Weinan E

Principles of Multiscale Modeling

• Gebundenes Buch

Produktbeschreibung

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. Written by a leading contributor to the field, this book 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. Simple illustrative examples ensure that technicalities do not prevent the reader from understanding key concepts.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 488
• Erscheinungstermin: 15. August 2011
• Englisch
• Abmessung: 256mm x 182mm x 29mm
• Gewicht: 1090g
• ISBN-13: 9781107096547
• ISBN-10: 1107096545
• Artikelnr.: 33352706

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

'[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