Reduced Basis Methods for Partial Differential Equations

Prof. Alfio Quarteroni, Dr. Andrea Manzoni and Federico Negri - Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.

"This textbook provides a basic introduction to reduced basis methods for partial differential equation. Written for undergrad and grad students in this fast growing field of numerical analysis and scientific computing, the methods described allow the authors to solve in real time or in a many-query context a parametric system or equation or to calculate a related output of interest. ... MATLAB software is provided as a companion to the book for a selected class of problem." (Gianluigi Rozza, Mathematical Reviews, October, 2016)

• 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.