Numerical Study of a Particle Method for Gradient Flows

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.Comment: 27 pages, 21 figure