Preliminaries
This chapter contains some standard results that we need in subsequent chapters. The material is arranged such that an unexperienced reader can read through it linearly. The experienced reader my bypass the chapter in the beginning and return to it when n
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Clemens Pechstein
Finite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems
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Clemens Pechstein Institute of Computational Mathematics Johannes Kepler University Linz Austria
ISSN 1439-7358 ISBN 978-3-642-23587-0 ISBN 978-3-642-23588-7 (eBook) DOI 10.1007/978-3-642-23588-7 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012953096 Math. Subj. Class. (2010): 65F08, 65N22, 65N30, 65N38, 65N55, 65Y05 c Springer-Verlag Berlin Heidelberg 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
F¨ur Astrid und Johanna
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Preface
The purpose of this book is to give a detailed and self-contained presentation of tearing and interconnecting methods for finite and boundary element discretizations of elliptic partial differential equations. This includes a description of the corresponding algorithms as well as a rigorous convergence theory. In particular, two issues are addressed which have not been treated in any previous monograph. Firstly, we consider also the case of boundary element tearing and interconnecting (BETI), the coupling of finite and boundary elements within the tearing and interconnecting framework, and the application to
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