# Phase-field model and its splitting numerical scheme for tissue growth

Darae Jeong, Junseok Kim

Research output: Contribution to journalArticle

2 Citations (Scopus)

### Abstract

We consider phase-field models and associated numerical methods for tissue growth. The model consists of the Cahn–Hilliard equation with a source term. In order to solve the equations accurately and efficiently, we propose a hybrid method based on an operator splitting method. First, we solve the contribution from the source term analytically and redistribute the increased mass around the tissue boundary position. Subsequently, we solve the Cahn–Hilliard equation using the nonlinearly gradient stable numerical scheme to make the interface transition profile smooth. We then perform various numerical experiments and find that there is a good agreement when these computational results are compared with analytic solutions.

Original language English 22-35 14 Applied Numerical Mathematics 117 https://doi.org/10.1016/j.apnum.2017.01.020 Published - 2017 Jul 1

### Fingerprint

Phase Field Model
Numerical Scheme
Cahn-Hilliard Equation
Tissue
Source Terms
Operator Splitting Method
Numerical methods
Hybrid Method
Analytic Solution
Computational Results
Numerical Methods
Numerical Experiment
Experiments
Model

### Keywords

• Cahn–Hilliard equation
• Multigrid method
• Operator splitting method
• Tissue growth

### ASJC Scopus subject areas

• Numerical Analysis
• Computational Mathematics
• Applied Mathematics

### Cite this

In: Applied Numerical Mathematics, Vol. 117, 01.07.2017, p. 22-35.

Research output: Contribution to journalArticle

title = "Phase-field model and its splitting numerical scheme for tissue growth",
abstract = "We consider phase-field models and associated numerical methods for tissue growth. The model consists of the Cahn–Hilliard equation with a source term. In order to solve the equations accurately and efficiently, we propose a hybrid method based on an operator splitting method. First, we solve the contribution from the source term analytically and redistribute the increased mass around the tissue boundary position. Subsequently, we solve the Cahn–Hilliard equation using the nonlinearly gradient stable numerical scheme to make the interface transition profile smooth. We then perform various numerical experiments and find that there is a good agreement when these computational results are compared with analytic solutions.",
keywords = "Cahn–Hilliard equation, Multigrid method, Operator splitting method, Tissue growth",
author = "Darae Jeong and Junseok Kim",
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language = "English",
volume = "117",
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journal = "Applied Numerical Mathematics",
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TY - JOUR

T1 - Phase-field model and its splitting numerical scheme for tissue growth

AU - Jeong, Darae

AU - Kim, Junseok

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We consider phase-field models and associated numerical methods for tissue growth. The model consists of the Cahn–Hilliard equation with a source term. In order to solve the equations accurately and efficiently, we propose a hybrid method based on an operator splitting method. First, we solve the contribution from the source term analytically and redistribute the increased mass around the tissue boundary position. Subsequently, we solve the Cahn–Hilliard equation using the nonlinearly gradient stable numerical scheme to make the interface transition profile smooth. We then perform various numerical experiments and find that there is a good agreement when these computational results are compared with analytic solutions.

AB - We consider phase-field models and associated numerical methods for tissue growth. The model consists of the Cahn–Hilliard equation with a source term. In order to solve the equations accurately and efficiently, we propose a hybrid method based on an operator splitting method. First, we solve the contribution from the source term analytically and redistribute the increased mass around the tissue boundary position. Subsequently, we solve the Cahn–Hilliard equation using the nonlinearly gradient stable numerical scheme to make the interface transition profile smooth. We then perform various numerical experiments and find that there is a good agreement when these computational results are compared with analytic solutions.

KW - Cahn–Hilliard equation

KW - Multigrid method

KW - Operator splitting method

KW - Tissue growth

UR - http://www.scopus.com/inward/record.url?scp=85011832021&partnerID=8YFLogxK

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U2 - 10.1016/j.apnum.2017.01.020

DO - 10.1016/j.apnum.2017.01.020

M3 - Article

AN - SCOPUS:85011832021

VL - 117

SP - 22

EP - 35

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -