An energy-stable generalized-α method for the Swift–Hohenberg equation

A. F. Sarmiento; L. F.R. Espath; P. Vignal; L. Dalcin; M. Parsani; V. M. Calo

doi:10.1016/j.cam.2017.11.004

An energy-stable generalized-α method for the Swift–Hohenberg equation

A. F. Sarmiento^*, L. F.R. Espath, P. Vignal, L. Dalcin, M. Parsani, V. M. Calo

^*Corresponding author for this work

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

22 Scopus citations

Abstract

We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-α method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift–Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time.

Original language	English (US)
Pages (from-to)	836-851
Number of pages	16
Journal	Journal of Computational and Applied Mathematics
Volume	344
DOIs	https://doi.org/10.1016/j.cam.2017.11.004
State	Published - Dec 15 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

Energy stability
Numerical dissipation
Numerical instability
Pattern formation
Swift–Hohenberg equation
Time integration

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2017.11.004

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title = "An energy-stable generalized-α method for the Swift–Hohenberg equation",

abstract = "We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-α method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift–Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time.",

keywords = "Energy stability, Numerical dissipation, Numerical instability, Pattern formation, Swift–Hohenberg equation, Time integration",

author = "Sarmiento, {A. F.} and Espath, {L. F.R.} and P. Vignal and L. Dalcin and M. Parsani and Calo, {V. M.}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = dec,

day = "15",

doi = "10.1016/j.cam.2017.11.004",

language = "English (US)",

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T1 - An energy-stable generalized-α method for the Swift–Hohenberg equation

AU - Sarmiento, A. F.

AU - Espath, L. F.R.

AU - Vignal, P.

AU - Dalcin, L.

AU - Parsani, M.

AU - Calo, V. M.

PY - 2018/12/15

Y1 - 2018/12/15

N2 - We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-α method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift–Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time.

AB - We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-α method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift–Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time.

KW - Energy stability

KW - Numerical dissipation

KW - Numerical instability

KW - Pattern formation

KW - Swift–Hohenberg equation

KW - Time integration

UR - http://www.scopus.com/inward/record.url?scp=85035243114&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2017.11.004

DO - 10.1016/j.cam.2017.11.004

M3 - Article

AN - SCOPUS:85035243114

SN - 0377-0427

VL - 344

SP - 836

EP - 851

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

An energy-stable generalized-α method for the Swift–Hohenberg equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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