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Higher-Order Numerical Methods for Transient Wave Equations

  • Gary C. Cohen

Part of the Scientific Computation book series (SCIENTCOMP)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Basic Definitions and Properties

    1. Front Matter
      Pages 1-1
    2. Gary C. Cohen
      Pages 3-13
    3. Gary C. Cohen
      Pages 15-24
    4. Gary C. Cohen
      Pages 25-30
  3. Finite Difference Methods

    1. Front Matter
      Pages 31-34
    2. Gary C. Cohen
      Pages 65-81
    3. Gary C. Cohen
      Pages 83-99
    4. Gary C. Cohen
      Pages 101-121
    5. Gary C. Cohen
      Pages 137-144
    6. Gary C. Cohen
      Pages 145-164
  4. Finite Element Methods

    1. Front Matter
      Pages 165-168
    2. Gary C. Cohen
      Pages 169-210
    3. Gary C. Cohen
      Pages 211-260
    4. Gary C. Cohen
      Pages 307-330
  5. Back Matter
    Pages 331-349

About this book

Introduction

Solving efficiently the wave equations involved in modeling acoustic, elastic or electromagnetic wave propagation remains a challenge both for research and industry. To attack the problems coming from the propagative character of the solution, the author constructs higher-order numerical methods to reduce the size of the meshes, and consequently the time and space stepping, dramatically improving storage and computing times. This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem. A central role is played by the notion of the dispersion relation for analyzing the methods. The last chapter is devoted to unbounded domains which are modeled using perfectly matched layer (PML) techniques. Numerical examples are given.

Keywords

Finite Difference Wave Equation Finite Elements Wave Propagation calculus electromagnetic wave modeling numerical methods scientific computation wave wave equation

Authors and affiliations

  • Gary C. Cohen
    • 1
  1. 1.Domaine de Voluceau RocquencourtINRIALe Chesnay CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04823-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07482-0
  • Online ISBN 978-3-662-04823-8
  • Series Print ISSN 1434-8322
  • Buy this book on publisher's site
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