Shape transformation using the modified Allen–Cahn equation

Hyundong Kim; Sungha Yoon; Jian Wang; Chaeyoung Lee; Sangkwon Kim; Jintae Park; Junseok Kim

doi:10.1016/j.aml.2020.106487

Shape transformation using the modified Allen–Cahn equation

Hyundong Kim, Sungha Yoon, Jian Wang, Chaeyoung Lee, Sangkwon Kim, Jintae Park, Junseok Kim

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

15 Citations (Scopus)

Abstract

In this paper, we propose a phase-field model for the shape transformation and its simple numerical method. The proposed phase-field model is based on the Allen–Cahn equation, which is a second-order nonlinear parabolic partial differential equation and originally arises from modeling phase separation in alloys. The numerical scheme is a hybrid method using the operator splitting method. To validate the proposed phase-field model for the shape transformation, we perform two- and three-dimensional shape metamorphosis. The proposed phase-field model is also compared with the linear interpolation. The computational results demonstrate that the proposed mathematical model satisfactorily and naturally simulate the shape transformation.

Original language	English
Article number	106487
Journal	Applied Mathematics Letters
Volume	107
DOIs	https://doi.org/10.1016/j.aml.2020.106487
Publication status	Published - 2020 Sept

Bibliographical note

Funding Information:
The corresponding author (J. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, South Korea ( NRF-2019R1A2C1003053 ).

Publisher Copyright:
© 2020 Elsevier Ltd

Keywords

Allen–Cahn equation
Metamorphosis
Phase-field
Shape transformation

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2020.106487

Cite this

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title = "Shape transformation using the modified Allen–Cahn equation",

abstract = "In this paper, we propose a phase-field model for the shape transformation and its simple numerical method. The proposed phase-field model is based on the Allen–Cahn equation, which is a second-order nonlinear parabolic partial differential equation and originally arises from modeling phase separation in alloys. The numerical scheme is a hybrid method using the operator splitting method. To validate the proposed phase-field model for the shape transformation, we perform two- and three-dimensional shape metamorphosis. The proposed phase-field model is also compared with the linear interpolation. The computational results demonstrate that the proposed mathematical model satisfactorily and naturally simulate the shape transformation.",

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AU - Kim, Hyundong

AU - Yoon, Sungha

AU - Wang, Jian

AU - Lee, Chaeyoung

AU - Kim, Sangkwon

AU - Park, Jintae

AU - Kim, Junseok

N1 - Funding Information: The corresponding author (J. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, South Korea ( NRF-2019R1A2C1003053 ). Publisher Copyright: © 2020 Elsevier Ltd

PY - 2020/9

Y1 - 2020/9

N2 - In this paper, we propose a phase-field model for the shape transformation and its simple numerical method. The proposed phase-field model is based on the Allen–Cahn equation, which is a second-order nonlinear parabolic partial differential equation and originally arises from modeling phase separation in alloys. The numerical scheme is a hybrid method using the operator splitting method. To validate the proposed phase-field model for the shape transformation, we perform two- and three-dimensional shape metamorphosis. The proposed phase-field model is also compared with the linear interpolation. The computational results demonstrate that the proposed mathematical model satisfactorily and naturally simulate the shape transformation.

AB - In this paper, we propose a phase-field model for the shape transformation and its simple numerical method. The proposed phase-field model is based on the Allen–Cahn equation, which is a second-order nonlinear parabolic partial differential equation and originally arises from modeling phase separation in alloys. The numerical scheme is a hybrid method using the operator splitting method. To validate the proposed phase-field model for the shape transformation, we perform two- and three-dimensional shape metamorphosis. The proposed phase-field model is also compared with the linear interpolation. The computational results demonstrate that the proposed mathematical model satisfactorily and naturally simulate the shape transformation.

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JO - Applied Mathematics Letters

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ER -

Shape transformation using the modified Allen–Cahn equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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