An energy-stable convex splitting for the phase-field crystal equation

Philippe Vignal; Lisandro Dalcin; Donald Brown; N. Collier; Victor M. Calo

doi:10.1016/j.compstruc.2015.05.029

An energy-stable convex splitting for the phase-field crystal equation

Philippe Vignal, Lisandro Dalcin, Donald Brown, N. Collier, Victor M. Calo

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

58 Scopus citations

Abstract

Abstract The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method. © 2015 Elsevier Ltd.

Original language	English (US)
Pages (from-to)	355-368
Number of pages	14
Journal	Computers & Structures
Volume	158
DOIs	https://doi.org/10.1016/j.compstruc.2015.05.029
State	Published - Oct 2015

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: KAUST, King Abdullah University of Science and Technology

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10.1016/j.compstruc.2015.05.029

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title = "An energy-stable convex splitting for the phase-field crystal equation",

abstract = "Abstract The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method. {\textcopyright} 2015 Elsevier Ltd.",

author = "Philippe Vignal and Lisandro Dalcin and Donald Brown and N. Collier and Calo, {Victor M.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: KAUST, King Abdullah University of Science and Technology",

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T1 - An energy-stable convex splitting for the phase-field crystal equation

AU - Vignal, Philippe

AU - Dalcin, Lisandro

AU - Brown, Donald

AU - Collier, N.

AU - Calo, Victor M.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: KAUST, King Abdullah University of Science and Technology

PY - 2015/10

Y1 - 2015/10

N2 - Abstract The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method. © 2015 Elsevier Ltd.

AB - Abstract The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method. © 2015 Elsevier Ltd.

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DO - 10.1016/j.compstruc.2015.05.029

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SN - 0045-7949

VL - 158

SP - 355

EP - 368

JO - Computers & Structures

JF - Computers & Structures

ER -

An energy-stable convex splitting for the phase-field crystal equation

Abstract

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