Principles of Multiscale Modeling

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

Informationen zum Autor 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. Klappentext A systematic discussion of the fundamental principles, written by a leading contributor to the field. Zusammenfassung 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. Inhaltsverzeichnis 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.

Zusammenfassung
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.

Inhalt
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.

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