An Adaptive Time-Stepping Algorithm for the Allen-Cahn Equation

Chaeyoung Lee, Jintae Park, Soobin Kwak, Sangkwon Kim, Yongho Choi, Seokjun Ham, Junseok Kim

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we present a simple and accurate adaptive time-stepping algorithm for the Allen-Cahn (AC) equation. The AC equation is a nonlinear partial differential equation, which was first proposed by Allen and Cahn for antiphase boundary motion and antiphase domain coarsening. The mathematical equation is a building block for modelling many interesting interfacial phenomena such as dendritic crystal growth, multiphase fluid flows, and motion by mean curvature. The proposed adaptive time-stepping algorithm is based on the Runge-Kutta-Fehlberg method, where the local truncation error is estimated by using fourth- and fifth-order numerical schemes. Computational experiments demonstrate that the proposed time-stepping technique is efficient in multiscale computations, i.e., both the fast and slow dynamics.

Original languageEnglish
Article number2731593
JournalJournal of Function Spaces
Volume2022
DOIs
Publication statusPublished - 2022

ASJC Scopus subject areas

  • Analysis

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