The heterogeneous multiscale method

Assyr Abdulle; Weinan E; Björn Engquist; Eric Vanden-Eijnden

doi:10.1017/S0962492912000025

The heterogeneous multiscale method

Assyr Abdulle, Weinan E, Björn Engquist, Eric Vanden-Eijnden

Mathematics

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

295 Scopus citations

Abstract

The heterogeneous multiscale method (HMM), a general framework for designing multiscale algorithms, is reviewed. Emphasis is given to the error analysis that comes naturally with the framework. Examples of finite element and finite difference HMM are presented. Applications to dynamical systems and stochastic simulation algorithms with multiple time scales, spall fracture and heat conduction in microprocessors are discussed.

Original language	English (US)
Pages (from-to)	1-87
Number of pages	87
Journal	Acta Numerica
Volume	21
DOIs	https://doi.org/10.1017/S0962492912000025
State	Published - May 2012

All Science Journal Classification (ASJC) codes

Numerical Analysis
General Mathematics

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10.1017/S0962492912000025

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title = "The heterogeneous multiscale method",

abstract = "The heterogeneous multiscale method (HMM), a general framework for designing multiscale algorithms, is reviewed. Emphasis is given to the error analysis that comes naturally with the framework. Examples of finite element and finite difference HMM are presented. Applications to dynamical systems and stochastic simulation algorithms with multiple time scales, spall fracture and heat conduction in microprocessors are discussed.",

author = "Assyr Abdulle and Weinan E and Bj{\"o}rn Engquist and Eric Vanden-Eijnden",

note = "Funding Information: We are grateful to Xiantao Li for his help in writing this article. The work of Abdulle is supported in part by the Swiss National Science Foundation under Grant 200021 134716/1. The work of E has been supported in part by ONR grant N00014-01-1-0674. The work of Engquist has been supported in part by NSF grant DMS1016577. The work of Vanden-Eijnden has been supported in part by grant DMS-0708140 from NSF and grant N00014-11-1-0345 from ONR.",

year = "2012",

month = may,

doi = "10.1017/S0962492912000025",

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AU - Abdulle, Assyr

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AU - Engquist, Björn

AU - Vanden-Eijnden, Eric

N1 - Funding Information: We are grateful to Xiantao Li for his help in writing this article. The work of Abdulle is supported in part by the Swiss National Science Foundation under Grant 200021 134716/1. The work of E has been supported in part by ONR grant N00014-01-1-0674. The work of Engquist has been supported in part by NSF grant DMS1016577. The work of Vanden-Eijnden has been supported in part by grant DMS-0708140 from NSF and grant N00014-11-1-0345 from ONR.

PY - 2012/5

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N2 - The heterogeneous multiscale method (HMM), a general framework for designing multiscale algorithms, is reviewed. Emphasis is given to the error analysis that comes naturally with the framework. Examples of finite element and finite difference HMM are presented. Applications to dynamical systems and stochastic simulation algorithms with multiple time scales, spall fracture and heat conduction in microprocessors are discussed.

AB - The heterogeneous multiscale method (HMM), a general framework for designing multiscale algorithms, is reviewed. Emphasis is given to the error analysis that comes naturally with the framework. Examples of finite element and finite difference HMM are presented. Applications to dynamical systems and stochastic simulation algorithms with multiple time scales, spall fracture and heat conduction in microprocessors are discussed.

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JO - Acta Numerica

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ER -

The heterogeneous multiscale method

Abstract

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