The gap-tooth method in particle simulations

C. William Gear; Ju Li; Ioannis G. Kevrekidis

doi:10.1016/j.physleta.2003.07.004

The gap-tooth method in particle simulations

C. William Gear
, Ju Li
, Ioannis G. Kevrekidis

Chemical & Biological Engineering

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

107 Scopus citations

Abstract

We explore the gap-tooth method for multiscale modeling of systems represented by microscopic physics-based simulators, when coarse-grained evolution equations are not available in closed form. A biased random walk particle simulation, motivated by the viscous Burgers equation, serves as an example. We construct macro-to-micro (lifting) and micro-to-macro (restriction) operators, and drive the coarse time-evolution by particle simulations in appropriately coupled microdomains ("teeth") separated by large spatial gaps. A macroscopically interpolative mechanism for communication between the teeth at the particle level is introduced. The results demonstrate the feasibility of a "closure-on-demand" approach to solving some hydrodynamics problems.

Original language	English (US)
Pages (from-to)	190-195
Number of pages	6
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	316
Issue number	3-4
DOIs	https://doi.org/10.1016/j.physleta.2003.07.004
State	Published - Sep 22 2003

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Keywords

Closure-on-demand
Gap-tooth
Lifting
Modeling
Multiscale
Restriction

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10.1016/j.physleta.2003.07.004

Cite this

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title = "The gap-tooth method in particle simulations",

abstract = "We explore the gap-tooth method for multiscale modeling of systems represented by microscopic physics-based simulators, when coarse-grained evolution equations are not available in closed form. A biased random walk particle simulation, motivated by the viscous Burgers equation, serves as an example. We construct macro-to-micro (lifting) and micro-to-macro (restriction) operators, and drive the coarse time-evolution by particle simulations in appropriately coupled microdomains ({"}teeth{"}) separated by large spatial gaps. A macroscopically interpolative mechanism for communication between the teeth at the particle level is introduced. The results demonstrate the feasibility of a {"}closure-on-demand{"} approach to solving some hydrodynamics problems.",

keywords = "Closure-on-demand, Gap-tooth, Lifting, Modeling, Multiscale, Restriction",

author = "Gear, \{C. William\} and Ju Li and Kevrekidis, \{Ioannis G.\}",

note = "Funding Information: This work was partially supported by the Air Force Office of Scientific Research (Dynamics and Control) and an NSF ITR grant (C.W.G., I.G.K.). J.L. acknowledges support by Honda R\&D Co., Ltd. and the OSU Transportation Research Endowment Program.",

year = "2003",

month = sep,

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doi = "10.1016/j.physleta.2003.07.004",

language = "English (US)",

volume = "316",

pages = "190--195",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

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TY - JOUR

T1 - The gap-tooth method in particle simulations

AU - Gear, C. William

AU - Li, Ju

AU - Kevrekidis, Ioannis G.

N1 - Funding Information: This work was partially supported by the Air Force Office of Scientific Research (Dynamics and Control) and an NSF ITR grant (C.W.G., I.G.K.). J.L. acknowledges support by Honda R&D Co., Ltd. and the OSU Transportation Research Endowment Program.

PY - 2003/9/22

Y1 - 2003/9/22

N2 - We explore the gap-tooth method for multiscale modeling of systems represented by microscopic physics-based simulators, when coarse-grained evolution equations are not available in closed form. A biased random walk particle simulation, motivated by the viscous Burgers equation, serves as an example. We construct macro-to-micro (lifting) and micro-to-macro (restriction) operators, and drive the coarse time-evolution by particle simulations in appropriately coupled microdomains ("teeth") separated by large spatial gaps. A macroscopically interpolative mechanism for communication between the teeth at the particle level is introduced. The results demonstrate the feasibility of a "closure-on-demand" approach to solving some hydrodynamics problems.

AB - We explore the gap-tooth method for multiscale modeling of systems represented by microscopic physics-based simulators, when coarse-grained evolution equations are not available in closed form. A biased random walk particle simulation, motivated by the viscous Burgers equation, serves as an example. We construct macro-to-micro (lifting) and micro-to-macro (restriction) operators, and drive the coarse time-evolution by particle simulations in appropriately coupled microdomains ("teeth") separated by large spatial gaps. A macroscopically interpolative mechanism for communication between the teeth at the particle level is introduced. The results demonstrate the feasibility of a "closure-on-demand" approach to solving some hydrodynamics problems.

KW - Closure-on-demand

KW - Gap-tooth

KW - Lifting

KW - Modeling

KW - Multiscale

KW - Restriction

UR - https://www.scopus.com/pages/publications/17344387998

UR - https://www.scopus.com/pages/publications/17344387998#tab=citedBy

U2 - 10.1016/j.physleta.2003.07.004

DO - 10.1016/j.physleta.2003.07.004

M3 - Article

AN - SCOPUS:17344387998

SN - 0375-9601

VL - 316

SP - 190

EP - 195

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 3-4

ER -

The gap-tooth method in particle simulations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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