.11

    https://doi.org/10.1016/j.advwatres.2016.04.016 [Citations: 13]

  14. The existence of continuous weak solutions with compact support for degenerate parabolic systems with exchange-type source

    Yang, Tianjie | Yuan, Guangwei

    Applicable Analysis, Vol. 103 (2024), Iss. 1 P.263

    https://doi.org/10.1080/00036811.2023.2182774 [Citations: 0]

  15. A class of new successive permutation iterative algorithms with the relaxation factor for radiation diffusion equation

    Pan, Yunming | Xu, Qiuyan | Liu, Zhiyong | Yang, Jiye

    Computational and Applied Mathematics, Vol. 42 (2023), Iss. 5

    https://doi.org/10.1007/s40314-023-02341-7 [Citations: 0]

  16. A Finite Volume Scheme Preserving Maximum Principle for the System of Radiation Diffusion Equations with Three-Temperature

    Yu, Yunlong | Chen, Xingding | Yuan, Guangwei

    SIAM Journal on Scientific Computing, Vol. 41 (2019), Iss. 1 P.B93

    https://doi.org/10.1137/18M1167024 [Citations: 12]

  17. Global existence for a class of non-equilibrium reaction–diffusion systems with flux limitation

    Yang, Tianjie | Yuan, Guangwei

    Nonlinear Analysis, Vol. 233 (2023), Iss. P.113305

    https://doi.org/10.1016/j.na.2023.113305 [Citations: 0]

  18. High-precision meshfree methods for solving 3D radiation diffusion problem in irregular spaces

    Ma, Nan | Xu, Qiuyan | Liu, Zhiyong | Yang, Jiye

    Computers & Mathematics with Applications, Vol. 169 (2024), Iss. P.163

    https://doi.org/10.1016/j.camwa.2024.06.013 [Citations: 0]

  19. Semi-implicit front capturing schemes for the degenerate nonlinear radiative diffusion equation

    Tang, Min | Zhang, Xiaojiang

    Journal of Computational Physics, Vol. 436 (2021), Iss. P.110290

    https://doi.org/10.1016/j.jcp.2021.110290 [Citations: 5]

  20. Numerical Treatment of State‐Dependent Permeability in Multiphysics Problems

    Stefansson, Ivar | Keilegavlen, Eirik

    Water Resources Research, Vol. 59 (2023), Iss. 8

    https://doi.org/10.1029/2023WR034686 [Citations: 1]

  21. Fast meshfree methods for nonlinear radiation diffusion equation

    Wang, Rong | Xu, Qiuyan | Liu, Zhiyong | Yang, Jiye

    Applied Mathematics and Computation, Vol. 438 (2023), Iss. P.127571

    https://doi.org/10.1016/j.amc.2022.127571 [Citations: 0]

  22. Monotone finite point method for non-equilibrium radiation diffusion equations

    Huang, Zhongyi | Li, Ye

    BIT Numerical Mathematics, Vol. 56 (2016), Iss. 2 P.659

    https://doi.org/10.1007/s10543-015-0573-x [Citations: 9]

  23. Finite volume element approximation for nonlinear diffusion problems with degenerate diffusion coefficients

    Wu, Dan | Yue, Jingyan | Yuan, Guangwei | Lv, Junliang

    Applied Numerical Mathematics, Vol. 140 (2019), Iss. P.23

    https://doi.org/10.1016/j.apnum.2019.01.013 [Citations: 7]

  24. Parallelization methods for solving three-temperature radiation-hydrodynamic problems

    Yuan, Guangwei | Yao, Yanzhong

    Discrete and Continuous Dynamical Systems - Series B, Vol. 21 (2016), Iss. 5 P.1651

    https://doi.org/10.3934/dcdsb.2016016 [Citations: 0]

  25. Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

    Cui, Xia | Yuan, Guang-wei | Shen, Zhi-jun

    Journal of Computational Physics, Vol. 313 (2016), Iss. P.415

    https://doi.org/10.1016/j.jcp.2016.02.061 [Citations: 2]