Spectral Methods Evolution to Complex Geometries and Applications to 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 their 1988 boo...

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Main Authors: Canuto, Claudio, Hussaini, M. Yousuff (Author), Quarteroni, Alfio (Author), Zang, Thomas A. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2007, 2007
Edition:1st ed. 2007
Series:Scientific Computation
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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100 1 |a Canuto, Claudio 
245 0 0 |a Spectral Methods  |h Elektronische Ressource  |b Evolution to Complex Geometries and Applications to Fluid Dynamics  |c by Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, Thomas A. Zang 
250 |a 1st ed. 2007 
260 |a Berlin, Heidelberg  |b Springer Berlin Heidelberg  |c 2007, 2007 
300 |a XXX, 596 p  |b online resource 
505 0 |a 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 
653 |a Functional analysis 
653 |a Computational Mathematics and Numerical Analysis 
653 |a Computer science / Mathematics 
653 |a Engineering Fluid Dynamics 
653 |a Hydraulic engineering 
653 |a Functional Analysis 
653 |a Numerical and Computational Physics, Simulation 
653 |a Mathematical physics 
653 |a Mathematical Methods in Physics 
653 |a Fluid- and Aerodynamics 
700 1 |a Hussaini, M. Yousuff  |e [author] 
700 1 |a Quarteroni, Alfio  |e [author] 
700 1 |a Zang, Thomas A.  |e [author] 
710 2 |a SpringerLink (Online service) 
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490 0 |a Scientific Computation 
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082 0 |a 515.7 
520 |a 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 their 1988 book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since then. This second new treatment, Evolution to Complex Geometries and Applications to Fluid Dynamics, provides an extensive overview of the essential algorithmic and theoretical aspects of spectral methods for complex geometries, in addition to detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries.  
520 |a The recent companion book 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 essential concepts and formulas from this book are included in the current text for the reader’s convenience 
520 |a Modern strategies for constructing spectral approximations in complex domains, such as spectral elements, mortar elements, and discontinuous Galerkin methods, as well as patching collocation, are introduced, analyzed, and demonstrated by means of numerous numerical examples. Representative simulations from continuum mechanics are also shown. Efficient domain decomposition preconditioners (of both Schwarz and Schur type) that are amenable to parallel implementation are surveyed. The discussion of spectral algorithms for fluid dynamics in single domains focuses on proven algorithms for the boundary-layer equations, linear and nonlinear stability analyses, incompressible Navier-Stokes problems, and both inviscid and viscous compressible flows. An overview of the modern approach to computing incompressible flows in general geometries using high-order, spectral discretizations is also provided.