Reduced Basis Methods For Partial Differential Equations
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Reduced Basis Methods For Partial Differential Equations
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Author : Alfio Quarteroni
language : en
Publisher: Springer
Release Date : 2015-08-19
Reduced Basis Methods For Partial Differential Equations written by Alfio Quarteroni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Mathematics categories.
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
Reduced Basis Methods For Partial Differential Equations With Stochastic Influences
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Author : Bernhard Wieland
language : de
Publisher:
Release Date : 2013
Reduced Basis Methods For Partial Differential Equations With Stochastic Influences written by Bernhard Wieland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Certified Reduced Basis Methods For Parametrized Partial Differential Equations
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Author : Jan S Hesthaven
language : en
Publisher: Springer
Release Date : 2015-08-20
Certified Reduced Basis Methods For Parametrized Partial Differential Equations written by Jan S Hesthaven and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-20 with Mathematics categories.
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.
Spectral And High Order Methods For Partial Differential Equations
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Author : Jan S. Hesthaven
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-29
Spectral And High Order Methods For Partial Differential Equations written by Jan S. Hesthaven and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-29 with Mathematics categories.
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.
Spectral And High Order Methods For Partial Differential Equations Icosahom 2016
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Author : Marco L. Bittencourt
language : en
Publisher: Springer
Release Date : 2017-11-07
Spectral And High Order Methods For Partial Differential Equations Icosahom 2016 written by Marco L. Bittencourt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.
This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
Spectral And High Order Methods For Partial Differential Equations Icosahom 2018
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Author : Spencer J. Sherwin
language : en
Publisher: Springer Nature
Release Date : 2020-08-11
Spectral And High Order Methods For Partial Differential Equations Icosahom 2018 written by Spencer J. Sherwin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-11 with Mathematics categories.
This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
Numerical Mathematics And Advanced Applications Enumath 2015
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Author : Bülent Karasözen
language : en
Publisher: Springer
Release Date : 2016-11-09
Numerical Mathematics And Advanced Applications Enumath 2015 written by Bülent Karasözen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-09 with Mathematics categories.
The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), held every 2 years, provides a forum for discussing recent advances in and aspects of numerical mathematics and scientific and industrial applications. The previous ENUMATH meetings took place in Paris (1995), Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011) and Lausanne (2013). This book presents a selection of invited and contributed lectures from the ENUMATH 2015 conference, which was organised by the Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, from September 14 to 18, 2015. It offers an overview of central recent developments in numerical analysis, computational mathematics, and applications in the form of contributions by leading experts in the field.
Real Time Reduced Order Computational Mechanics
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Author : Gianluigi Rozza
language : en
Publisher: Springer Nature
Release Date : 2024-05-23
Real Time Reduced Order Computational Mechanics written by Gianluigi Rozza and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-23 with Mathematics categories.
The book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity. This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme “Mathematical Analysis, Modelling and Applications”, especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling. In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The RBniCS Project contains an implementation in FEniCS of the reduced order modeling techniques (such as certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for parametric problems that will be introduced in this booklet.
Error Control Adaptive Discretizations And Applications Part 2
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Author :
language : en
Publisher: Elsevier
Release Date : 2024-10-31
Error Control Adaptive Discretizations And Applications Part 2 written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-31 with Science categories.
Error Control, Adaptive Discretizations, and Applications, Volume 59, Part Two highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems,An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations. - Covers multi-scale modeling - Includes updates on data-driven modeling - Presents the latest information on large deformations of multi-scale materials
Uncertainty Modeling For Engineering Applications
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Author : Flavio Canavero
language : en
Publisher: Springer
Release Date : 2018-12-29
Uncertainty Modeling For Engineering Applications written by Flavio Canavero and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-29 with Technology & Engineering categories.
This book provides an overview of state-of-the-art uncertainty quantification (UQ) methodologies and applications, and covers a wide range of current research, future challenges and applications in various domains, such as aerospace and mechanical applications, structure health and seismic hazard, electromagnetic energy (its impact on systems and humans) and global environmental state change. Written by leading international experts from different fields, the book demonstrates the unifying property of UQ theme that can be profitably adopted to solve problems of different domains. The collection in one place of different methodologies for different applications has the great value of stimulating the cross-fertilization and alleviate the language barrier among areas sharing a common background of mathematical modeling for problem solution. The book is designed for researchers, professionals and graduate students interested in quantitatively assessing the effects of uncertainties in their fields of application. The contents build upon the workshop “Uncertainty Modeling for Engineering Applications” (UMEMA 2017), held in Torino, Italy in November 2017.