@Article{JCM-37-112,
author = {Xu , Fei and Luo , Fusheng},
title = {A Cascadic Multigrid Method for Semilinear Elliptic Equations},
journal = {Journal of Computational Mathematics},
year = {2018},
volume = {37},
number = {1},
pages = {112--129},
abstract = {<p style="text-align: justify;">This paper introduce a cascadic multigrid method for solving semilinear elliptic equations
based on a multilevel correction method. Instead of the common costly way of directly
solving semilinear elliptic equation on a very fine space, the new method contains some
smoothing steps on a series of multilevel finite element spaces and some solving steps to
semilinear elliptic equations on a very coarse space. To prove the efficiency of the new
method, we derive two results, one of the optimal convergence rate by choosing the appropriate
sequence of finite element spaces and the number of smoothing steps, and the other
of the optimal computational work by applying the parallel computing technique. Moreover,
the requirement of bounded second order derivatives of nonlinear term in the existing
multigrid methods is reduced to a bounded first order derivative in the new method. Some
numerical experiments are presented to validate our theoretical analysis.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1710-m2017-0067},
url = {http://global-sci.org/intro/article_detail/jcm/12652.html}
}