Year: 2020
Author: Ming Li, Zhoushun Zheng, Kejia Pan, Xiaoqiang Yue
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 3 : pp. 620–634
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.090120.260320
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 3 : pp. 620–634
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Semilinear Poisson equation Richardson extrapolation sixth-order accuracy Newton’s method multiscale multigrid.