Description:
Systémes multi-échelles is an introduction to the modelling and the simulation of multiscale problems, which are now ubiquitous in many fields of scientific computing: materials science, fluid mechanics, molecular simulation, chemical engineering, ... The standard techniques, such as homogeneization techniques, are presented, along with the most recent and advanced ones, such as the micromacro modelling of non-newtonian fluids. Mathematical objects and theories as diverse as partial differential equations, stochastic differential equations, calculus of variations, are introduced and manipulated
Review Quotes:
From the reviews:
"This book results from a course on multiscale models given by the author. It provides an interesting introduction to the topic focusing on conceptual aspects ... . As intended the material could be an excellent basis for a special topics course in an applied math or computational science curriculum." (Martin Burger, Mathematical Reviews, Issue, 2007 g)
"This book is a course which introduces the reader into the problematics of multi-scale systems from the point of view of applied mathematics. ... The theme of the course is presented through several examples, most of them coming from the mechanics of solids, from physics, chemistry ... . The course contains six chapters, each accompanied by a specific selective bibiliography. At the end of the book a complete list of references is given, containing 49 authors, the quotes being from after 1990." (Lidia Elena Kozma, Zentralblatt MATH, Vol. 1109 (11), 2007)