Acta Numerica

Research Article

The heterogeneous multiscale method*

Assyr Abdullea1, E Weinana2, Björn Engquista3 and Eric Vanden-Eijndena4

a1 ANMC, Mathematics Section, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland E-mail:

a2 Beijing International Center for Mathematical Research, Peking University, Beijing, China and Department of Mathematics and PACM, Princeton University, Princeton, USA E-mail:

a3 Department of Mathematics, University of Texas, Austin, USA E-mail:

a4 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.


* Colour online for monochrome figures available at