Reduced Basis Methods for Partial Differential Equations An Introduction /

• Main Authors: Quarteroni, Alfio (Author), Manzoni, Andrea (Author), Negri, Federico (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: UNITEXT, 92
• Subjects: Mathematics.; Partial differential equations.; Mathematical models.; Applied mathematics.; Engineering mathematics.; Fluid mechanics.; Partial Differential Equations.; Mathematical Modeling and Industrial Mathematics.; Appl.Mathematics/Computational Methods of Engineering.; Engineering Fluid Dynamics.

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...

Table of Contents:

• 1 Introduction
• 2 Representative problems: analysis and (high-fidelity) approximation
• 3 Getting parameters into play
• 4 RB method: basic principle, basic properties
• 5 Construction of reduced basis spaces
• 6 Algebraic and geometrical structure
• 7 RB method in actions
• 8 Extension to nonaffine problems
• 9 Extension to nonlinear problems
• 10 Reduction and control: a natural interplay
• 11 Further extensions
• 12 Appendix A Elements of functional analysis.