redbKIT
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.
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References in zbMATH (referenced in 208 articles , 1 standard article )
Showing results 1 to 20 of 208.
Sorted by year (- Benaceur, Amina: Reducing sensors for transient heat transfer problems by means of variational data assimilation (2021)
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- Dölz, Jürgen; Egger, Herbert; Schlottbom, Matthias: A model reduction approach for inverse problems with operator valued data (2021)
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- Gu, Haotian; Xin, Jack; Zhang, Zhiwen: Error estimates for a POD method for solving viscous G-equations in incompressible cellular flows (2021)
- Henríquez, Fernando; Schwab, Christoph: Shape holomorphy of the Calderón projector for the Laplacian in (\mathbbR^2) (2021)
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- Karatzas, Efthymios N.; Rozza, Gianluigi: A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements (2021)
- Keil, Tim; Mechelli, Luca; Ohlberger, Mario; Schindler, Felix; Volkwein, Stefan: A non-conforming dual approach for adaptive trust-region reduced basis approximation of PDE-constrained parameter optimization (2021)
- Koc, Birgul; Rubino, Samuele; Schneier, Michael; Singler, John; Iliescu, Traian: On optimal pointwise in time error bounds and difference quotients for the proper orthogonal decomposition (2021)
- Lu, Chuan; Zhu, Xueyu: Bifidelity data-assisted neural networks in nonintrusive reduced-order modeling (2021)
- Lye, Kjetil O.; Mishra, Siddhartha; Ray, Deep; Chandrashekar, Praveen: Iterative surrogate model optimization (ISMO): an active learning algorithm for PDE constrained optimization with deep neural networks (2021)