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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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