An Efficient Newton Multiscale Multigrid Method for 2D Semilinear Poisson Equations
Ming Li, Zhoushun Zheng, Kejia Pan, Xiaoqiang Yue
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Source: Crossref
Published: Jun 12, 2020
DOI: 10.4208/eajam.090120.260320
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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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