a1 ANMC, Mathematics Section, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland E-mail: email@example.com
a2 Beijing International Center for Mathematical Research, Peking University, Beijing, China and Department of Mathematics and PACM, Princeton University, Princeton, USA E-mail: firstname.lastname@example.org
a3 Department of Mathematics, University of Texas, Austin, USA E-mail: email@example.com
a4 Courant Institute of Mathematical Sciences, New York University, New York, USA E-mail: firstname.lastname@example.org
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.
* Colour online for monochrome figures available at journals.cambridge.org/anu.