A Stabilized Second Order Exponential Time Differencing Multistep Method for Thin Film Growth Model Without Slope Selection

Wenbin Chen; Weijia Li; Zhiwen Luo; Cheng Wang; Xiaoming Wang

doi:10.1051/m2an/2019054

A Stabilized Second Order Exponential Time Differencing Multistep Method for Thin Film Growth Model Without Slope Selection

Wenbin Chen
, Weijia Li
, Zhiwen Luo
, Cheng Wang
, Xiaoming Wang

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

Abstract

In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. an artificial stabilizing term $ A{\tau}^2\frac{\mathrm{\partial}{\Delta}^2u}{\mathrm{\partial}t}$ is added to the physical model to achieve energy stability, with ETD-Based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed o ∞(0,T;o 2) error analysis are provided based on the energy method, with a careful estimate of the aliasing error. in addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.

Original language	American English
Pages (from-to)	727-750
Number of pages	24
Journal	ESAIM: Mathematical Modelling and Numerical Analysis
Volume	54
Issue number	3
DOIs	https://doi.org/10.1051/m2an/2019054
State	Published - May 1 2020

Keywords

Convergence Analysis
Epitaxial Thin Film Growth
Exponential Time Differencing
Long Time Energy Stability
Second Order Scheme

Disciplines

Mathematics
Statistics and Probability

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10.1051/m2an/2019054License: CC BY

https://doi.org/10.1051/m2an/2019054

Cite this

@article{09d0de7486af45888decec9d2f8e35a9,

title = "A Stabilized Second Order Exponential Time Differencing Multistep Method for Thin Film Growth Model Without Slope Selection",

abstract = " In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. an artificial stabilizing term \$ A\{\textbackslash{}tau\}\textasciicircum{}2\textbackslash{}frac\{\textbackslash{}mathrm\{\textbackslash{}partial\}\{\textbackslash{}Delta\}\textasciicircum{}2u\}\{\textbackslash{}mathrm\{\textbackslash{}partial\}t\}\$ is added to the physical model to achieve energy stability, with ETD-Based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed o ∞(0,T;o 2) error analysis are provided based on the energy method, with a careful estimate of the aliasing error. in addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.",

keywords = "Convergence Analysis, Epitaxial Thin Film Growth, Exponential Time Differencing, Long Time Energy Stability, Second Order Scheme",

author = "Wenbin Chen and Weijia Li and Zhiwen Luo and Cheng Wang and Xiaoming Wang",

note = "Publisher Copyright: {\textcopyright} EDP Sciences, SMAI 2020.",

year = "2020",

month = may,

day = "1",

doi = "10.1051/m2an/2019054",

language = "American English",

volume = "54",

pages = "727--750",

journal = "ESAIM: Mathematical Modelling and Numerical Analysis",

issn = "2804-7214",

number = "3",

}

TY - JOUR

T1 - A Stabilized Second Order Exponential Time Differencing Multistep Method for Thin Film Growth Model Without Slope Selection

AU - Chen, Wenbin

AU - Li, Weijia

AU - Luo, Zhiwen

AU - Wang, Cheng

AU - Wang, Xiaoming

N1 - Publisher Copyright: © EDP Sciences, SMAI 2020.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. an artificial stabilizing term $ A{\tau}^2\frac{\mathrm{\partial}{\Delta}^2u}{\mathrm{\partial}t}$ is added to the physical model to achieve energy stability, with ETD-Based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed o ∞(0,T;o 2) error analysis are provided based on the energy method, with a careful estimate of the aliasing error. in addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.

AB - In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. an artificial stabilizing term $ A{\tau}^2\frac{\mathrm{\partial}{\Delta}^2u}{\mathrm{\partial}t}$ is added to the physical model to achieve energy stability, with ETD-Based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed o ∞(0,T;o 2) error analysis are provided based on the energy method, with a careful estimate of the aliasing error. in addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.

KW - Convergence Analysis

KW - Epitaxial Thin Film Growth

KW - Exponential Time Differencing

KW - Long Time Energy Stability

KW - Second Order Scheme

UR - https://scholarsmine.mst.edu/math_stat_facwork/1203

UR - https://doi.org/10.1051/m2an/2019054

U2 - 10.1051/m2an/2019054

DO - 10.1051/m2an/2019054

M3 - Article

SN - 2804-7214

VL - 54

SP - 727

EP - 750

JO - ESAIM: Mathematical Modelling and Numerical Analysis

JF - ESAIM: Mathematical Modelling and Numerical Analysis

IS - 3

ER -

A Stabilized Second Order Exponential Time Differencing Multistep Method for Thin Film Growth Model Without Slope Selection

Abstract

Keywords

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