Related papers: Convergence of a particle method for diffusive gra…

We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow…

A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the fluid velocity field…

We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of…

We consider special upwinding Petrov-Galerkin discretizations for convection-diffusion problems. For the one dimensional case with a standard continuous linear element as the trial space and a special exponential bubble test space, we prove…

Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…

Discrete particle simulations are widely used to study large-scale particulate flows in complex geometries where particle-particle and particle-fluid interactions require an adequate representation but the computational cost has to be kept…

Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…

We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…

The Discrete Particle Method (DPM) is used to model granular flows down an inclined chute. We observe three major regimes: static piles, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes…

In this paper we analyze the convergence of the splitting method for shallow water equations. In particular, we give an analytical estimation of the time step which is necessary for the convergence and then we study the behaviour of the…

We consider dry granular flow down an inclined chute with a localised contraction theoretically and numerically. The flow regimes are predicted through a novel extended one-dimensional hydraulic theory. A discrete particle method validated…

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…

The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…

We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved…

We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution…

Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…

Particulate flows have been largely studied under the simplifying assumptions of one-way coupling regime where the disperse phase do not react-back on the carrier fluid. In the context of turbulent flows, many non trivial phenomena such as…

Particle advection is the approach for extraction of integral curves from vector fields. Efficient parallelization of particle advection is a challenging task due to the problem of load imbalance, in which processes are assigned unequal…

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…