swMATH ID: 12977
Software Authors: Quarteroni, Alfio; Manzoni, Andrea; Negri, Federico
Description: Reduced basis methods for partial differential equations. An introduction. 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. Reduced basis methods for partial differential equations. An introduction. 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.
Homepage: https://github.com/redbkit
Source Code: https://github.com/redbkit
Dependencies: Matlab
Related Software: rbMIT; GitHub; Adam; FEniCS; Loewner; FreeFem++; pyMOR; Matlab; PMTK; NGSolve; TensorFlow; hapod; SINDy; PRMLT; ITHACA-FV; SyFi; LifeV; RBniCS; libMesh; Gmsh
Cited in: 272 Publications
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Cited by 460 Authors

27 Rozza, Gianluigi
19 Quarteroni, Alfio M.
17 Hesthaven, Jan S.
17 Manzoni, Andrea
15 Stabile, Giovanni
12 Luo, Zhendong
10 Iliescu, Traian
10 Taddei, Tommaso
8 Urban, Karsten
7 Ballarin, Francesco
7 Benner, Peter
7 Dal Santo, Niccolò
7 Deparis, Simone
7 Patera, Anthony T.
7 Schwab, Christoph
6 Chen, Yanlai
6 Karatzas, Efthymios N.
6 Maday, Yvon
6 Pagani, Stefano
5 Chen, Peng
5 Gugercin, Serkan
5 Guo, Mengwu
5 Ohlberger, Mario
4 Dede’, Luca
4 Mola, Andrea
4 Mou, Changhong
4 Narayan, Akil C.
4 Rave, Stephan David
4 Smetana, Kathrin
4 Veroy, Karen
4 Wang, Zhu
4 Zhang, Lei
3 Afkham, Babak Maboudi
3 Ali, Mazen
3 Alla, Alessandro
3 Chacón Rebollo, Tomás
3 Gómez Mármol, Macarena
3 Gunzburger, Max D.
3 Héas, Patrick
3 Herzet, Cédric
3 Hijazi, Saddam
3 Koc, Birgul
3 Koutsourelakis, Phaedon-Stelios
3 Mishra, Siddhartha
3 Mohebujjaman, Muhammad
3 Nobile, Fabio
3 Perotto, Simona
3 Quaini, Annalisa
3 Regazzoni, Francesco
3 Ripamonti, Nicolò
3 Schindler, Felix
3 Schneier, Michael
3 Scovazzi, Guglielmo
3 Singler, John R.
3 Teng, Fei
3 Wang, Qian
3 Wells, David R.
3 Xie, Xuping
3 Yano, Masayuki
3 Zhang, Zhenying
2 Antil, Harbir
2 Beattie, Christopher A.
2 Benaceur, Amina
2 Bluck, Michael J.
2 Brunton, Steven L.
2 Buhr, Andreas
2 Chen, Tianheng
2 Cohen, Albert
2 Delgado Ávila, Enrique
2 Ehrlacher, Virginie
2 Elman, Howard C.
2 Farthing, Matthew W.
2 Feng, Xinlong
2 Gao, Zhen
2 Georgaka, Sokratia
2 Ghattas, Omar N.
2 Girfoglio, Michele
2 Gosea, Ion Victor
2 Greif, Constantin
2 Grepl, Martin A.
2 Grigo, Constantin
2 Heinkenschloss, Matthias
2 Hess, Martin Wilfried
2 Jiang, Lijian
2 Jiang, Wenrui
2 Kamilis, Dimitris
2 Kärcher, Mark
2 Khurshudyan, Asatur Zh.
2 Kressner, Daniel
2 Kutyniok, Gitta
2 Kutz, J. Nathan
2 Le Clainche, Soledad
2 Li, Qiuqi
2 Li, Richen
2 Liao, Qifeng
2 Longo, Marcello
2 Lorenzi, Stefano
2 Ma, Lingling
2 Nouveau, Léo
2 Nouy, Anthony
...and 360 more Authors
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Cited in 56 Serials

38 Computer Methods in Applied Mechanics and Engineering
37 SIAM Journal on Scientific Computing
32 Journal of Computational Physics
17 Journal of Scientific Computing
16 Advances in Computational Mathematics
14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
11 Computers & Mathematics with Applications
11 SIAM/ASA Journal on Uncertainty Quantification
9 SIAM Journal on Numerical Analysis
5 Journal of Mathematical Analysis and Applications
4 Computers and Fluids
4 Journal of Computational and Applied Mathematics
4 Communications in Computational Physics
3 Applied Numerical Mathematics
3 Computational Geosciences
3 Archives of Computational Methods in Engineering
3 Communications in Applied and Industrial Mathematics
2 Computational Mechanics
2 Applied Mathematics Letters
2 SIAM Journal on Matrix Analysis and Applications
2 Applied Mathematical Modelling
2 SIAM Journal on Mathematical Analysis
2 ETNA. Electronic Transactions on Numerical Analysis
2 International Journal of Computational Fluid Dynamics
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Advances in Difference Equations
2 SMAI Journal of Computational Mathematics
1 Acta Mechanica
1 Classical and Quantum Gravity
1 Wave Motion
1 Mathematics of Computation
1 Integral Equations and Operator Theory
1 Numerische Mathematik
1 SIAM Journal on Control and Optimization
1 Zeitschrift für Analysis und ihre Anwendungen
1 Bulletin of the Iranian Mathematical Society
1 Acta Mathematicae Applicatae Sinica. English Series
1 Constructive Approximation
1 Journal of Nonlinear Science
1 Continuum Mechanics and Thermodynamics
1 Journal of Inverse and Ill-Posed Problems
1 Vietnam Journal of Mathematics
1 Chaos
1 Discrete Dynamics in Nature and Society
1 Journal of Numerical Mathematics
1 SIAM Journal on Applied Dynamical Systems
1 Multiscale Modeling & Simulation
1 Acta Numerica
1 Inverse Problems in Science and Engineering
1 Unitext
1 Journal of Nonlinear Science and Applications
1 SIAM Journal on Financial Mathematics
1 Mathematical Control and Related Fields
1 Stochastic and Partial Differential Equations. Analysis and Computations
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys

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