Brabazon, KJ, Hubbard, ME and Jimack, PK (2014) Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient. Computers and Mathematics with Applications, 68 (12A). 1619 - 1634. ISSN 0898-1221
Abstract
Nonlinear multigrid methods such as the Full Approximation Scheme (FAS) and Newton-multigrid (Newton-MG) are well established as fast solvers for nonlinear PDEs of elliptic and parabolic type. In this paper we consider Newton-MG and FAS iterations applied to second order differential operators with nonlinear diffusion coefficient. Under mild assumptions arising in practical applications, an approximation (shown to be sharp) of the execution time of the algorithms is derived, which demonstrates that Newton-MG can be expected to be a faster iteration than a standard FAS iteration for a finite element discretisation. Results are provided for elliptic and parabolic problems, demonstrating a faster execution time as well as greater stability of the Newton-MG iteration. Results are explained using current theory for the convergence of multigrid methods, giving a qualitative insight into how the nonlinear multigrid methods can be expected to perform in practice.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 Elsevier Ltd. All rights reserved. NOTICE: this is the author’s version of a work that was accepted for publication in Computers and Mathematics with Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Mathematics with Applications, 68, 12A, (2014) DOI 10.1016/j.camwa.2014.11.002 |
Keywords: | Nonlinear multigrid; Newton's method; Nonlinear diffusion |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 20 Feb 2015 10:06 |
Last Modified: | 17 Jan 2018 05:15 |
Published Version: | http://dx.doi.org/10.1016/j.camwa.2014.11.002 |
Status: | Published |
Publisher: | Elsevier Ltd |
Identification Number: | 10.1016/j.camwa.2014.11.002 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:82958 |