Multiscale Methods: Averaging and Homogenization
Multiscale Methods: Averaging and Homogenization
复制标题
DOI：
--
复制
发表时间：
2008-02
期刊：
影响因子：
--
通讯作者：
G. Pavliotis;A. Stuart
中科院分区：
文献类型：
--
作者：
G. Pavliotis;A. Stuart
多尺度方法的介绍为读者提供了方法的许多用途和应用的广泛概述。这本书开始设置学科领域的理论基础，并继续发展一个统一的方法来简化具有多个尺度的广泛问题，通过扰动扩展;微分方程和随机过程在一个统一的框架中进行研究。这本书最后概述了一系列的理论工具，用来证明通过微扰展开得到的简化模型。该材料的介绍特别适合那些希望在应用中利用多尺度方法的数学家，科学家和工程师。大量的例子说明了如何应用多尺度方法来解决各种问题。然后，练习使读者能够建立自己的技能，并将其付诸实践。在书中提出的结果的扩展和概括，以及参考文献，在每章末尾的讨论和参考书目部分提供。二十一章都有练习。
This introduction to multiscale methods gives readers a broad overview of the many uses and applications of the methods. The book begins by setting the theoretical foundations of the subject area, and moves on to develop a unified approach to the simplification of a wide range of problems which possess multiple scales, via perturbation expansions; differential equations and stochastic processes are studied in one unified framework. The book concludes with an overview of a range of theoretical tools used to justify the simplified models derived via the perturbation expansions. The presentation of the material is particularly suited to the range of mathematicians, scientists and engineers who want to exploit multiscale methods in applications. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable readers to build their own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter. All of the twenty-one chapters are supplemented with exercises.