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-Dec-2016
Date of Acceptance: 26-Oct-2016
URI: http://hdl.handle.net/10044/1/43032
DOI: https://dx.doi.org/10.3934/krm.2017025
ISSN: 1937-5093
Publisher: American Institute of Mathematical Sciences (AIMS)
Start Page: 613
End Page: 641
Journal / Book Title: Kinetic and Related Models
Volume: 10
Issue: 3
Copyright Statement: © 2017 American Institute of Mathematical Sciences
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM120001
EP/K008404/1
Keywords: Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Particle method
diffusion
aggregation
gradient flow
discrete gradient flow
JKO scheme
POROUS-MEDIUM EQUATION
DIFFUSION-EQUATIONS
GAMMA-CONVERGENCE
GRANULAR MEDIA
AGGREGATION
SCHEME
MODEL
Applied Mathematics
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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