Penta, R. and Gerisch, A. (2018) An introduction to asymptotic homogenization. In: Gerisch, A., Penta, R. and Lang, J. (eds.) Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization, and Applications. Series: Lecture notes in computational science and engineering, 122 (122). Springer, pp. 1-26. ISBN 9783319733708 (doi: 10.1007/978-3-319-73371-5_1)
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Abstract
We present an introduction to the asymptotic homogenization technique as a follow up of the four hours course held at the International Workshop on Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization, and Applications (M3TB2015) at TU Darmstadt (Germany) on 28 September 2015. The content is well-known, although revisited to provide a first insight to scientists and (especially) students who are unaware of the topic. We present the technique via three simple and instructive examples (one-dimensional and multi-dimensional diffusion and the Stokes’s problem for porous media) remarking on the role of regularity assumptions (periodicity vs. local boundedness) and non-dimensionalization, which are sometimes not sufficiently clarified in the existing literature.
| Item Type: | Book Sections |
|---|---|
| Status: | Published |
| Glasgow Author(s) Enlighten ID: | Penta, Dr Raimondo |
| Authors: | Penta, R., and Gerisch, A. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Publisher: | Springer |
| ISSN: | 1439-7358 |
| ISBN: | 9783319733708 |
| Published Online: | 17 March 2017 |
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