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The heterogeneous multiscale method*

Published online by Cambridge University Press:  19 April 2012

Assyr Abdulle
ANMC, Mathematics Section, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland E-mail:
E Weinan
Beijing International Center for Mathematical Research, Peking University, Beijing, China and Department of Mathematics and PACM, Princeton University, Princeton, USA E-mail:
Björn Engquist
Department of Mathematics, University of Texas, Austin, USA E-mail:
Eric Vanden-Eijnden
Courant Institute of Mathematical Sciences, New York University, New York, USA E-mail:


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.

Research Article
Copyright © Cambridge University Press 2012

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* Colour online for monochrome figures available at