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