Boltzmann to Landau from the Gradient Flow Perspective

Carrillo, José Antonio Ortega; Delgadino, Matías G.; Wu, Jeremy

doi:10.48550/arxiv.2107.07252

Cited by 3 publications

(2 citation statements)

References 39 publications

(88 reference statements)

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“…Carrillo et al [6] rigorously studied the gradient flow structure under a tailored metric inspired by the gradient flow structure to the Boltzmann equation [18]. The gradient flow structures of both equations are rigorously connected through the grazing collision limit via Γ-convergence of the gradient flows [5].…”

Section: Introductionmentioning

confidence: 99%

A particle method for the homogeneous Landau equation

Carrillo

Wang

et al. 2020

Journal of Computational Physics: X

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We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation in plasma physics. The methods are stochastic variations of the particle methods proposed by Carrillo et al. [J. Comput. Phys.: X 7: 100066, 2020] using the random batch strategy. The collisions only take place inside the small but randomly selected batches so that the computational cost is reduced to O(N ) per time step. Meanwhile, our methods can preserve the conservation of mass, momentum, energy and the decay of entropy. Several numerical examples are performed to validate our methods.

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Section: Introductionmentioning

confidence: 99%

A particle method for the homogeneous Landau equation

Carrillo

Wang

et al. 2020

Journal of Computational Physics: X

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“…See also [1] for a different gradient flow description of the inhomogeneous granular medium equation. Recently, the authors of [11] made a connection between the gradient flow structures of the (homogeneous) Boltzmann and Landau equations. These results indicate that an appropriate gradient flow structure can link the inelastic Boltzmann equation and the aggregation equation.…”

Section: Introductionmentioning

confidence: 99%

On a novel gradient flow structure for the aggregation equation

Esposito¹,

Gvalani²,

Schlichting³

et al. 2021

Preprint

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The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow for the nonlocal interaction energy is well-known. Starting from the spatially homogeneous inelastic Boltzmann equation, a formal Taylor expansion reveals a link between this equation and the aggregation equation with an appropriately chosen interaction potential. Inspired by this formal link and the fact that the associated aggregation equation also dissipates the kinetic energy, we present a novel way of interpreting the aggregation equation as a gradient flow, in the sense of curves of maximal slope, of the kinetic energy, rather than the usual interaction energy, with respect to an appropriately constructed transportation metric on the space of probability measures.

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Random Batch Particle Methods for the Homogeneous Landau Equation

Carrillo¹,

Jin²,

Tang³

2022

CICP

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We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation in plasma physics. The methods are stochastic variations of the particle methods proposed by Carrillo et al. [J. Comput. Phys.: X 7: 100066, 2020] using the random batch strategy. The collisions only take place inside the small but randomly selected batches so that the computational cost is reduced to O(N) per time step. Meanwhile, our methods can preserve the conservation of mass, momentum, energy and the decay of entropy. Several numerical examples are performed to validate our methods.

show abstract

Boltzmann to Landau from the Gradient Flow Perspective

Cited by 3 publications

References 39 publications

A particle method for the homogeneous Landau equation

A particle method for the homogeneous Landau equation

On a novel gradient flow structure for the aggregation equation

Random Batch Particle Methods for the Homogeneous Landau Equation

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