Numerical study of a particle method for gradient flows

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Title: Numerical study of a particle method for gradient flows
Author(s): Patacchini, FS
Carrillo de la Plata, JA
Huang, Y
Wolansky, G
Item Type: Journal Article
Abstract: We study the numerical behaviour of a particle method for gradient ows involving linear and nonlinear di usion. This method relies on the discretisation of the energy via non- overlapping balls centred at the particles. The resulting scheme preserves the gradient ow structure at the particle level and enables us to obtain a gradient descent formulation after time discretisation. We give several simulations to illustrate the validity of this method, as well as a detailed study of one-dimensional aggregation-di usion equations.
Publication Date: 1-Sep-2017
Date of Acceptance: 26-Oct-2016
DOI: 10.3934/krm.2017025
ISSN: 1937-5093
Publisher: American Institute of Mathematical Sciences (AIMS)
Journal / Book Title: Kinetic and Related Models
Copyright Statement: This paper is embargoed until publication.
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (E
Funder's Grant Number: WM120001
Keywords: Applied Mathematics
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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