Numerical Study of a Particle Method for Gradient Flows
Analysis of PDEs
2016-12-07 v3 Numerical Analysis
Abstract
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting scheme preserves the gradient flow 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-diffusion equations.
Cite
@article{arxiv.1512.03029,
title = {Numerical Study of a Particle Method for Gradient Flows},
author = {J. A. Carrillo and Y. Huang and F. S. Patacchini and G. Wolansky},
journal= {arXiv preprint arXiv:1512.03029},
year = {2016}
}
Comments
27 pages, 21 figures