Getting Acquainted with Homogenization and Multiscale
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Beschreibung
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.
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.
Development of an intuitive understanding that complements rigorous mathematics Makes advanced mathematical tools and concepts accessible to non-experts Presentations in all Chapters is supplied with exercises
Autor*in
Leonid Berlyand
Themen in »Getting Acquainted with Homogenization and Multiscale«
Multiscale Homogenization Effective coefficients Asymptotic expansion Gamma-convergence Two-scale convergence Continuum limit Stochastic homogenizaiton Cell problem Plasticity Composite material Heterogeneous media partial differential equations
Stimmen zu »Getting Acquainted with Homogenization and Multiscale«
“This book is an invitation to the young researcher to start using modern asymptotic methods of the applied mathematics of multiscale systems.” (Adrian Muntean, zbMATH 1441.35001, 2020)
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