Spectral Methods: Fundamentals in Single Domains (Scientific Computation) by Claudio Canuto (PDF)

Description

Since the publication of “Spectral Methods in Fluid Dynamics” 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.

User’s Reviews

Editorial Reviews: Review 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) From the Back Cover 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. About the Author 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”. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I would regard this book as a must to have with its second volume for researchers working in the field of the use of spectral Methods.This is a high level book , recommended for postgraduate students.The reader must satisfy the following coverage of the following modules to feel confident in understanding the book.Linear Algebra 15%Numerical Analysis 25%Fourier Analysis and the use of Fourier methods for solving differential equations 40%Turbulence 10%Hilbert and Banach Spaces 10%Tensor Calculus 10%I have neglected the aspect of coding in the previous list.The first 4 chapters are very important and cannot be skipped. The last three come secondary and are not necessary to cover except if your work is related to them.

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