A practical adaptive grid method for the Allen–Cahn equation

Darae Jeong; Yibao Li; Yongho Choi; Chaeyoung Lee; Junxiang Yang; Junseok Kim

doi:10.1016/j.physa.2021.125975

A practical adaptive grid method for the Allen–Cahn equation

Darae Jeong, Yibao Li, Yongho Choi, Chaeyoung Lee, Junxiang Yang, Junseok Kim

Department of Mathematics

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

6 Citations (Scopus)

Abstract

We present a simple and practical adaptive finite difference method for the Allen–Cahn (AC) equation in the two-dimensional space. We use a temporally adaptive narrow band domain embedded in the uniform discrete rectangular domain. The narrow band domain is defined as a neighboring region of the interface. We employ a recently developed explicit hybrid numerical scheme for the AC equation. Therefore, the computational algorithm on the narrow band discrete domain is simple and fast. We demonstrate the high performance of the proposed adaptive method for the AC equation through various computational experiments.

Original language	English
Article number	125975
Journal	Physica A: Statistical Mechanics and its Applications
Volume	573
DOIs	https://doi.org/10.1016/j.physa.2021.125975
Publication status	Published - 2021 Jul 1

Bibliographical note

Funding Information:
The first author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). This study was supported by 2018 Research Grant (PoINT) from Kangwon National University, Republic of Korea. Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416, No. 11631012). The corresponding author (J.S. 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-2019R1A2C1003053).

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Adaptive grid
Allen–Cahn equation
Finite difference scheme
Motion by mean curvature

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

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10.1016/j.physa.2021.125975

Cite this

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title = "A practical adaptive grid method for the Allen–Cahn equation",

abstract = "We present a simple and practical adaptive finite difference method for the Allen–Cahn (AC) equation in the two-dimensional space. We use a temporally adaptive narrow band domain embedded in the uniform discrete rectangular domain. The narrow band domain is defined as a neighboring region of the interface. We employ a recently developed explicit hybrid numerical scheme for the AC equation. Therefore, the computational algorithm on the narrow band discrete domain is simple and fast. We demonstrate the high performance of the proposed adaptive method for the AC equation through various computational experiments.",

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author = "Darae Jeong and Yibao Li and Yongho Choi and Chaeyoung Lee and Junxiang Yang and Junseok Kim",

note = "Funding Information: The first author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). This study was supported by 2018 Research Grant (PoINT) from Kangwon National University, Republic of Korea. Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416, No. 11631012). The corresponding author (J.S. 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-2019R1A2C1003053). Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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AU - Lee, Chaeyoung

AU - Yang, Junxiang

AU - Kim, Junseok

N1 - Funding Information: The first author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). This study was supported by 2018 Research Grant (PoINT) from Kangwon National University, Republic of Korea. Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416, No. 11631012). The corresponding author (J.S. 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-2019R1A2C1003053). Publisher Copyright: © 2021 Elsevier B.V.

PY - 2021/7/1

Y1 - 2021/7/1

N2 - We present a simple and practical adaptive finite difference method for the Allen–Cahn (AC) equation in the two-dimensional space. We use a temporally adaptive narrow band domain embedded in the uniform discrete rectangular domain. The narrow band domain is defined as a neighboring region of the interface. We employ a recently developed explicit hybrid numerical scheme for the AC equation. Therefore, the computational algorithm on the narrow band discrete domain is simple and fast. We demonstrate the high performance of the proposed adaptive method for the AC equation through various computational experiments.

AB - We present a simple and practical adaptive finite difference method for the Allen–Cahn (AC) equation in the two-dimensional space. We use a temporally adaptive narrow band domain embedded in the uniform discrete rectangular domain. The narrow band domain is defined as a neighboring region of the interface. We employ a recently developed explicit hybrid numerical scheme for the AC equation. Therefore, the computational algorithm on the narrow band discrete domain is simple and fast. We demonstrate the high performance of the proposed adaptive method for the AC equation through various computational experiments.

KW - Adaptive grid

KW - Allen–Cahn equation

KW - Finite difference scheme

KW - Motion by mean curvature

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ER -

A practical adaptive grid method for the Allen–Cahn equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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