34 citations · 83 across the 11 of their papers we have counts for
14 papers
Gradient flows of interacting Laguerre cells as discrete porous media flows
Andrea Natale
We study a class of discrete models in which a collection of particles evolves in time following the gradient flow of an energy depending on the cell areas of an associated Laguerr…
From geodesic extrapolation to a variational BDF2 scheme for Wasserstein gradient flows
Thomas Gallouët, Andrea Natale, Gabriele Todeschi
We introduce a time discretization for Wasserstein gradient flows based on the classical Backward Differentiation Formula of order two. The main building block of the scheme is the…
Efficient preconditioners for solving dynamical optimal transport via interior point methods
Enrico Facca, Gabriele Todeschi, Andrea Natale +1
In this paper we address the numerical solution of the quadratic optimal transport problem in its dynamical form, the so-called Benamou-Brenier formulation. When solved using inter…
Convergence of a Lagrangian discretization for barotropic fluids and porous media flow
Thomas Gallouët, Quentin Merigot, Andrea Natale
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential ene…
Computation of Optimal Transport with Finite Volumes
Andrea Natale, Gabriele Todeschi
We construct Two-Point Flux Approximation (TPFA) finite volume schemes to solve the quadratic optimal transport problem in its dynamic form, namely the problem originally introduce…
A mixed finite element discretization of dynamical optimal transport
Andrea Natale, Gabriele Todeschi
In this paper we introduce a new class of finite element discretizations of the quadratic optimal transport problem based on its dynamical formulation. These generalize to the fini…
TPFA Finite Volume Approximation of Wasserstein Gradient Flows
Andrea Natale, Gabriele Todeschi
Numerous infinite dimensional dynamical systems arising in different fields have been shown to exhibit a gradient flow structure in the Wasserstein space. We construct Two Point Fl…
Metric completion of with the right-invariant metric
Simone Di Marino, Andrea Natale, Rabah Tahraoui +1
We consider the group of smooth increasing diffeomorphisms Diff on the unit interval endowed with the right-invariant metric. We compute the metric completion of this space w…
Generalized compressible flows and solutions of the H(div) geodesic problem
Thomas Gallouët, Andrea Natale, François-Xavier Vialard
We study the geodesic problem on the group of diffeomorphism of a domain MRd, equipped with the H(div) metric. The geodesic equations coincide with the Camassa-Holm equati…
Embedding Camassa-Holm equations in incompressible Euler
François-Xavier Vialard, Andrea Natale
In this article, we show how to embed the so-called CH2 equations into the geodesic flow of the Hdiv metric in 2D, which, itself, can be embedded in the incompressible Euler equati…
Scale-selective dissipation in energy-conserving finite element schemes for two-dimensional turbulence
Andrea Natale, Colin J. Cotter
We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our atten…
A variational H(div) finite element discretisation approach for perfect incompressible fluids
Andrea Natale, Colin J. Cotter
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, w…
High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling
Lawrence Mitchell, Eike Hermann Müller
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and co…
On the shallow atmosphere approximation in finite element dynamical cores
C. J. Cotter, D. A. Ham, A. T. T. McRae +2
We provide an approach to implementing the shallow atmosphere approximation in three dimensional finite element discretisations for dynamical cores. The approach makes use of the f…