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dc.contributor.authorAllouch, Samer
dc.contributor.authorLucchesi, Marco
dc.contributor.authorMaître, O. P. Le
dc.contributor.authorMustapha, K. A.
dc.contributor.authorKnio, Omar
dc.date.accessioned2017-12-28T07:32:15Z
dc.date.available2017-12-28T07:32:15Z
dc.date.issued2017-07-12
dc.identifier.urihttp://hdl.handle.net/10754/626535
dc.description.abstractThis work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green's function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.
dc.publisherarXiv
dc.relation.urlhttp://arxiv.org/abs/1707.03871v1
dc.relation.urlhttp://arxiv.org/pdf/1707.03871v1
dc.rightsArchived with thanks to arXiv
dc.titleParticle Simulation of Fractional Diffusion Equations
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.eprint.versionPre-print
dc.contributor.institutionCNRS, LIMSI, Universit´e de Paris Saclay, Orsay, France
dc.contributor.institutionKing Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
dc.identifier.arxivid1707.03871
kaust.personAllouch, Samer
kaust.personLucchesi, Marco
kaust.personKnio, Omar
dc.versionv1
refterms.dateFOA2018-06-13T11:11:18Z


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