東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Reduced basis methods for partial di...

Quarteroni, Alfio.

Linked to FindBook

Google Book

Amazon

博客來

Reduced basis methods for partial differential equations = an introduction /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Reduced basis methods for partial differential equations/ by Alfio Quarteroni, Andrea Manzoni, Federico Negri.
Reminder of title:	an introduction /
Author:	Quarteroni, Alfio.
other author:	Manzoni, Andrea.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xiv, 296 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Differential equations, Partial. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-15431-2
ISBN:	9783319154312$q(electronic bk.)

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.73..

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$q(electronic bk.)

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

518115
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Reduced basis methods for partial differential equations = an introduction /
LDR:02869nmm a2200325 a 4500 001 2028670
003 DE-He213
005 20160714143349.0
006 m d
007 cr nn 008maaau
008 160908s2016 gw s 0 eng d
020 $a 9783319154312$q(electronic bk.)
020 $a 9783319154305$q(paper)
024 7 $a 10.1007/978-3-319-15431-2 $2 doi
035 $a 978-3-319-15431-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.353 $2 23
090 $a QA377 $b .Q1 2016
100 1 $a Quarteroni, Alfio. $3 628971
245 1 0 $a Reduced basis methods for partial differential equations $h [electronic resource] : $b an introduction / $c by Alfio Quarteroni, Andrea Manzoni, Federico Negri.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a xiv, 296 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a UNITEXT, $x 2038-5714 ; $v v.92
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.
650 0 $a Differential equations, Partial. $3 518115
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 891089
650 2 4 $a Appl.Mathematics/Computational Methods of Engineering. $3 890892
650 2 4 $a Engineering Fluid Dynamics. $3 891349
700 1 $a Manzoni, Andrea. $3 2179211
700 1 $a Negri, Federico. $3 2179212
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a UNITEXT ; $v v.73. $3 2068584
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-15431-2
950 $a Mathematics and Statistics (Springer-11649)