A Minimization Method for The Double-Well Energy Functional

2018/09/06 by Qian Zhang, Long Chen, Zhang, Qian +3
Computer Science · Engineering · Materials Science · #Advanced Mathematical Modeling in Engineering #Aluminum Alloy Microstructure Properties #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1809.01839

openalex publication_date 2018/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed convex set and is shown to be unconditionally energy stable. By the minimization approach, we also derive an variant of the first-order scheme for the Allen-Cahn equation, which has been constructed in the context of Invariant Energy Quadratization, and prove its unconditional energy stability.

Citations

• Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: Application of a semi-implicit Fourier spectral method

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