Boltzmann to Landau from the gradient flow perspective

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

doi:10.1016/j.na.2022.112824

Cited by 13 publications

(8 citation statements)

References 34 publications

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“…The most important case corresponds to d = 3 with γ = −3 associated with the physical interaction in plasmas. This case is usually called the Coulomb case because it can be derived from the Boltzmann equation in the grazing collision limit when particles interact via Coulomb forces [16,39,11]. The main formal properties of Q rely on the following reformulation…”

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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“…Carrillo et al [8] rigorously studied the gradient flow structure under a tailored metric inspired by that to the Boltzmann equation [19]. The gradient flow structures of both equations are rigorously connected through the grazing collision limit via Γ-convergence of the gradient flows [7].…”

Section: Introductionmentioning

confidence: 99%

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.

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“…Definition 1.1 provides a general model for functions found in areas such as mean field games [1], machine learning [4,42], physics [9,17], optimal transportation [11,14,18,24,34], operator theory [15,25,41], statistics [22,43], matrix analysis [23], mathematical programming [28,35], information theory [33,50], inverse problems [39], and economics [49]. Although it appears for instance in [9,33,50], the preperspective ϕ s is of limited use in variational problems due to its lack of lower semicontinuity and convexity.…”

Section: Introductionmentioning

confidence: 99%

Perspective Functions with Nonlinear Scaling

Briceño-Arias¹,

Combettes²,

Silva³

2022

Preprint

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The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we investigate an extension of this construct in which the scaling variable is replaced by a nonlinear term. Our construction is placed in the general context of locally convex spaces and it generates a lower semicontinuous convex function under broad assumptions on the underlying functions. Various convex-analytical properties are established and closed-form expressions are derived. Several applications are presented.

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Boltzmann to Landau from the gradient flow perspective

Cited by 13 publications

References 34 publications

A particle method for the homogeneous Landau equation

A particle method for the homogeneous Landau equation

Random Batch Particle Methods for the Homogeneous Landau Equation

Perspective Functions with Nonlinear Scaling

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