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

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

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Synopsis

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.

Science & MathematicsMathematicsCalculus & mathematical analysisDifferential calculus & equationsScience & MathematicsMathematicsCalculus & mathematical analysisIntegral calculus & equationsScience & MathematicsMathematicsCalculus & mathematical analysisNumerical analysis Publisher: Springer International Publishing AG Publication Date: 13/04/2016 ISBN-13: 9783319266435  Details: Type: Hardback Format: Books
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