Retarded Potentials and Time Domain Boundary Integral Equations

A Road Map

  • Francisco-Javier Sayas

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 50)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Francisco-Javier Sayas
    Pages 1-19
  3. Francisco-Javier Sayas
    Pages 21-38
  4. Francisco-Javier Sayas
    Pages 39-58
  5. Francisco-Javier Sayas
    Pages 59-81
  6. Francisco-Javier Sayas
    Pages 83-101
  7. Francisco-Javier Sayas
    Pages 103-110
  8. Francisco-Javier Sayas
    Pages 111-140
  9. Francisco-Javier Sayas
    Pages 141-155
  10. Francisco-Javier Sayas
    Pages 157-170
  11. Francisco-Javier Sayas
    Pages 171-181
  12. Back Matter
    Pages 183-242

About this book

Introduction

This book offers a thorough and self-contained exposition of the mathematics of time-domain boundary integral equations associated to the wave equation, including applications to scattering of acoustic and elastic waves. The book offers two different approaches for the analysis of these integral equations, including a systematic treatment of their numerical discretization using Galerkin (Boundary Element) methods in the space variables and Convolution Quadrature in the time variable. The first approach follows classical work started in the late eighties, based on Laplace transforms estimates. This approach has been refined and made more accessible by tailoring the necessary mathematical tools, avoiding an excess of generality. A second approach contains a novel point of view that the author and some of his collaborators have been developing in recent years, using the semigroup theory of evolution equations to obtain improved results. The extension to electromagnetic waves is explained in one of the appendices.

Keywords

Acoustics Boundary integral equation Retarded potentials Variational methods Wave equation

Authors and affiliations

  • Francisco-Javier Sayas
    • 1
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-26645-9
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-26643-5
  • Online ISBN 978-3-319-26645-9
  • Series Print ISSN 0179-3632
  • Series Online ISSN 2198-3712
  • About this book