4 research outputs found
Discrete gradients in short-range molecular dynamics simulations
Discrete gradients (DG) or more exactly discrete gradient methods are time
integration schemes that are custom-built to preserve first integrals or
Lyapunov functions of a given ordinary differential equation (ODE). In
conservative molecular dynamics (MD) simulations, the energy of the system is
constant and therefore a first integral of motion. Hence, discrete gradient
methods seem to be a natural choice as an integration scheme in conservative
molecular dynamics simulations
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Discrete gradient methods for solving variational image regularisation models
Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting