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Certified Reduced Basis Methods for Parametrized Partial Differential Equations de Jan S Hesthaven

Certified Reduced Basis Methods for Parametrized Partial Differential Equations: SpringerBriefs in Mathematics

Autor Jan S Hesthaven, Gianluigi Rozza, Benjamin Stamm
en Limba Engleză Paperback – sep 2015
This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
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Specificații

ISBN-13: 9783319224695
ISBN-10: 3319224697
Pagini: 120
Ilustrații: XIII, 131 p. 32 illus., 27 illus. in color.
Dimensiuni: 155 x 235 x 8 mm
Greutate: 0.22 kg
Ediția:1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria SpringerBriefs in Mathematics

Locul publicării:Cham, Switzerland

Public țintă

Research

Cuprins

1 Introduction and Motivation.- 2 Parametrized Differential Equations.- 3 Reduced Basis Methods.- 4 Certified Error Control.- 5 The Empirical Interpolation Method.- 6 Beyond the Basics.- 7 Appendix A Mathematical Preliminaries.

Recenzii

“This book provides comprehensive coverage of major aspects of the RB method, from derivation, analysis and implementation of the method to simulation of application problems. … an introduction to this emerging field for a general audience interested in scientific computing.” (Mario Ohlberger, Mathematical Reviews, December, 2016) 
“This book fills an important gap in the literature. It is an excellent starting point for young scholars approaching this new world, since it gives a well-balanced combination of theoretical aspects, practical details, and examples. … It also gives a nice picture of the research in this field, particularly in the last two chapters which address advanced (yet crucial) topics.” (Alessandro Veneziani, SIAM Review, Vol. 59 (1), 2016)

Textul de pe ultima copertă

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

Caracteristici

The first book to introduce certified reduced basis methods for parametrized partial differentiation equations Unique focus on both the mathematical aspects and algorithmic elements of the methods Essential examples provide a point of departure for the development of more advanced applications Includes supplementary material: sn.pub/extras