202
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

An efficient extrapolation full multigrid method for elliptic problems in two and three dimensions

, & ORCID Icon
Pages 1183-1198 | Received 04 Jun 2018, Accepted 07 Aug 2020, Published online: 03 Sep 2020
 

Abstract

An extrapolation full multigrid (EXFMG) method is proposed for solving the large linear systems arising from linear finite element discretization of two- (2D) and three-dimensional (3D) elliptic boundary value problems. A good initial guess on the next finer grid is constructed through combining Richardson extrapolation and quadratic FE interpolation for the numerical solutions on two-level of grids (current and previous grids). And the FE linear system on the next finer grid is solved to obtain the EXFMG solution with discretization-level accuracy by performing one or two multigrid cycles with Gauss–Seidel smoother. Moreover, Richardson extrapolation is further used to achieve higher-order accuracy. The numerical results of five typical elliptic problems including one 2D problem and four 3D problems are conducted to show the effectiveness and efficiency of the EXFMG algorithm.

2010 AMS Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by Science Challenge Project [grant number TZ2016002], the National Natural Science Foundation of China [grant number 41874086], the Excellent Youth Foundation of Hunan Province of China [grant number 2018JJ1042], and the Natural Science Foundation of Yunnan Province of China [grant number 2017FH001-012].

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,129.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.