IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v399y2021ics0096300321000631.html
   My bibliography  Save this article

A modulus-based multigrid method for nonlinear complementarity problems with application to free boundary problems with nonlinear source terms

Author

Listed:
  • Zhang, Li-Li

Abstract

To overcome the dependence of the convergence rate on the grid size in the existing modulus-based method, we present a modulus-based multigrid method to efficiently solve the nonlinear complementarity problems. In this paper, the nonlinear complementarity problems under consideration arise from free boundary problems with nonlinear source terms. The two-grid local Fourier analysis is given to predict the asymptotic convergence factor and the optimal relaxation parameter of the presented modulus-based multigrid method, and the predictions are agreement with the experimental results. Numerical results also show that both W- and F-cycles significantly outperform the existing modulus-based method and achieve asymptotic optimality in terms of grid-independent convergence rate and linear CPU time when the grid is refined.

Suggested Citation

  • Zhang, Li-Li, 2021. "A modulus-based multigrid method for nonlinear complementarity problems with application to free boundary problems with nonlinear source terms," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    • Handle: RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000631
    DOI: 10.1016/j.amc.2021.126015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321000631
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dai, Ping-Fan & Li, Jicheng & Bai, Jianchao & Qiu, Jinming, 2019. "A preconditioned two-step modulus-based matrix splitting iteration method for linear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 542-551.
    2. Zheng, Hua & Vong, Seakweng & Liu, Ling, 2019. "A direct preconditioned modulus-based iteration method for solving nonlinear complementarity problems of H-matrices," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 396-405.
    3. Xia, Zechen & Li, Chenliang, 2015. "Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 34-42.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Baohua Huang & Wen Li, 2023. "A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 345-381, September.
    2. Zhang, Yongxiong & Zheng, Hua & Lu, Xiaoping & Vong, Seakweng, 2023. "Modulus-based synchronous multisplitting iteration methods without auxiliary variable for solving vertical linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    3. Zheng, Hua & Vong, Seakweng & Liu, Ling, 2019. "A direct preconditioned modulus-based iteration method for solving nonlinear complementarity problems of H-matrices," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 396-405.
    4. Zheng, Hua & Vong, Seakweng, 2021. "On the modulus-based successive overrelaxation iteration method for horizontal linear complementarity problems arising from hydrodynamic lubrication," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    5. Hua Zheng & Ling Liu, 2019. "The Sign-Based Methods for Solving a Class of Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 480-499, February.
    6. Bharat Kumar & Deepmala & A. Dutta & A. K. Das, 2023. "More on matrix splitting modulus-based iterative methods for solving linear complementarity problem," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 1003-1020, June.
    7. Ping-Fan Dai & Shi-Liang Wu, 2022. "The GUS-Property and Modulus-Based Methods for Tensor Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 976-1006, December.
    8. Ali, Rashid & Akgul, Ali, 2024. "A new matrix splitting generalized iteration method for linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    9. Zheng, Hua & Vong, Seakweng, 2020. "On convergence of the modulus-based matrix splitting iteration method for horizontal linear complementarity problems of H+-matrices," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    10. Zhang, Yongxiong & Zheng, Hua & Vong, Seakweng & Lu, Xiaoping, 2023. "A two-step parallel iteration method for large sparse horizontal linear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 438(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000631. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.