An explicit hybrid method for the nonlocal Allen-Cahn equation

Chaeyoung Lee; Sungha Yoon; Jintae Park; Junseok Kim

doi:10.3390/SYM12081218

An explicit hybrid method for the nonlocal Allen-Cahn equation

Chaeyoung Lee, Sungha Yoon, Jintae Park, Junseok Kim

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

3 Citations (Scopus)

Abstract

We extend the explicit hybrid numerical method for solving the Allen-Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.

Original language	English
Article number	1218
Journal	Symmetry
Volume	12
Issue number	8
DOIs	https://doi.org/10.3390/SYM12081218
Publication status	Published - 2020 Aug

Bibliographical note

Funding Information:
Funding: The first author (C. Lee) was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2019R1A6A3A13094308). The corresponding author (J.S. Kim) expresses thanks for the support from the BK21 PLUS program.

Publisher Copyright:
© 2020 by the authors.

Keywords

Explicit hybrid method
Nonlocal allen-cahn equation
Operator splitting
Space-time dependent lagrange multiplier

ASJC Scopus subject areas

Computer Science (miscellaneous)
Chemistry (miscellaneous)
General Mathematics
Physics and Astronomy (miscellaneous)

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10.3390/SYM12081218

Cite this

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title = "An explicit hybrid method for the nonlocal Allen-Cahn equation",

abstract = "We extend the explicit hybrid numerical method for solving the Allen-Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.",

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author = "Chaeyoung Lee and Sungha Yoon and Jintae Park and Junseok Kim",

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AU - Yoon, Sungha

AU - Park, Jintae

AU - Kim, Junseok

N1 - Funding Information: Funding: The first author (C. Lee) was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2019R1A6A3A13094308). The corresponding author (J.S. Kim) expresses thanks for the support from the BK21 PLUS program. Publisher Copyright: © 2020 by the authors.

PY - 2020/8

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N2 - We extend the explicit hybrid numerical method for solving the Allen-Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.

AB - We extend the explicit hybrid numerical method for solving the Allen-Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.

KW - Explicit hybrid method

KW - Nonlocal allen-cahn equation

KW - Operator splitting

KW - Space-time dependent lagrange multiplier

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An explicit hybrid method for the nonlocal Allen-Cahn equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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