Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, Thomas A. Zang

Spectral Methods (eBook, PDF)

Fundamentals in Single Domains

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 581
• Erscheinungstermin: 23. September 2007
• Englisch
• ISBN-13: 9783540307266
• Artikelnr.: 37371049

Autorenporträt

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".

Inhaltsangabe

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.

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Fundamentals of Fluid Dynamics.- Single-Domain Algorithms and Applications for Stability Analysis.- Single-Domain Algorithms and Applications for Incompressible Flows.- Single-Domain Algorithms and Applications for Compressible Flows.- Discretization Strategies for Spectral Methods in Complex Domains.- Solution Strategies for Spectral Methods in Complex Domains.- General Algorithms for Incompressible Navier-Stokes Equations.- Spectral Methods Primer.

Rezensionen

Aus den Rezensionen: "... Schön ist ... dass die Autoren klar Tendenzen der spektralen Methoden der letzten 20 Jahre aufzeigen ... Im Einzelnen findet der interessierte Leser ... viele interessante Details zu Fragen der polynomialen Approximation und ... eine ausführliche Diskussion spektraler Methoden für zahlreiche Modellprobleme ... Insgesamt ist es ... sichtlich eine lohnenswerte Quelle für alle, die spektrale Methoden lieben. Und man kann gespannt sein, wie im Band 2 komplexere Gebiete und Probleme der Strömungsmechanik behandelt werden." (H.-G. Roos, in: ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, 2007, Vol. 87, Issue 1, S. 69)

From the reviews:

"In 2006 Canuto, Quarteroni and Zang presented us on 550 pages a new book on spectral methods ... . Now the second new book ('Evolution of complex geometrics and application to fluid dynamics', CHQZ3) is published and it contains further 600 pages on spectral methods. ... the book presents the actual state-of-the-art of spectral methods and yields for the active researcher a nice comprehensive survey on the modern theory and an excellent bibliography." (H.-G. Roos, Zentralblatt für Angewandte Mathematik und Mechanik, Vol. 88 (1), 2008)

"This book is ... dedicated to the application of spectral methods in fluid dynamics. ... the main objective of the new book is to modernize the classical spectral methods, accounting for advances in the theory and extensive application of multidomain spectral methods in fluid dynamics. ... This is a very useful book for graduate students, research mathematicians, geoscientists, physicists, and engineers interested in modern methods of numerical analysis, mathematical modeling and computational fluid dynamics." (Yuri N. Skiba, Mathematical Reviews, Issue 2009 d)