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作者:

Xu, Fei (Xu, Fei.) | Huang, Qiumei (Huang, Qiumei.) (学者:黄秋梅)

收录:

Scopus SCIE

摘要:

This paper is to introduce a type of cascadic multigrid method for coupled semilinear elliptic equations. Instead of solving the coupled semilinear elliptic equation on a very fine finite element space directly, the new scheme needs to solve a decoupled linear system by some smoothing steps on each of multilevel finite element spaces and solve a coupled semilinear elliptic equation on a coarse space. By choosing the appropriate number of smoothing steps on different finite element spaces, the corresponding optimal convergence rate and optimal computation work can be derived. Besides, the adaptive cascadic multigrid method for coupled semilinear elliptic equations and its analysis are also presented theoretically and numerically. Moreover, the requirement of bounded second order derivatives of the nonlinear term in the existing multigrid methods is reduced to the Lipschitz continuation property in the presented new scheme. Some numerical experiments are presented to validate our theoretical analysis.

关键词:

Adaptive multigrid method Cascadic multigrid method Coupled semilinear elliptic equation Finite element method

作者机构:

  • [ 1 ] [Xu, Fei]Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China
  • [ 2 ] [Huang, Qiumei]Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China

通讯作者信息:

  • [Xu, Fei]Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China

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来源 :

NUMERICAL ALGORITHMS

ISSN: 1017-1398

年份: 2020

期: 2

卷: 83

页码: 485-510

2 . 1 0 0

JCR@2022

ESI学科: MATHEMATICS;

ESI高被引阀值:15

JCR分区:1

被引次数:

WoS核心集被引频次: 4

SCOPUS被引频次: 4

ESI高被引论文在榜: 0 展开所有

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中文被引频次:

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