Maximum Principle Preserving Schemes for Binary Systems with Long-range Interactions

2020/04/26 by Xiang Xu, Xu, Xiang, Yanxiang Zhao +1 · 2 citations
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena #Theoretical and Computational Physics #nanoparticles nucleation surface interactions

paper · pdf · doi:10.48550/arxiv.2004.12309

openalex publication_date 2020/04/26 · openalex created_date 2020/05/01 · openalex updated_date 2026/07/28

Abstract

We study some maximum principle preserving and energy stable schemes for the Allen-Cahn-Ohta-Kawasaki model with fixed volume constraint. With the inclusion of a nonlinear term in the Ohta-Kawasaki free energy functional, we show that the Allen-Cahn-Ohta-Kawasaki dynamics is maximum principle preserving. We further design some first order energy stable numerical schemes which inherit the maximum principle preservation in both semi-discrete and fully-discrete levels. Furthermore, we apply the maximum principle preserving schemes to a general framework for binary systems with long-range interactions. We also present some numerical results to support our theoretical findings.

Citations

• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows

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