Principles of multiscale modeling

de Weinan E

"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"-- "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 one of the leading contributors 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. The book begins with a discussion of the analytical techniques in multiscale analysis, including matched asymptotics, averaging, homogenization, renormalization group methods and the Mori-Zwanzig formalism. A summary of the classical numerical techniques that use multiscale ideas is also provided. This is followed by a discussion of the physical principles and physical laws at different scales. The author then 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, ranging from differential equations with multiscale coefficients to time scale problems and rare events. Each chapter ends with an extensive list of references to which the reader can refer for further details. 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. Whenever possible, simple examples are used to illustrate the underlying ideas"--