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Reduced basis methods for partial differential equations = an introduction /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Reduced basis methods for partial differential equations/ by Alfio Quarteroni, Andrea Manzoni, Federico Negri.
其他題名:	an introduction /
作者:	Quarteroni, Alfio.
其他作者:	Manzoni, Andrea.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	xiv, 296 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Differential equations, Partial. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-15431-2
ISBN:	9783319154312

Reduced basis methods for partial differential equations = an introduction /
Quarteroni, Alfio.

Reduced basis methods for partial differential equationsan introduction /[electronic resource] :by Alfio Quarteroni, Andrea Manzoni, Federico Negri. - Cham :Springer International Publishing :2016. - xiv, 296 p. :ill. (some col.), digital ;24 cm. - UNITEXT,v.922038-5714 ;. - UNITEXT ;v.85..

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.

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.

ISBN: 9783319154312

Standard No.: 10.1007/978-3-319-15431-2doiSubjects--Topical Terms:

527784
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

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505 0 $a 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.
520 $a 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.
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