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 - <p style="text-align: justify;">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.<br/></p>