Weinan ECambridge University Press, 7/7/2011EAN 9781107096547, ISBN10: 1107096545Hardcover, 488 pages, 25.4 x 18 x 2.6 cmLanguage: EnglishPhysical 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.Preface1. Introduction2. Analytical methods3. Classical multiscale algorithms4. The hierarchy of physical models5. Examples of multi-physics models6. Capturing the macroscale behavior7. Resolving local events or singularities8. Elliptic equations with multiscale coefficients9. Problems with multiple time scales10. Rare events11. Some perspectivesIndex.
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