Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient

Brabazon, Keeran J. and Hubbard, Matthew E. and Jimack, Peter K. (2014) Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient. Computers and Mathematics with Applications, 68 (12A). pp. 1619-1634. ISSN 0898-1221

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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.

Item Type: Article
Keywords: Nonlinear multigrid; Newton’s method; Nonlinear diffusion
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1016/j.camwa.2014.11.002
Depositing User: Hubbard, Matthew
Date Deposited: 27 Feb 2017 09:33
Last Modified: 13 Oct 2017 01:43
URI: http://eprints.nottingham.ac.uk/id/eprint/40817

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