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arxiv: 2003.10413 · v3 · pith:SSOMVYVD · submitted 2020-03-23 · math.NA · cs.NA

A Variational Lagrangian Scheme for a Phase Field Model: A Discrete Energetic Variational Approach

Chun Liu , Yiwei Wang This is my paper

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classification math.NA cs.NA
keywords variationalmodelschemeapproachdiscreteenergeticenergy-dissipationequilibrium
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In this paper, we propose a variational Lagrangian scheme for a modified phase-field model, which can compute the equilibrium states for the original Allen-Cahn type model. Our discretization is based on a prescribed energy-dissipation law in terms of the flow map. By employing a discrete energetic variational approach, this scheme preserves the variational structure of the original energy-dissipation law and is energy stable. Plentiful numerical tests show that, by choosing the initial value properly, our methods can produce the desired equilibrium and capture the thin diffuse interface with a small number of mesh points.

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  1. Particle-based Energetic Variational Inference

    stat.ML 2020-04 unverdicted novelty 7.0

    Energetic variational inference derives existing particle-based VI methods from energy-dissipation laws and proposes an approximation-then-variation scheme that preserves particle-level structure while reducing KL divergence.