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

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

9 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

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

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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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AU - Jeong, Darae

AU - Li, Yibao

AU - Choi, Yongho

AU - Lee, Chaeyoung

AU - Yang, Junxiang

AU - Kim, Junseok

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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SN - 0378-4371

VL - 573

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 125975

ER -

A practical adaptive grid method for the Allen–Cahn equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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