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Retarded Potentials and Time Domain Boundary Integral Equations

A Road Map

  • Book
  • © 2016

Overview

Authors:
  1. Francisco-Javier Sayas

    1. Department of Mathematical Sciences, University of Delaware, Newark, USA

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  • Full description of the rudiments of the vector-valued distributions as needed for the theory of time domain integral equations
  • First detailed exposition of the mathematical techniques for boundary integral equations for the wave equation
  • Large collection of problems and exercises

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xv
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  2. The retarded layer potentials

    • Francisco-Javier Sayas
    Pages 1-19

  3. From time domain to Laplace domain

    • Francisco-Javier Sayas
    Pages 21-38

  4. From Laplace domain to time domain

    • Francisco-Javier Sayas
    Pages 39-58

  5. Convolution Quadrature

    • Francisco-Javier Sayas
    Pages 59-81

  6. The discrete layer potentials

    • Francisco-Javier Sayas
    Pages 83-101

  7. A general class of second order differential equations

    • Francisco-Javier Sayas
    Pages 103-110

  8. Time domain analysis of the single layer potential

    • Francisco-Javier Sayas
    Pages 111-140

  9. Time domain analysis of the double layer potential

    • Francisco-Javier Sayas
    Pages 141-155

  10. Full discretization revisited

    • Francisco-Javier Sayas
    Pages 157-170

  11. Patterns, extensions, and conclusions

    • Francisco-Javier Sayas
    Pages 171-181

  12. Back Matter

    Pages 183-242
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematical Sciences, University of Delaware, Newark, USA

    Francisco-Javier Sayas

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