Spectral Methods And Their Applications

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Spectral Methods and Their Applications

Benyu Guo
Spectral Methods and Their Applications Book PDF

Author : Benyu Guo
Publisher : World Scientific
Page : 364 pages
File Size : 40,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9810233337

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Spectral Methods and Their Applications by Benyu Guo Pdf

This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.

Spectral Methods

Jie Shen,Tao Tang,Li-Lian Wang
Spectral Methods Book PDF

Author : Jie Shen,Tao Tang,Li-Lian Wang
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 50,6 Mb
Release : 2011-08-25
Category : Mathematics
ISBN : 9783540710417

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Spectral Methods by Jie Shen,Tao Tang,Li-Lian Wang Pdf

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.

Numerical Analysis of Spectral Methods

David Gottlieb,Steven A. Orszag
Numerical Analysis of Spectral Methods Book PDF

Author : David Gottlieb,Steven A. Orszag
Publisher : SIAM
Page : 167 pages
File Size : 51,7 Mb
Release : 1977-01-01
Category : Technology & Engineering
ISBN : 9780898710236

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Numerical Analysis of Spectral Methods by David Gottlieb,Steven A. Orszag Pdf

A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.

Spectral Methods in Chemistry and Physics

Bernard Shizgal
Spectral Methods in Chemistry and Physics Book PDF

Author : Bernard Shizgal
Publisher : Springer
Page : 431 pages
File Size : 53,8 Mb
Release : 2015-01-07
Category : Science
ISBN : 9789401794541

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Spectral Methods in Chemistry and Physics by Bernard Shizgal Pdf

This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications to space physics are discussed. The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations. The eigenvalue spectra of the linear operators in the Boltzmann, Fokker-Planck and Schrödinger equations are studied with spectral and pseudospectral methods based on non-classical orthogonal polynomials. The numerical methods referred to as the Discrete Ordinate Method, Differential Quadrature, the Quadrature Discretization Method, the Discrete Variable Representation, the Lagrange Mesh Method, and others are discussed and compared. MATLAB codes are provided for most of the numerical results reported in the book - see Link under 'Additional Information' on the the right-hand column.

Spectral Methods in Fluid Dynamics

Claudio Canuto,M.Yousuff Hussaini,Alfio Quarteroni,Thomas A., Jr. Zang
Spectral Methods in Fluid Dynamics Book PDF

Author : Claudio Canuto,M.Yousuff Hussaini,Alfio Quarteroni,Thomas A., Jr. Zang
Publisher : Springer Science & Business Media
Page : 582 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642841088

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Spectral Methods in Fluid Dynamics by Claudio Canuto,M.Yousuff Hussaini,Alfio Quarteroni,Thomas A., Jr. Zang Pdf

This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.

Spectral Methods for Uncertainty Quantification

Olivier Le Maitre,Omar M Knio
Spectral Methods for Uncertainty Quantification Book PDF

Author : Olivier Le Maitre,Omar M Knio
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 41,7 Mb
Release : 2010-03-11
Category : Science
ISBN : 9789048135202

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Spectral Methods for Uncertainty Quantification by Olivier Le Maitre,Omar M Knio Pdf

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

Implementing Spectral Methods for Partial Differential Equations

David A. Kopriva
Implementing Spectral Methods for Partial Differential Equations Book PDF

Author : David A. Kopriva
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 46,5 Mb
Release : 2009-05-27
Category : Mathematics
ISBN : 9789048122615

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Implementing Spectral Methods for Partial Differential Equations by David A. Kopriva Pdf

This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.

Mathematics and the Aesthetic

Nathalie Sinclair,William Higginson
Mathematics and the Aesthetic Book PDF

Author : Nathalie Sinclair,William Higginson
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 45,6 Mb
Release : 2007-12-28
Category : Mathematics
ISBN : 9780387381459

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Mathematics and the Aesthetic by Nathalie Sinclair,William Higginson Pdf

This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Spectral Methods

Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang
Spectral Methods Book PDF

Author : Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang
Publisher : Springer Science & Business Media
Page : 585 pages
File Size : 43,9 Mb
Release : 2007-09-23
Category : Science
ISBN : 9783540307266

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Spectral Methods by Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang Pdf

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.

Spectral Methods in Surface Superconductivity

Søren Fournais,Bernard Helffer
Spectral Methods in Surface Superconductivity Book PDF

Author : Søren Fournais,Bernard Helffer
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 50,5 Mb
Release : 2010-06-15
Category : Mathematics
ISBN : 9780817647964

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Spectral Methods in Surface Superconductivity by Søren Fournais,Bernard Helffer Pdf

This book examines in detail the nonlinear Ginzburg–Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg–Landau parameter kappa. Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.

Spectral Algorithms

Ravindran Kannan,Santosh Vempala
Spectral Algorithms Book PDF

Author : Ravindran Kannan,Santosh Vempala
Publisher : Now Publishers Inc
Page : 153 pages
File Size : 52,9 Mb
Release : 2009
Category : Computers
ISBN : 9781601982742

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Spectral Algorithms by Ravindran Kannan,Santosh Vempala Pdf

Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.

The Application of the Chebyshev-Spectral Method in Transport Phenomena

Weidong Guo,Gérard Labrosse,Ranga Narayanan
The Application of the Chebyshev Spectral Method in Transport Phenomena Book PDF

Author : Weidong Guo,Gérard Labrosse,Ranga Narayanan
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 49,9 Mb
Release : 2013-01-26
Category : Science
ISBN : 9783642340888

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The Application of the Chebyshev-Spectral Method in Transport Phenomena by Weidong Guo,Gérard Labrosse,Ranga Narayanan Pdf

Transport phenomena problems that occur in engineering and physics are often multi-dimensional and multi-phase in character. When taking recourse to numerical methods the spectral method is particularly useful and efficient. The book is meant principally to train students and non-specialists to use the spectral method for solving problems that model fluid flow in closed geometries with heat or mass transfer. To this aim the reader should bring a working knowledge of fluid mechanics and heat transfer and should be readily conversant with simple concepts of linear algebra including spectral decomposition of matrices as well as solvability conditions for inhomogeneous problems. The book is neither meant to supply a ready-to-use program that is all-purpose nor to go through all manners of mathematical proofs. The focus in this tutorial is on the use of the spectral methods for space discretization, because this is where most of the difficulty lies. While time dependent problems are also of great interest, time marching procedures are dealt with by briefly introducing and providing a simple, direct, and efficient method. Many examples are provided in the text as well as numerous exercises for each chapter. Several of the examples are attended by subtle points which the reader will face while working them out. Some of these points are deliberated upon in endnotes to the various chapters, others are touched upon in the book itself.

Spectral Methods in MATLAB

Lloyd N. Trefethen
Spectral Methods in MATLAB Book PDF

Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 179 pages
File Size : 51,7 Mb
Release : 2000-07-01
Category : Mathematics
ISBN : 9780898714654

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Spectral Methods in MATLAB by Lloyd N. Trefethen Pdf

Mathematics of Computing -- Numerical Analysis.

Chebyshev and Fourier Spectral Methods

John P. Boyd
Chebyshev and Fourier Spectral Methods Book PDF

Author : John P. Boyd
Publisher : Courier Corporation
Page : 690 pages
File Size : 54,9 Mb
Release : 2001-12-03
Category : Mathematics
ISBN : 9780486411835

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Chebyshev and Fourier Spectral Methods by John P. Boyd Pdf

Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Spectral and High-order Methods with Applications

Jie Shen,Tao Tang
Spectral and High order Methods with Applications Book PDF

Author : Jie Shen,Tao Tang
Publisher : Unknown
Page : 224 pages
File Size : 45,7 Mb
Release : 2006
Category : Calculus
ISBN : 7030177223

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Spectral and High-order Methods with Applications by Jie Shen,Tao Tang Pdf

中国科学院科学出版基金资助出版。