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Principles of Multiscale Modeling

Author: Weinan E, Princeton University, New Jersey

Date Published: August 2011
availability: In stock
format: Hardback
isbn: 9781107096547

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About the Authors

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
"Written by a leader in modern applied mathematics, Principles of Multiscale Modeling is a unified and well-organized synthesis of the physical ideas and mathematical techniques behind the multiscale approach to understanding physical phenomena. It is ambitious in scope and in its insistence on taking seriously all stages in multiscale modeling, from fundamental physical models to efficient computational algorithms by way of rigorous mathematical analysis. I am not aware of any other work that covers all those topics with equal attention and rigor."
Nicholas Kevlahan, Physics Today
Throughout all the chapters, the author displays a certain joy in writing, so the reading flows easily and the reader finds a panoramic path into a forest of concepts. This is a reason to read the book and have it in one's personal library."
-- Polo Maria Mariano, Mathematical reviews
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Product details
- Date Published: August 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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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.