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Motion by Mean Curvature with Constraints Using a Modified Allen–Cahn Equation

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Abstract

In this article, we present a simple and accurate computational scheme for motion by mean curvature with constraints using a modified Allen–Cahn (AC) equation. The modified AC equation contains a nonlinear source term which enforces the constraints such as volume and average mean curvature. We use a linear convex splitting-type method with Fourier spectral method to numerically solve the modified AC equation. We perform several characteristic computational tests to demonstrate the efficiency and accuracy of the proposed method. The computational results confirm the robust and high performance of the proposed algorithm.

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Acknowledgements

The authors thank the reviewers for the constructive and helpful comments on the revision of this article.

Funding

C. Lee was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2022R1C1C2003896). H. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Republic of Korea (NRF-2020R1A6A3A13077105). The corresponding author (J. Kim) was supported by Korea University Grant.

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Authors and Affiliations

  1. Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea

    Soobin Kwak, Chaeyoung Lee, Seungyoon Kang & Junseok Kim

  2. Department of Mathematics, Kwangwoon University, Seoul, 01897, Republic of Korea

    Hyun Geun Lee

  3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Yibao Li

  4. School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510275, China

    Junxiang Yang

  5. Institute for the Advanced Study of Human Biology (WPI-ASHBi), Kyoto University Institute for Advanced Study, Kyoto University, Kyoto, 6068501, Japan

    Hyundong Kim

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  1. Soobin Kwak
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Correspondence to Junseok Kim.

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Kwak, S., Lee, H.G., Li, Y. et al. Motion by Mean Curvature with Constraints Using a Modified Allen–Cahn Equation. J Sci Comput 92, 16 (2022). https://doi.org/10.1007/s10915-022-01862-3

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