Nicht aus der Schweiz? Besuchen Sie lehmanns.de

Reduced Basis Methods for Partial Differential Equations

An Introduction
Buch | Softcover
XI, 296 Seiten
2015 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-15430-5 (ISBN)

Lese- und Medienproben

Reduced Basis Methods for Partial Differential Equations - Alfio Quarteroni, Andrea Manzoni, Federico Negri
CHF 74,85 inkl. MwSt

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

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

1 Introduction.- 2 Representative problems: analysis and (high-fidelity) approximation.- 3 Getting parameters into play.- 4 RB method: basic principle, basic properties.- 5 Construction of reduced basis spaces.- 6 Algebraic and geometrical structure.- 7 RB method in actions.- 8 Extension to nonaffine problems.- 9 Extension to nonlinear problems.- 10 Reduction and control: a natural interplay.- 11 Further extensions.- 12 Appendix A Elements of functional analysis.

"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)

Erscheint lt. Verlag 27.7.2015
Reihe/Serie La Matematica per il 3+2
UNITEXT
Zusatzinfo XI, 296 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 534 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte Computational complexity reduction • Finite Element Method • Parametrized differential problems • Partial differential equations • Reduced basis methods • reduced order modeling
ISBN-10 3-319-15430-3 / 3319154303
ISBN-13 978-3-319-15430-5 / 9783319154305
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich

von Tilo Arens; Frank Hettlich; Christian Karpfinger …

Buch | Hardcover (2022)
Springer Spektrum (Verlag)
CHF 109,95