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.Read more
- 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
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 TodaySee more reviews
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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- 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
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
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