Retarded Potentials and Time Domain Boundary Integral Equations A Ro
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 diff
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Francisco-Javier Sayas
Retarded Potentials and Time Domain Boundary Integral Equations A Road Map
Springer Series in Computational Mathematics Editorial Board: R.E. Bank R.L. Graham W. Hackbusch J. Stoer R.S. Varga H. Yserentant
More information about this series at http://www.springer.com/series/797
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Francisco-Javier Sayas
Retarded Potentials and Time Domain Boundary Integral Equations A Road Map
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Francisco-Javier Sayas Department of Mathematical Sciences University of Delaware Newark, DE, USA
ISSN 0179-3632 ISSN 2198-3712 (electronic) Springer Series in Computational Mathematics ISBN 978-3-319-26643-5 ISBN 978-3-319-26645-9 (eBook) DOI 10.1007/978-3-319-26645-9 Library of Congress Control Number: 2015955727 Mathematics Subject Classification (2010): 65M38, 65M12, 65R20, 65J08, 45A05, 45B05, 35L20, 35D30, 35Q61 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Dedicated to my parents (Elena y Antonio, mamá y papá) for their unconditional support of my crazy American adventure
Preface
In these notes I try to show the way through the relatively difficult theory of retarded layer potentials and integral operators for the acoustic wave equation in two and three dimensions. I will also introduce convolution quadrature techniques for the time discretization of potentials and integral equations, giving the reader a taste of their challenging but exciting theory and their huge and partly unexplored potentialities. Part of the aim of these notes has been to set a clear path to learn the mathematical techniques needed to understand time domain boundary integral equations. This is part of a joint effort with Antonio Laliena (Universidad de Zaragoza, Spain), Lehel Banjai’s research group (formerly at the Max-PlanckInstitut in Leipzig, Germany, and at the time o
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