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...

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Bibliographic Details
Main Authors:	Quarteroni, Alfio (Author), Manzoni, Andrea (Author), Negri, Federico (Author)
Format:	Book
Language:	English
Published:	Cham ; New York : Springer, [2016]
Series:	Unitext ; 92.
Subjects:	Differential equations, Partial. System von partiellen Differentialgleichungen.

Table of Contents:

1 Introduction
2 Representative problems: analysis and (high-fidelity) approximation
3 RB method: basic principle, basic properties
4 On the algebraic and geometric structure of RB methods
5 The theoretical rationale behind
6 Construction of RB spaces by SVD-POD
7 Construction of RB spaces by the greedy algorithm-- 8 RB methods in Action: Setting up the problem
9 RB methods in Action: Computing the solution
10 Extension to Nonaffine problem
11 Extension to nonlinear problems
12 Reduction and control
Appendix A Basic theoretical tools.