Reduced Basis Methods for Partial Differential Equations An Introduc
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE
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Mathematics ISBN 978-3-319-15430-5
9 783319 154305 springer.com
1 Reduced Basis Methods for Partial Differential Equations
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing.
Quarteroni .BO[POJt/FHSJ
Reduced Basis Methods for Partial Differential Equations
92
Alfio Quarteroni Andrea Manzoni Federico Negri
Reduced Basis Methods for Partial Differential Equations An Introduction
123
UNITEXT
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UNITEXT – La Matematica per il 3+2 Volume 92
Editor-in-chief A. Quarteroni Series editors L. Ambrosio P. Biscari C. Ciliberto M. Ledoux W.J. Runggaldier
More information about this series at http://www.springer.com/series/5418
Alfio Quarteroni · Andrea Manzoni · Federico Negri
Reduced Basis Methods for Partial Differential Equations An Introduction
Alfio Quarteroni Ecole Polytechnique Fédérale de Lausanne Lausanne, Switzerland
Andrea Manzoni Ecole Polytechnique Fédérale de Lausanne Lausanne, Switzerland
Federico Negri Ecole Polytechnique Fédérale de Lausanne Lausanne, Switzerland
ISSN 2038-5722 ISSN 2038-5757 (electronic) UNITEXT – La Matematica per il 3+2 ISBN 978-3-319-15430-5 ISBN 978-3-319-15431-2 (eBook) DOI 10.1007/978-3-319-15431-2 Library of Congress Control Number: 2015930287 Springer Cham Heidelberg New York Dordrecht London © 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
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