マルチスケールモデリングの原理 Principles of Multiscale Modeling

E, Weinan

Cambridge University Press（2011/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 488 p.／サイズ 71 b/w illus., 13 colour illus.
• 言語 ENG
• 商品コード 9781107096547
• DDC分類 620.0011

基本説明

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. Ideal for graduate students, scientists and engineers who are interested in modeling and doing it right.

Full Description

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.

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.