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Volume 10, Issue 3
An Efficient Newton Multiscale Multigrid Method for 2D Semilinear Poisson Equations

Ming Li, Zhoushun Zheng, Kejia Pan & Xiaoqiang Yue

DOI: 10.4208/eajam.090120.260320

East Asian J. Appl. Math., 10 (2020), pp. 620-634.

Published online: 2020-06

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  • 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.

  • Keywords

Semilinear Poisson equation, Richardson extrapolation, sixth-order accuracy, Newton’s method, multiscale multigrid.

  • AMS Subject Headings

65N30, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-620, author = {Li , MingZheng , ZhoushunPan , Kejia and Yue , Xiaoqiang}, title = {An Efficient Newton Multiscale Multigrid Method for 2D Semilinear Poisson Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.090120.260320}, url = {http://global-sci.org/intro/article_detail/eajam/16985.html} }
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.

Li , MingZheng , ZhoushunPan , Kejia and Yue , Xiaoqiang. (2020). An Efficient Newton Multiscale Multigrid Method for 2D Semilinear Poisson Equations. East Asian Journal on Applied Mathematics. 10 (3). 620-634. doi:10.4208/eajam.090120.260320
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