Numerical study of a particle method for gradient flows
File(s)jko_scheme.pdf (548.94 KB)
Accepted version
Author(s)
Patacchini, FS
Carrillo de la Plata, JA
Huang, Y
Wolansky, G
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.
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.
Date Issued
2016-12-01
Date Acceptance
2016-10-26
Citation
Kinetic and Related Models, 2016, 10 (3), pp.613-641
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
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM120001
EP/K008404/1
Subjects
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