Overview
- The first textbook on reduced basis methods, an approximation technique that has become very popular and successful in engineering and applied sciences
- Offers a balanced presentation of theoretical and computational aspects supported by a broad variety of relevant problems
- A first mathematically-driven foray into the field of reduced order modeling
- Includes supplementary material: sn.pub/extras
Part of the book series: UNITEXT (UNITEXT, volume 92)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit
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Authors and Affiliations
About the authors
Prof. Alfio Quarteroni, Dr. Andrea Manzoni and Federico Negri - Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
Bibliographic Information
Book Title: Reduced Basis Methods for Partial Differential Equations
Book Subtitle: An Introduction
Authors: Alfio Quarteroni, Andrea Manzoni, Federico Negri
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-3-319-15431-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-15430-5Published: 27 July 2015
eBook ISBN: 978-3-319-15431-2Published: 19 August 2015
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 1
Number of Pages: XI, 296
Topics: Partial Differential Equations, Mathematical Modeling and Industrial Mathematics, Mathematical and Computational Engineering, Engineering Fluid Dynamics