dc.contributor.author Allouch, Samer dc.contributor.author Lucchesi, Marco dc.contributor.author Maître, O. P. Le dc.contributor.author Mustapha, K. A. dc.contributor.author Knio, Omar dc.date.accessioned 2017-12-28T07:32:15Z dc.date.available 2017-12-28T07:32:15Z dc.date.issued 2017-07-12 dc.identifier.uri http://hdl.handle.net/10754/626535 dc.description.abstract This 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.publisher arXiv dc.relation.url http://arxiv.org/abs/1707.03871v1 dc.relation.url http://arxiv.org/pdf/1707.03871v1 dc.rights Archived with thanks to arXiv dc.title Particle Simulation of Fractional Diffusion Equations dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Applied Mathematics and Computational Science Program dc.eprint.version Pre-print dc.contributor.institution CNRS, LIMSI, Universit´e de Paris Saclay, Orsay, France dc.contributor.institution King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia dc.identifier.arxivid 1707.03871 kaust.person Allouch, Samer kaust.person Lucchesi, Marco kaust.person Knio, Omar dc.version v1 refterms.dateFOA 2018-06-13T11:11:18Z
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