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

作者：

Highlights：

• We present a modulus-based multigrid method to efficiently solve the nonlinear complementarity problems (NCPs) arising 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 for NCPs, and the predictions are agreement with the experimental results.

• Numerical results show that both W- and F-cycles significantly outperform the existing modulus-based method for NCPs and achieve asymptotic optimality in terms of grid-independent convergence rate and linear CPU time when the grid is refined.

摘要

•We present a modulus-based multigrid method to efficiently solve the nonlinear complementarity problems (NCPs) arising 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 for NCPs, and the predictions are agreement with the experimental results.•Numerical results show that both W- and F-cycles significantly outperform the existing modulus-based method for NCPs and achieve asymptotic optimality in terms of grid-independent convergence rate and linear CPU time when the grid is refined.

论文关键词：Nonlinear complementarity problem,Free boundary problem,Modulus-based multigrid method,Local Fourier analysis

论文评审过程：Received 3 July 2020, Revised 15 December 2020, Accepted 17 January 2021, Available online 1 February 2021, Version of Record 1 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126015