An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations

Handle URI:
http://hdl.handle.net/10754/597516
Title:
An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
Authors:
Burrage, Kevin; Hale, Nicholas; Kay, David
Abstract:
Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.
Citation:
Burrage K, Hale N, Kay D (2012) An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations. SIAM Journal on Scientific Computing 34: A2145–A2172. Available: http://dx.doi.org/10.1137/110847007.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2012
DOI:
10.1137/110847007
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This author's work was supported by award KUK-C1-013-04 from King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBurrage, Kevinen
dc.contributor.authorHale, Nicholasen
dc.contributor.authorKay, Daviden
dc.date.accessioned2016-02-25T12:41:16Zen
dc.date.available2016-02-25T12:41:16Zen
dc.date.issued2012-01en
dc.identifier.citationBurrage K, Hale N, Kay D (2012) An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations. SIAM Journal on Scientific Computing 34: A2145–A2172. Available: http://dx.doi.org/10.1137/110847007.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/110847007en
dc.identifier.urihttp://hdl.handle.net/10754/597516en
dc.description.abstractFractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis author's work was supported by award KUK-C1-013-04 from King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectFinite elementsen
dc.subjectFractional diffusionen
dc.subjectNumerical solversen
dc.titleAn Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equationsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionQueensland University of Technology QUT, Brisbane, Australiaen
kaust.grant.numberKUK-C1-013-04en
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