http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Reduced basis methods for partial differential equations
xi, 296 pages : illustrations (some color) ; 24 cm.
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. 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.
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.
Alfio Quarteroni, Andrea Manzoni, Federico Negri.
Includes bibliographical references (pages 281-292) and index.
System von partiellen Differentialgleichungen