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Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations

  • Book
  • © 2017

Overview

Authors:
  1. Gary Cohen

    1. INRIA-Saclay, Le Chesnay, France

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  2. Sébastien Pernet

    1. The french aerospace lab, ONERA, Toulouse, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Provides a survey of methods for time domain wave propagation problems
  • Features novel, efficient algorithms for solving wave equations
  • Includes accurate dispersion analysis and error estimates for hybrid meshes for the wave equations
  • Includes supplementary material: sn.pub/extras

Part of the book series: Scientific Computation (SCIENTCOMP)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Classical Continuous Models and Their Analysis

    • Gary Cohen, Sébastien Pernet
    Pages 1-37

  3. Definition of Different Types of Finite Elements

    • Gary Cohen, Sébastien Pernet
    Pages 39-93

  4. Hexahedral and Quadrilateral Spectral Elements for Acoustic Waves

    • Gary Cohen, Sébastien Pernet
    Pages 95-173

  5. Discontinuous Galerkin Methods

    • Gary Cohen, Sébastien Pernet
    Pages 175-232

  6. The Maxwell’s System and Spurious Modes

    • Gary Cohen, Sébastien Pernet
    Pages 233-283

  7. Approximating Unbounded Domains

    • Gary Cohen, Sébastien Pernet
    Pages 285-313

  8. Time Approximation

    • Gary Cohen, Sébastien Pernet
    Pages 315-354

  9. Some Complex Models

    • Gary Cohen, Sébastien Pernet
    Pages 355-381
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Keywords

About this book

This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.
This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulation
of waves.

Reviews

“In this book finite elements and discontinuous Galerkin (DG) methods are employed for the solution of wave equations. The book consists of a preface and eight chapters. Each chapter concludes with a list of references. It is an excellent reference for researchers working on numerical solutions of transient wave equations. It can also be used as a textbook for a graduate course … .” (Beny Neta, Mathematical Reviews, April, 2017)

“This monograph presents much of the progress made during the last two decades in the numerical solution of hyperbolic equations like the acoustics and Maxwell's equation as well as in linear elastodynamic systems. … the book is full of mathematical analysis, but also manypractical aspects and a lot of numerical results are given. … the book may be also quite useful for practitioners.” (Rolf Dieter Grigorieff, zbMATH 1360.65233, 2017)

Authors and Affiliations

  • INRIA-Saclay, Le Chesnay, France

    Gary Cohen

  • The french aerospace lab, ONERA, Toulouse, France

    Sébastien Pernet

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