ENGLISH

Retarded Potentials and Time Domain Boundary Integral Equations: A Road Map

By Francisco-Javier Sayas (auth.)

Book information

Publisher
Springer International Publishing
Year
2016
ISBN
978-3-319-26643-5, 978-3-319-26645-9
DOI
10.1007/978-3-319-26645-9
Language
english
Format
PDF
Filesize
2 MB (2186686 bytes)
Series
Springer Series in Computational Mathematics 50
Edition
1
Pages
XV, 242\251
Time added
2016-07-20 04:00:00
Integral Equations; Partial Differential Equations

Description

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.

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