Multiscale Methods

Averaging and Homogenization

  • Grigorios A. Pavliotis
  • Andrew M. Stuart

Part of the Texts Applied in Mathematics book series (TAM, volume 53)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 1-10
  3. Background

    1. Front Matter
      Pages 11-11
    2. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 13-35
    3. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 37-57
    4. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 59-72
    5. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 73-84
    6. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 85-101
    7. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 103-124
  4. Perturbation Expansions

    1. Front Matter
      Pages 125-125
    2. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 127-135
    3. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 137-143
    4. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 145-156
    5. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 157-182
    6. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 183-202
    7. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 203-226
    8. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 227-236
  5. Theory

    1. Front Matter
      Pages 237-237
    2. Grigorios A. Pavliotis, Andrew M. Stuart
      Pages 239-244

About this book

Introduction

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.

Grigorios Pavliotis is a Lecturer of Mathematics at Imperial College London.

Andrew Stuart is a Professor of Mathematics at Warwick University.

 

 

 

Keywords

Averaging Computer-Aided Design (CAD) Homogenization Markov Methods Multiscale Pavliotis Probability theory Stuart calculus differential equation partial differential equation

Authors and affiliations

  • Grigorios A. Pavliotis
    • 1
  • Andrew M. Stuart
    • 2
  1. 1.Department of MathematicsImperial College LondonLondonUnited Kingdom
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-73829-1
  • Copyright Information Springer Science+Business Media, LLC 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-73828-4
  • Online ISBN 978-0-387-73829-1
  • Series Print ISSN 0939-2475
  • About this book