A Second-order Time-Accurate Unconditionally Stable Method for a Gradient Flow for the Modica–Mortola Functional

Seokjun Ham, Soobin Kwak, Chaeyoung Lee, Gyeonggyu Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

Abstract

In this study, we present a second-order time-accurate unconditionally stable numerical method for a gradient flow for the Modica–Mortola functional with an equispaced multiple well potential. The proposed second-order time-accurate unconditionally stable numerical method is based on the operator splitting method. The nonlinear and linear terms in the gradient flow are solved analytically and using the Fourier spectral method, respectively. The numerical solutions in each step are bounded for any time step size and the overall scheme is temporally second-order accurate. We prove theoretically the unconditional stability and boundedness of the numerical solutions. In addition, several numerical tests are conducted to demonstrate the performance of the proposed method.

Original languageEnglish
Article number63
JournalJournal of Scientific Computing
Volume95
Issue number2
DOIs
Publication statusPublished - 2023 May

Bibliographical note

Funding Information:
The first author (S. Ham) was supported by the National Research Foundation (NRF), Korea, under project BK21 FOUR. The corresponding author (J.S. Kim) expresses thanks for the support from the BK21 FOUR program. The authors would like to thank the reviewers for their useful comments and suggestions that helped to improve the paper.

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Fourier spectral method
  • Modica–Mortola functional
  • Unconditionally stable scheme

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Numerical Analysis
  • General Engineering
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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