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Asymptotic and numerical homogenization

Published online by Cambridge University Press:  25 April 2008

B. Engquist  and
P. E. Souganidis
B. Engquist
Affiliation:
Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA E-mail: engquist@math.utexas.edusouganid@math.utexas.edu
P. E. Souganidis
Affiliation:
Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA E-mail: engquist@math.utexas.edusouganid@math.utexas.edu
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Extract

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.

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Type
Research Article
Information
Acta Numerica , Volume 17 , May 2008 , pp. 147 - 190
Copyright
Copyright © Cambridge University Press 2008

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