An introduction to asymptotic homogenization

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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