An Efficient Newton Multiscale Multigrid Method for 2D Semilinear Poisson Equations

An Efficient Newton Multiscale Multigrid Method for 2D Semilinear Poisson Equations

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.

Author Details

Ming Li

Zhoushun Zheng

Kejia Pan

Xiaoqiang Yue

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