Certified Reduced Basis Methods for Parametrized Partial Differential Equations
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Beschreibung
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.
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.
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
Autor*in
Jan S Hesthaven
Themen in »Certified Reduced Basis Methods for Parametrized Partial Differential Equations«
Applied mathematics Earth sciences Empirical interpolation PDE Reduced basis methods Time-dependent problems partial differential equations
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“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)()