Acta Numerica
- Acta Numerica (2008), 17 : pp 147-190
- Copyright © Cambridge University Press 2008
- DOI: 10.1017/S0962492906360011 (About DOI)
- Published online: 25 April 2008
Research Article
Asymptotic and numerical homogenization
B. Engquista1 and P. E. Souganidisa1
a1 Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA E-mail: engquist@math.utexas.edu souganid@math.utexas.edu
Homogenization is an important mathematical framework for developing effective models of differential equations with oscillations. We include in the presentation techniques for deriving effective equations, a brief discussion on analysis of related limit processes and numerical methods that are based on homogenization principles. We concentrate on first- and second-order partial differential equations and present results concerning both periodic and random media for linear as well as nonlinear problems. In the numerical sections, we comment on computations of multi-scale problems in general and then focus on projection-based numerical homogenization and the heterogeneous multi-scale method.
