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

Li-Li Zhang

Applied Mathematics and Computation, 2021, vol. 399, issue C

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.

Keywords: Nonlinear complementarity problem; Free boundary problem; Modulus-based multigrid method; Local Fourier analysis (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000631

DOI: 10.1016/j.amc.2021.126015

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