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Author : Hans G. Kaper
Publisher : Birkhauser
ISBN 13 : 9780817613723
Total Pages : 423 pages
Book Rating : 4.6/5 (137 download)
Download or read book Spectral Methods in Linear Transport Theory written by Hans G. Kaper and published by Birkhauser. This book was released on 1982-11-01 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H. G. Kaper
Publisher : Birkhäuser
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.:/5 (41 download)
Download or read book Spectral Methods in Linear Transport Theory written by H. G. Kaper and published by Birkhäuser. This book was released on 1982 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniele Funaro
Publisher : Springer Science & Business Media
ISBN 13 : 9783540626497
Total Pages : 228 pages
Book Rating : 4.6/5 (264 download)
Download or read book Spectral Elements for Transport-Dominated Equations written by Daniele Funaro and published by Springer Science & Business Media. This book was released on 1997-04-17 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with the numerical approximation of various PDEs using the spectral element method, with particular emphasis for elliptic equations dominated by first-order terms. It provides a simple introduction to spectral elements with additional new tools (upwind grids and preconditioners). Applications to fluid dynamics and semiconductor devices are considered, as well as in other models were transport-diffusion equations arise. The aim is to provide the reader with both introductive and more advanced material on spectral Legendre collocation methods. The book however does not cover all the aspects of spectral methods. Engineers, physicists and applied mathematicians may study how to implement the collocation method and use the results to improve their computational codes.
Author : Claudio Canuto
Publisher : Springer Science & Business Media
ISBN 13 : 3540307265
Total Pages : 585 pages
Book Rating : 4.5/5 (43 download)
Download or read book Spectral Methods written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2007-09-23 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Bernard Shizgal
Publisher : Springer
ISBN 13 : 9401794545
Total Pages : 431 pages
Book Rating : 4.4/5 (17 download)
Download or read book Spectral Methods in Chemistry and Physics written by Bernard Shizgal and published by Springer. This book was released on 2015-01-07 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Aref Jeribi
Publisher : Springer
ISBN 13 : 3319175661
Total Pages : 608 pages
Book Rating : 4.3/5 (191 download)
Download or read book Spectral Theory and Applications of Linear Operators and Block Operator Matrices written by Aref Jeribi and published by Springer. This book was released on 2015-07-04 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.
Author : Claudio Canuto
Publisher : Springer Science & Business Media
ISBN 13 : 3540307281
Total Pages : 616 pages
Book Rating : 4.5/5 (43 download)
Download or read book Spectral Methods written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2007-06-30 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: 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. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.
Author : Greenberg
Publisher : Birkhäuser
ISBN 13 : 303485675X
Total Pages : 339 pages
Book Rating : 4.0/5 (348 download)
Download or read book Modern Mathematical Methods in Transport Theory written by Greenberg and published by Birkhäuser. This book was released on 2013-11-22 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Eleventh International Transport Theory Conference and Symposium in honor of the sixty-fifth birthday of Kenneth Case and the sixtieth birthday of Paul Zweifel was held in Blacksburg, Virginia, during May 22-26, 1989, on the campus of Virginia Polytechnic Institute and State University (Virginia Tech). This volume consists of a selection of the invited papers delivered at the Conference, and represents a cross section of the research currently being carried out in the field of transport theory. The volume is divided into two sections. The Symposium lectures are intended each to summarize an important aspect of transport theory, as well as to present timely new results of the author's research interest. The Conference lectures are contributions of each author on his current research. As has been the custom in this series of conferences, each lecturer was invited to participate by the organizing committee of the Conference: W. Greenberg, Virginia Tech, chairman; V. Boffi, Universita di Firenze; N. Corngold, California Institute of Technology; B. Ganapol, University of Arizona; N. McCormick, University of Washington; P. Nelson, Texas Tech; G. Pomraning, University of California, Los Angeles. The Eleventh International Transport Theory Conference was funded by generous con tributions from Science Applications International Corporation, R. Beyster, president, and from Virginia Polytechnic Institute and State University. Conference participants, and, we believe, researchers in this and related areas, are indebted to these organizations. We would like to thank Lamberto Rondoni, in the graduate program at Virginia Tech, for proofreading manuscripts of all the Italian contributors.
Author : Jan S. Hesthaven
Publisher : Cambridge University Press
ISBN 13 : 113945952X
Total Pages : 4 pages
Book Rating : 4.1/5 (394 download)
Download or read book Spectral Methods for Time-Dependent Problems written by Jan S. Hesthaven and published by Cambridge University Press. This book was released on 2007-01-11 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.
Author : Ben-yu Guo
Publisher : World Scientific
ISBN 13 : 9814496642
Total Pages : 359 pages
Book Rating : 4.8/5 (144 download)
Download or read book Spectral Methods And Their Applications written by Ben-yu Guo and published by World Scientific. This book was released on 1998-05-05 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : John P. Boyd
Publisher : Courier Corporation
ISBN 13 : 0486411834
Total Pages : 690 pages
Book Rating : 4.4/5 (864 download)
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : I.W. Knowles
Publisher : Elsevier
ISBN 13 : 0080871666
Total Pages : 401 pages
Book Rating : 4.0/5 (88 download)
Download or read book Spectral Theory of Differential Operators written by I.W. Knowles and published by Elsevier. This book was released on 1981-01-01 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory of Differential Operators
Author : Paul Nelson
Publisher : CRC Press
ISBN 13 : 1000946541
Total Pages : 479 pages
Book Rating : 4.0/5 (9 download)
Download or read book Transport Theory written by Paul Nelson and published by CRC Press. This book was released on 2023-05-31 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes seminal papers on technical subjects—transport theory, invariant imbedding, and integral equations—presented as contributions to honour George Milt Wing in celebration of his 65th birth anniversary in 1988.
Author : M. Mokhtar-Kharroubi
Publisher : World Scientific
ISBN 13 : 9789810228699
Total Pages : 372 pages
Book Rating : 4.2/5 (286 download)
Download or read book Mathematical Topics in Neutron Transport Theory written by M. Mokhtar-Kharroubi and published by World Scientific. This book was released on 1997 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some recent mathematical developments about neutron transport equations. Several different topics are dealt with including regularity of velocity averages, spectral analysis of transport operators, inverse problems, nonlinear problems arising in the stochastic theory of neutron chain fissions, compactness properties of perturbed of 0-semigroups in Banach spaces with applications to transport theory, Miyadera perturbations of c0-semigroups in Banach spaces with applications to singular transport equations, a thorough analysis of the leading eigenelements of transport operators and their approximation, scattering theory. Besides the new problems addressed in this book a unification and extension of the classical spectral analysis of neutron transport equations is given.
Author : James J. Duderstadt
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 630 pages
Book Rating : 4.3/5 (91 download)
Download or read book Transport Theory written by James J. Duderstadt and published by John Wiley & Sons. This book was released on 1979 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems after each chapter
Author : Hassan Emamirad
Publisher : Springer Nature
ISBN 13 : 9811623732
Total Pages : 179 pages
Book Rating : 4.8/5 (116 download)
Download or read book Scattering Theory for Transport Phenomena written by Hassan Emamirad and published by Springer Nature. This book was released on 2021-06-27 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scattering theory for transport phenomena was initiated by P. Lax and R. Phillips in 1967. Since then, great progress has been made in the field and the work has been ongoing for more than half a century. This book shows part of that progress. The book is divided into 7 chapters, the first of which deals with preliminaries of the theory of semigroups and C*-algebra, different types of semigroups, Schatten–von Neuman classes of operators, and facts about ultraweak operator topology, with examples using wavelet theory. Chapter 2 goes into abstract scattering theory in a general Banach space. The wave and scattering operators and their basic properties are defined. Some abstract methods such as smooth perturbation and the limiting absorption principle are also presented. Chapter 3 is devoted to the transport or linearized Boltzmann equation, and in Chapter 4 the Lax and Phillips formalism is introduced in scattering theory for the transport equation. In their seminal book, Lax and Phillips introduced the incoming and outgoing subspaces, which verify their representation theorem for a dissipative hyperbolic system initially and also matches for the transport problem. By means of these subspaces, the Lax and Phillips semigroup is defined and it is proved that this semigroup is eventually compact, hence hyperbolic. Balanced equations give rise to two transport equations, one of which can satisfy an advection equation and one of which will be nonautonomous. For generating, the Howland semigroup and Howland’s formalism must be used, as shown in Chapter 5. Chapter 6 is the highlight of the book, in which it is explained how the scattering operator for the transport problem by using the albedo operator can lead to recovery of the functionality of computerized tomography in medical science. The final chapter introduces the Wigner function, which connects the Schrödinger equation to statistical physics and the Husimi distribution function. Here, the relationship between the Wigner function and the quantum dynamical semigroup (QDS) can be seen.
Author : Jussi Behrndt
Publisher : Springer Science & Business Media
ISBN 13 : 3764389117
Total Pages : 261 pages
Book Rating : 4.7/5 (643 download)
Download or read book Spectral Theory in Inner Product Spaces and Applications written by Jussi Behrndt and published by Springer Science & Business Media. This book was released on 2009-01-21 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a collection of research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17. This work discusses topics such as linear relations, singular perturbations, de Branges spaces, nonnegative matrices, and abstract kinetic equations.
