Structure Preserving Primal Dual Methods for Gradient Flows with Nonlinear Mobility Transport Distances

Carrillo, José A.; Wang, Li; Wei, Chaozhen

doi:10.1137/23m1562068

SIAM J. Numer. Anal.

2024

DOI: 10.1137/23m1562068

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Structure Preserving Primal Dual Methods for Gradient Flows with Nonlinear Mobility Transport Distances

José A. Carrillo,

Li Wang,

Chaozhen Wei

Abstract: \mathrm{ \mathrm{ \mathrm{\mathrm{ \mathrm{ . \mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{. \mathrm{\mathrm{\mathrm{\mathrm{ .© 2024 \mathrm{ \mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{\mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \mathrm{ \m… Show more

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Cited by 3 publications

References 34 publications

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Adaptive hyperbolic-cross-space mapped Jacobi method on unbounded domains with applications to solving multidimensional spatiotemporal integrodifferential equations

Deng,

Shao,

Mogilner

et al. 2025

Journal of Computational Physics

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Adaptive hyperbolic-cross-space mapped Jacobi method on unbounded domains with applications to solving multidimensional spatiotemporal integrodifferential equations

Deng,

Shao,

Mogilner

et al. 2025

Journal of Computational Physics

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Mean field control of droplet dynamics with high-order finite-element computations

Fu,

Ji,

Pazner

et al. 2024

J. Fluid Mech.

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Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting and transport. This paper studies a class of mean field control formulations for these droplet dynamics, which can be used to control and manipulate droplets in applications. We first formulate the droplet dynamics as gradient flows of free energies in modified optimal transport metrics with nonlinear mobilities. We then design an optimal control problem for these gradient flows. As an example, a lubrication equation for a thin volatile liquid film laden with an active suspension is developed, with control achieved through its activity field. Lastly, we apply the primal–dual hybrid gradient algorithm with high-order finite-element methods to simulate the proposed mean field control problems. Numerical examples, including droplet formation, bead-up/spreading, transport, and merging/splitting on a two-dimensional spatial domain, demonstrate the effectiveness of the proposed mean field control mechanism.

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Proximity Operators of Perspective Functions with Nonlinear Scaling

Briceño-Arias,

Combettes,

Silva

2024

SIAM J. Optim.

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Structure Preserving Primal Dual Methods for Gradient Flows with Nonlinear Mobility Transport Distances

Cited by 3 publications

References 34 publications

Adaptive hyperbolic-cross-space mapped Jacobi method on unbounded domains with applications to solving multidimensional spatiotemporal integrodifferential equations

Adaptive hyperbolic-cross-space mapped Jacobi method on unbounded domains with applications to solving multidimensional spatiotemporal integrodifferential equations

Mean field control of droplet dynamics with high-order finite-element computations

Proximity Operators of Perspective Functions with Nonlinear Scaling

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