Getting Acquainted with Homogenization and Multiscale

• Main Authors: Berlyand, Leonid (Author, http://id.loc.gov/vocabulary/relators/aut), Rybalko, Volodymyr (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Compact Textbooks in Mathematics,
• Subjects: Computer mathematics.; Applied mathematics.; Engineering mathematics.; Partial differential equations.; Computational Science and Engineering.; Mathematical and Computational Engineering.; Partial Differential Equations.
• Physical Description: XVIII, 178 p. 42 illus., 14 illus. in color. online resource.
• ISBN: 9783030017774
• ISSN: 2296-4568
• DOI: 10.1007/978-3-030-01777-4

The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.