Retarded potentials and time domain boundary integral equations [electronic resource] : a road map / Francisco-Javier Sayas.
2016
QA825
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Title
Retarded potentials and time domain boundary integral equations [electronic resource] : a road map / Francisco-Javier Sayas.
ISBN
9783319266459 (electronic book)
3319266454 (electronic book)
9783319266435
3319266454 (electronic book)
9783319266435
Published
Switzerland : Springer, 2016.
Language
English
Description
1 online resource (xv, 242 pages) : illustrations.
Item Number
10.1007/978-3-319-26645-9 doi
Call Number
QA825
Dewey Decimal Classification
515/.96
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed April 20, 2016).
Series
Springer series in computational mathematics ; 50.
Available in Other Form
Print version: 9783319266435
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Table of Contents
The retarted layer potentials
From time domain to Laplace domain
From Laplace domain to time domain
Convulution Quadrature
The Discrete layer potentials
A General Class of Second Order Differential Equations.- Time domain analysis of the single layer potential.- Time domain analysis of the double layer potential.- Full discretization revisited
Patterns, Extensions, and Conclusions
Appendices.
From time domain to Laplace domain
From Laplace domain to time domain
Convulution Quadrature
The Discrete layer potentials
A General Class of Second Order Differential Equations.- Time domain analysis of the single layer potential.- Time domain analysis of the double layer potential.- Full discretization revisited
Patterns, Extensions, and Conclusions
Appendices.