The Resource Reduced Basis Methods for Partial Differential Equations : An Introduction, by Alfio Quarteroni, Andrea Manzoni, Federico Negri, (electronic resource)

Reduced Basis Methods for Partial Differential Equations : An Introduction, by Alfio Quarteroni, Andrea Manzoni, Federico Negri, (electronic resource)

Label
Reduced Basis Methods for Partial Differential Equations : An Introduction
Title
Reduced Basis Methods for Partial Differential Equations
Title remainder
An Introduction
Statement of responsibility
by Alfio Quarteroni, Andrea Manzoni, Federico Negri
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Quarteroni, Alfio
Image bit depth
0
LC call number
QA370-380
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Manzoni, Andrea.
  • Negri, Federico.
  • SpringerLink
Series statement
UNITEXT,
Series volume
92
http://library.link/vocab/subjectName
  • Mathematics
  • Partial differential equations
  • Mathematical models
  • Applied mathematics
  • Engineering mathematics
  • Fluid mechanics
  • Mathematics
  • Partial Differential Equations
  • Mathematical Modeling and Industrial Mathematics
  • Appl.Mathematics/Computational Methods of Engineering
  • Engineering Fluid Dynamics
Label
Reduced Basis Methods for Partial Differential Equations : An Introduction, by Alfio Quarteroni, Andrea Manzoni, Federico Negri, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
XI, 296 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783319154312
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-15431-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-15431-2
Label
Reduced Basis Methods for Partial Differential Equations : An Introduction, by Alfio Quarteroni, Andrea Manzoni, Federico Negri, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
XI, 296 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783319154312
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-15431-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-15431-2

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