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Principles of Multiscale Modeling

  • Author: Weinan E, Princeton University, New Jersey
  • Date Published: July 2011
  • availability: In stock
  • format: Hardback
  • isbn: 9781107096547

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  • Physical phenomena can be modeled at varying degrees of complexity and at different scales. Multiscale modeling provides a framework, based on fundamental principles, for constructing mathematical and computational models of such phenomena, by examining the connection between models at different scales. This book, by a leading contributor to the field, is the first to provide a unified treatment of the subject, covering, in a systematic way, the general principles of multiscale models, algorithms and analysis. After discussing the basic techniques and introducing the fundamental physical models, the author focuses on the two most typical applications of multiscale modeling: capturing macroscale behavior and resolving local events. The treatment is complemented by chapters that deal with more specific problems. Throughout, the author strikes a balance between precision and accessibility, providing sufficient detail to enable the reader to understand the underlying principles without allowing technicalities to get in the way.

    • This first unified treatment of the subject should become the definitive introduction
    • Ideal for graduate students, scientists and engineers who are interested in modeling and doing it right
    • Extensive end-of-chapter reference lists are provided
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    Reviews & endorsements

    '[This] book can be considered as the standard work in this research field and is a rich source for this topic … It is a valuable book and serves as a useful tool for newcomers and researchers working on these problems … highly recommended.' Willi-Hans Steeb, Zentralblatt MATH

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    Product details

    • Date Published: July 2011
    • format: Hardback
    • isbn: 9781107096547
    • length: 488 pages
    • dimensions: 254 x 180 x 26 mm
    • weight: 1.09kg
    • contains: 71 b/w illus. 13 colour illus.
    • availability: In stock
  • Table of Contents

    Preface
    1. Introduction
    2. Analytical methods
    3. Classical multiscale algorithms
    4. The hierarchy of physical models
    5. Examples of multi-physics models
    6. Capturing the macroscale behavior
    7. Resolving local events or singularities
    8. Elliptic equations with multiscale coefficients
    9. Problems with multiple time scales
    10. Rare events
    11. Some perspectives
    Index.

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    Principles of Multiscale Modeling

    Weinan E

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  • Instructors have used or reviewed this title for the following courses

    • Partial Differential Equations
  • Author

    Weinan E, Princeton University, New Jersey
    Weinan E's research is concerned with developing and exploring the mathematical framework and computational algorithms needed to address problems that arise in the study of various scientific and engineering disciplines, ranging from mechanics to materials science to chemistry. He has held positions at New York University, the Institute for Advanced Study in Princeton, Peking University, and Princeton University, where he currently is Professor in the Department of Mathematics and in the Program in Applied and Computational Mathematics. His research has been recognised by numerous awards, including the 2003 Collatz Prize of ICIAM, and the 2009 Ralph E. Kleinman Prize, from SIAM.

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