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dc.contributor.authorBurrage, Kevin
dc.contributor.authorHale, Nicholas
dc.contributor.authorKay, David
dc.date.accessioned2016-02-25T12:41:16Z
dc.date.available2016-02-25T12:41:16Z
dc.date.issued2012-01
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.
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/110847007
dc.identifier.urihttp://hdl.handle.net/10754/597516
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.
dc.description.sponsorshipThis author's work was supported by award KUK-C1-013-04 from King Abdullah University of Science and Technology (KAUST).
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectFinite elements
dc.subjectFractional diffusion
dc.subjectNumerical solvers
dc.titleAn Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
dc.typeArticle
dc.identifier.journalSIAM Journal on Scientific Computing
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
dc.contributor.institutionQueensland University of Technology QUT, Brisbane, Australia
kaust.grant.numberKUK-C1-013-04


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