Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth

Tim P. Schulze; Peter Smereka; E. Weinan

doi:10.1016/S0021-9991(03)00208-0

Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth

Tim P. Schulze
, Peter Smereka
, E. Weinan

Mathematics

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

48 Scopus citations

Abstract

We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.

Original language	English (US)
Pages (from-to)	197-211
Number of pages	15
Journal	Journal of Computational Physics
Volume	189
Issue number	1
DOIs	https://doi.org/10.1016/S0021-9991(03)00208-0
State	Published - Jul 20 2003

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

Access to Document

10.1016/S0021-9991(03)00208-0

Cite this

@article{7e9fb52907d5474bba14da4d7bcdbc9d,

title = "Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth",

abstract = "We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.",

author = "Schulze, \{Tim P.\} and Peter Smereka and E. Weinan",

note = "Funding Information: The authors would like to acknowledge support through ONR Grant N00014-010100674 (W.E.). Additional support was provided by NSF Grant DMS 0103825 (T.P.S.) and DMS 0207402 (P.S.). We would also like to thank Eric Vanden-Eijnden for helpful discussions.",

year = "2003",

month = jul,

day = "20",

doi = "10.1016/S0021-9991(03)00208-0",

language = "English (US)",

volume = "189",

pages = "197--211",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth

AU - Schulze, Tim P.

AU - Smereka, Peter

AU - Weinan, E.

N1 - Funding Information: The authors would like to acknowledge support through ONR Grant N00014-010100674 (W.E.). Additional support was provided by NSF Grant DMS 0103825 (T.P.S.) and DMS 0207402 (P.S.). We would also like to thank Eric Vanden-Eijnden for helpful discussions.

PY - 2003/7/20

Y1 - 2003/7/20

N2 - We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.

AB - We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.

UR - https://www.scopus.com/pages/publications/0037777636

UR - https://www.scopus.com/pages/publications/0037777636#tab=citedBy

U2 - 10.1016/S0021-9991(03)00208-0

DO - 10.1016/S0021-9991(03)00208-0

M3 - Article

AN - SCOPUS:0037777636

SN - 0021-9991

VL - 189

SP - 197

EP - 211

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this