Principles of Multiscale Modeling

A systematic discussion of the fundamental principles, written by a leading contributor to the field.

Weinan E (Author)

9781107096547, Cambridge University Press

Hardback, published 7 July 2011

488 pages, 71 b/w illus. 13 colour illus.
25.4 x 18 x 2.6 cm, 1.09 kg

'[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

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.

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.

Subject Areas: Mathematical modelling [PBWH]