1# Library to Find Best eBook for Read
Author : Martin A. Grepl
Release : 2011
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Certified Reduced Basis Methods for Nonaffine Linear Time-varying Partial Differential Equations by : Martin A. Grepl
Download or read book Certified Reduced Basis Methods for Nonaffine Linear Time-varying Partial Differential Equations written by Martin A. Grepl. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jan S Hesthaven
Release : 2015-08-20
Genre : Mathematics
Kind : eBook
Book Rating : 700/5 ( reviews)
Book Synopsis Certified Reduced Basis Methods for Parametrized Partial Differential Equations by : Jan S Hesthaven
Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven. This book was released on 2015-08-20. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Alfio Quarteroni
Release : 2015-08-19
Genre : Mathematics
Kind : eBook
Book Rating : 311/5 ( reviews)
Book Synopsis Reduced Basis Methods for Partial Differential Equations by : Alfio Quarteroni
Download or read book Reduced Basis Methods for Partial Differential Equations written by Alfio Quarteroni. This book was released on 2015-08-19. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Yuri Olegovich Solodukhov
Release : 2005
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Reduced-basis Methods Applied to Locally Non-affine and Locally Non-linear Partial Differential Equations by : Yuri Olegovich Solodukhov
Download or read book Reduced-basis Methods Applied to Locally Non-affine and Locally Non-linear Partial Differential Equations written by Yuri Olegovich Solodukhov. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: (Cont.) Numerical results are provided with respect to the accuracy and computational savings provided by the described reduced basis methods.
Author : Peter Benner
Release : 2017-07-06
Genre : Science
Kind : eBook
Book Rating : 81X/5 ( reviews)
Book Synopsis Model Reduction and Approximation by : Peter Benner
Download or read book Model Reduction and Approximation written by Peter Benner. This book was released on 2017-07-06. Available in PDF, EPUB and Kindle. Book excerpt: Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.
