An extrapolation accelerated multiscale Newton-MG method for fourth-order compact discretizations of semilinear Poisson equations

An extrapolation accelerated multiscale Newton-multigrid (EMNMG) method is proposed to solve two-dimensional semilinear Poisson equations. The nine-point fourth-order compact schemes are used to approximate the nonlinear Poisson equations. In order to accelerate Newton-MG method for calculating the...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) Vol. 113; pp. 189 - 197
Main Authors: Hu, Hongling, Li, Ming, Pan, Kejia, Wu, Pinxia
Format: Journal Article
Language:English
Published: Oxford Elsevier Ltd 01.05.2022
Elsevier BV
Subjects:
Algorithms
Discretization
Extrapolation
Finite difference method
Fourth-order compact scheme
Interpolation
Multigrid algorithm
Nonlinear term
Poisson equation
Polynomials
Extrapolation
Poisson equation
Fourth-order compact scheme
Nonlinear term
Multigrid algorithm
ISSN:0898-1221, 1873-7668
Online Access:Get full text
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Summary:An extrapolation accelerated multiscale Newton-multigrid (EMNMG) method is proposed to solve two-dimensional semilinear Poisson equations. The nine-point fourth-order compact schemes are used to approximate the nonlinear Poisson equations. In order to accelerate Newton-MG method for calculating the finite difference (FD) solution on the finest grid, a quite good initial guess is constructed from the fourth-order FD solutions at two coarse levels by using Richardson extrapolation and bi-quartic polynomial interpolation, which greatly reduces the number of Newton iterations required. A completed extrapolation technique is adopted to generate a sixth-order extrapolated solution on entire finest grid cheaply. Numerical results are given to show that our proposed EMNMG algorithm can achieve high accuracy and keep less cost simultaneously.
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2022.03.003