TY - JOUR T1 - An Efficient Newton Multiscale Multigrid Method for 2D Semilinear Poisson Equations AU - Li , Ming AU - Zheng , Zhoushun AU - Pan , Kejia AU - Yue , Xiaoqiang JO - East Asian Journal on Applied Mathematics VL - 3 SP - 620 EP - 634 PY - 2020 DA - 2020/06 SN - 10 DO - http://doi.org/10.4208/eajam.090120.260320 UR - https://global-sci.org/intro/article_detail/eajam/16985.html KW - Semilinear Poisson equation, Richardson extrapolation, sixth-order accuracy, Newton’s method, multiscale multigrid. AB -

An efficient Newton multiscale multigrid (Newton-MSMG) for solving large nonlinear systems arising in the fourth-order compact difference discretisation of 2D semilinear Poisson equations is presented. The Newton-MG method is employed to calculate approximation solutions on coarse and fine grids and then a completed Richardson extrapolation is used to construct a sixth-order extrapolated solution on the entire fine grid directly. The method is applied to two nonlinear Poisson-Boltzmann equations and numerical simulations show that the Newton-MSMG method is a cost-effective approach with the sixth-order accuracy.