Principles of Multiscale Modeling 1st Edition by Weinan E (PDF)

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.

User’s Reviews

Editorial Reviews: Review “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 TodayThroughout 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 Book Description A systematic discussion of the fundamental principles, written by a leading contributor to the field. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Written by a very distinguished mathematician and leader in modern applied mathematics, 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.People in science and engineering get familiar with multiscale modeling naturally via the multigrid algorithm for elliptic partial differential equations. However, in this book, the author presents an unusually extensive view that brings about everything from moving contact line problem to the sheet-like structures that sustain very large elastic deformations,and from fast summation methods to domain decomposition.This book can be divided into two parts: background materials and general topics. The background materials include an introduction to the fundamental physical models, ranging from continuum mechanics to quantum mechanics, and basic analytical techniques for multiscale problems, such as averaging methods, homogenization methods, renormalization group methods and matched asymptotics as well as classical numerical techniques that use multiscale ideas. The general topics cover examples of multi-physics models, where these are analytical models that use multi-physics coupling explicitly; numerical methods for capturing the macroscopic behavior of complex systems with the help of microscopic models, in cases when empirical macroscopic models are inadequate; numerical methods for coupling macroscopic and microscopic models locally in order to better resolve localized singularities, defects or other events. It is important to realize that multiscale modeling is not just about developing algorithms, it is also about developing better physical models. In this book, the hierarchy of multi-physics modeling is proposed in the introduction and multiscale algorithms are discussed for elliptic equations with multiscale coefficients, problems that have multiple time scales and rare events.This book is well-organized and combined the physical models and mathematical analysis behind the multiscale approach to understanding the essence of physical phenomena. Other books on the subject seem to concentrate on some aspect. For instance, Multiscale Finite Element Methods: Theory and Applications (Springer, 2009), by Yalchin Efendiev and Thomas Hou, emphasizes on computational methods.This book reflects its author’s very outstanding ability in mathematical analysis, physics, and scientific computing. It is the only work I have known that covers all those topics so strictly and equally in rigorous mathematical analysis, fundamental physical models and efficient numerical algorithms. This excellent book with very high quality is found in such Cambridge University Press series as the Cambridge Texts in Applied Mathematics and the Cambridge Monographs on Applied and Computational Mathematics. I think this book is uniquely suitable for those who want to study the highest achievements in this field.

⭐

⭐

Keywords

Free Download Principles of Multiscale Modeling 1st Edition in PDF format
Principles of Multiscale Modeling 1st Edition PDF Free Download
Download Principles of Multiscale Modeling 1st Edition 2011 PDF Free
Principles of Multiscale Modeling 1st Edition 2011 PDF Free Download
Download Principles of Multiscale Modeling 1st Edition PDF
Free Download Ebook Principles of Multiscale Modeling 1st Edition