Overview
- The most comprehensive and up-to-date theory and state-of-the-art algorithms of spectral methods
- The authors pioneered Spectral Methods in Fluid Dynamics Calculations
- This was their theme in the 1988 edition of this book
- In the meantime the technique became an important tool in Scientific Computing and so the authors fulfilled the need for a monograph addressing students as well
- Includes supplementary material: sn.pub/extras
Part of the book series: Scientific Computation (SCIENTCOMP)
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About this book
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 forfluid dynamics in simple and complex geometries.
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Keywords
Table of contents (8 chapters)
Reviews
From the reviews:
"The main aim of the book is to discuss the approximations of solutions to ordinary and partial differential equations in single domains by expansions in smooth, global basis functions. … furnishes a comprehensive discussion of the mathematical theory of spectral methods in single domains … . All chapters are enhanced with material on Galerkin method … . The discussion of direct and iterative solution methods is endowed with numerical examples that illustrate the key properties of various spectral approximations and solution algorithms." (Nina Shokina, Zentralblatt MATH, Vol. 1093 (19), 2006)
Authors and Affiliations
About the authors
The authors are among the leading researchers in the field of computational fluid dynamics and have pioneered and promoted the "Spectral Methods in Fluid Dynamics".
Bibliographic Information
Book Title: Spectral Methods
Book Subtitle: Fundamentals in Single Domains
Authors: Claudio Canuto, M. Youssuff Hussaini, Alfio Quarteroni, Thomas A. Zang
Series Title: Scientific Computation
DOI: https://doi.org/10.1007/978-3-540-30726-6
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Hardcover ISBN: 978-3-540-30725-9Published: 04 April 2006
Softcover ISBN: 978-3-642-06800-3Published: 19 October 2010
eBook ISBN: 978-3-540-30726-6Published: 23 September 2007
Series ISSN: 1434-8322
Series E-ISSN: 2198-2589
Edition Number: 1
Number of Pages: XXII, 581
Number of Illustrations: 96 b/w illustrations, 10 illustrations in colour
Topics: Classical and Continuum Physics, Numerical and Computational Physics, Simulation, Computational Mathematics and Numerical Analysis, Mathematical Methods in Physics, Engineering Fluid Dynamics, Fluid- and Aerodynamics