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

Soobin Kwak; Hyun Geun Lee; Yibao Li; Junxiang Yang; Chaeyoung Lee; Hyundong Kim; Seungyoon Kang; Junseok Kim

doi:10.1007/s10915-022-01862-3

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

Soobin Kwak, Hyun Geun Lee, Yibao Li, Junxiang Yang, Chaeyoung Lee, Hyundong Kim, Seungyoon Kang, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Article number	16
Journal	Journal of Scientific Computing
Volume	92
Issue number	1
DOIs	https://doi.org/10.1007/s10915-022-01862-3
Publication status	Published - 2022 Jul

Keywords

Finite difference method
Fourier spectral method
Motion by mean curvature
Phase-field model

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
Engineering(all)
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1007/s10915-022-01862-3

Cite this

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title = "Motion by Mean Curvature with Constraints Using a Modified Allen–Cahn Equation",

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.",

keywords = "Finite difference method, Fourier spectral method, Motion by mean curvature, Phase-field model",

author = "Soobin Kwak and Lee, {Hyun Geun} and Yibao Li and Junxiang Yang and Chaeyoung Lee and Hyundong Kim and Seungyoon Kang and Junseok Kim",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = jul,

doi = "10.1007/s10915-022-01862-3",

language = "English",

volume = "92",

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AU - Kwak, Soobin

AU - Lee, Hyun Geun

AU - Li, Yibao

AU - Yang, Junxiang

AU - Lee, Chaeyoung

AU - Kim, Hyundong

AU - Kang, Seungyoon

AU - Kim, Junseok

N1 - Funding Information: 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. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/7

Y1 - 2022/7

N2 - 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.

AB - 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.

KW - Finite difference method

KW - Fourier spectral method

KW - Motion by mean curvature

KW - Phase-field model

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DO - 10.1007/s10915-022-01862-3

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SN - 0885-7474

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JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

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M1 - 16

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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