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\begin{document}

\title{High accuracy extrapolation cascadic Newton multigrid computation for
two-dimensional nonlinear Poisson equations}



\author[1]{Ming Li}%
\author[1]{Chenglin LI}%
\affil[1]{Honghe University}%


\vspace{-1em}



  
  \date{May 16, 2024}


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\begin{abstract}
An extrapolation cascadic Newton multigrid (ECNMG) method is proposed
for high accuracy numerical solutions of two-dimensional nonlinear
Poisson~equations, by incorporating the fourth-order compact difference
schemes, the extrapolation techniques and the existing Newton multigrid
method. A series of grid level dependent computational~tolerances~are
discussed to distribute computational cost on different grids, and an
extrapolation interpolation strategy and a bi-quartic polynomial
interpolation are used for two fourth-order approximations from current
and previous grids to provide an extremely accurate initial guess on the
next finer grid, which can greatly reduce the iterations of the Newton
multigrid computation for computing an approximation with
discretization-level accuracy. Additionally, a completed Richardson
extrapolation technique is adopted for the fourth-order computed
solution to generate a sixth-order extrapolated solution cheaply.
Numerical results of two-dimensional nonlinear Poisson-Boltzmann
equations with five different fourth-order compact difference schemes
are conducted to demonstrate the new ECNMG~algorithm achieve sixth-order
accuracy and keep less cost simultaneously, more efficient than the
existing Newton-MG method.%
\end{abstract}%



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\textbf{Hosted file}

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