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Integral equation methods for evolutionary PDEa convolution quadrature approach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Integral equation methods for evolutionary PDEby Lehel Banjai, Francisco-Javier Sayas.
Reminder of title:	a convolution quadrature approach /
Author:	Banjai, Lehel.
other author:	Sayas, Francisco-Javier.
Published:	Cham :Springer International Publishing :2022.
Description:	xix, 268 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Integral equations.
Online resource:	https://doi.org/10.1007/978-3-031-13220-9
ISBN:	9783031132209$q(electronic bk.)

Integral equation methods for evolutionary PDEa convolution quadrature approach /
Banjai, Lehel.

Integral equation methods for evolutionary PDEa convolution quadrature approach /[electronic resource] :by Lehel Banjai, Francisco-Javier Sayas. - Cham :Springer International Publishing :2022. - xix, 268 p. :ill., digital ;24 cm. - Springer series in computational mathematics,v. 592198-3712 ;. - Springer series in computational mathematics ;42..

1 Some examples of causal convolutions -- 2 Convolution quadrature for hyperbolic symbols -- 3 Algorithms for CQ: linear multistep methods -- 4 Acoustic scattering in the time domain -- 5 Runge-Kutta CQ -- 6 Transient electromagnetism -- 7 Boundary-field formulations -- 8 Parabolic problems -- 9 Data sparse methods and other topics.

This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method. Properties of convolution quadrature, based on both linear multistep and Runge-Kutta methods, are explained in detail, always with wave propagation problems in mind. Main algorithms for implementing the discrete schemes are described and illustrated by short Matlab codes; translation to other languages can be found on the accompanying GitHub page. The codes are used to present numerous numerical examples to give the reader a feeling for the qualitative behaviour of the discrete schemes in practice. Applications to acoustic and electromagnetic scattering are described with an emphasis on the acoustic case where the fully discrete schemes for sound-soft and sound-hard scattering are developed and analysed in detail. A strength of the book is that more advanced applications such as linear and non-linear impedance boundary conditions and FEM/BEM coupling are also covered. While the focus is on wave scattering, a chapter on parabolic problems is included which also covers the relevant fast and oblivious algorithms. Finally, a brief description of data sparse techniques and modified convolution quadrature methods completes the book. Suitable for graduate students and above, this book is essentially self-contained, with background in mathematical analysis listed in the appendix along with other useful facts. Although not strictly necessary, some familiarity with boundary integral equations for steady state problems is desirable.

ISBN: 9783031132209$q(electronic bk.)

Standard No.: 10.1007/978-3-031-13220-9doiSubjects--Topical Terms:

185303
Integral equations.

LC Class. No.: QA431

Dewey Class. No.: 515.45

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520 $a This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method. Properties of convolution quadrature, based on both linear multistep and Runge-Kutta methods, are explained in detail, always with wave propagation problems in mind. Main algorithms for implementing the discrete schemes are described and illustrated by short Matlab codes; translation to other languages can be found on the accompanying GitHub page. The codes are used to present numerous numerical examples to give the reader a feeling for the qualitative behaviour of the discrete schemes in practice. Applications to acoustic and electromagnetic scattering are described with an emphasis on the acoustic case where the fully discrete schemes for sound-soft and sound-hard scattering are developed and analysed in detail. A strength of the book is that more advanced applications such as linear and non-linear impedance boundary conditions and FEM/BEM coupling are also covered. While the focus is on wave scattering, a chapter on parabolic problems is included which also covers the relevant fast and oblivious algorithms. Finally, a brief description of data sparse techniques and modified convolution quadrature methods completes the book. Suitable for graduate students and above, this book is essentially self-contained, with background in mathematical analysis listed in the appendix along with other useful facts. Although not strictly necessary, some familiarity with boundary integral equations for steady state problems is desirable.
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