Spectral Methods : Fundamentals in Single Domains

Berlin, Heidelberg : Springer Berlin Heidelberg, 2006

Abstract/Sommario: Introduction -- Polynomial Approximation -- Basic Approaches to Constructing Spectral Methods -- Algebraic Systems and Solution Techniques -- Basic Approaches to Constructing Spectral Methods -- Algebraic Systems and Solution Techniques -- Global Approximation Results -- Theory of Stability and Convergence for Spectral Methods -- Analysis of Model Boundary-Value Problems -- Appendices A-E. - Since the publication of "Spectral Methods in Fluid Dynamics", spectral methods, particularly i ...; [leggi tutto] Introduction -- Polynomial Approximation -- Basic Approaches to Constructing Spectral Methods -- Algebraic Systems and Solution Techniques -- Basic Approaches to Constructing Spectral Methods -- Algebraic Systems and Solution Techniques -- Global Approximation Results -- Theory of Stability and Convergence for Spectral Methods -- Analysis of Model Boundary-Value Problems -- Appendices A-E. - Since the publication of "Spectral Methods in Fluid Dynamics", spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of the earlier book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since 1988. The initial treatment Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions. The first half of the book provides the algorithmic details of orthogonal expansions, transform methods, spectral discretization of differential equations plus their boundary conditions, and solution of the discretized equations by direct and iterative methods. The second half furnishes a comprehensive discussion of the mathematical theory of spectral methods on single domains, including approximation theory, stability and convergence, and illustrative applications of the theory to model boundary-value problems. Both the algorithmic and theoretical discussions cover spectral methods on tensor-product domains, triangles and tetrahedra. All chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is greatly expanded as are the set of numerical examples that illustrate the key properties of the various types of spectral approximations and the solution algorithms. A companion book "Evolution to Complex Geometries and Applications to Fluid Dynamics" contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries and provides detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries [comprimi]

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Campo	Valore
Descrizione	Spectral Methods : Fundamentals in Single Domains / by Claudio Canuto, M. Youssuff Hussaini, Alfio Quarteroni, Thomas A. Zang. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006. - XXII, 563 p. 106 illus ; digital. - (Scientific Computation)
Specifiche	[Supporto spec. Risorsa elettr.] Risorsa remota
Note	Springer eBooks. - Printed edition: 9783540307259
Collezione	[Fa parte di] Scientific Computation [Vai al dettaglio]
Autori	Canuto, Claudio - [Responsabilità principale] Hussaini, M. Youssuff - [Responsabilità secondaria] Quarteroni, Alfio - [Responsabilità secondaria] SpringerLink (Online service) - [Responsabilità secondaria] Zang, Thomas A. - [Responsabilità secondaria]
Soggetto	Computational Mathematics and Numerical Analysis Computer science - Mathematics Engineering Fluid Dynamics Fluids Hydraulic engineering Mathematical Methods in Physics Mathematical Physics Mechanics Numerical and Computational Methods Physics
Classificazione	530.1 - Teorie della fisica e fisica matematica
Lingua	Inglese
Numeri	ISBN: 978-3-540-30726-6 DOI: 10.1007/978-3-540-30726-6 N. catalogo straniero: QC1-999 (Library of Congress Call Number)
ID scheda	129048
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