More than 1,900 Springer Protocols eBooks at just $9.99 each! Get yours today>>

La Matematica per il 3+2

Reduced Basis Methods for Partial Differential Equations

An Introduction

Authors: Quarteroni, Alfio, Manzoni, Andrea, Negri, Federico

  • 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
see more benefits

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-3-319-15431-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-15430-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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

About the authors

Prof. Alfio Quarteroni, Dr. Andrea Manzoni and Federico Negri - Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.

Reviews

“This textbook provides a basic introduction to reduced basis methods for partial differential equation. Written for undergrad and grad students in this fast growing field of numerical analysis and scientific computing, the methods described allow the authors to solve in real time or in a many-query context a parametric system or equation or to calculate a related output of interest. … MATLAB software is provided as a companion to the book for a selected class of problem.” (Gianluigi Rozza, Mathematical Reviews, October, 2016)


Table of contents (12 chapters)

  • Introduction

    Quarteroni, Alfio (et al.)

    Pages 1-10

  • Representative Problems: Analysis and (High-Fidelity) Approximation

    Quarteroni, Alfio (et al.)

    Pages 11-38

  • RB Methods: Basic Principles, Basic Properties

    Quarteroni, Alfio (et al.)

    Pages 39-72

  • On the Algebraic and Geometric Structure of RB Methods

    Quarteroni, Alfio (et al.)

    Pages 73-86

  • The Theoretical Rationale Behind

    Quarteroni, Alfio (et al.)

    Pages 87-113

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-3-319-15431-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-319-15430-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Reduced Basis Methods for Partial Differential Equations
Book Subtitle
An Introduction
Authors
Series Title
La Matematica per il 3+2
Series Volume
92
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-15431-2
DOI
10.1007/978-3-319-15431-2
Softcover ISBN
978-3-319-15430-5
Series ISSN
2038-5722
Edition Number
1
Number of Pages
XI, 296
Topics