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Chebyshev and Fourier Spectral Methods

Chebyshev and Fourier Spectral Methods PDF Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486141926
Category : Mathematics
Languages : en
Pages : 688
Book Description
Completely revised text applies spectral methods to boundary value, eigenvalue, and time-dependent problems, but also covers cardinal functions, matrix-solving methods, coordinate transformations, much more. Includes 7 appendices and over 160 text figures.

Chebyshev and Fourier Spectral Methods

Chebyshev and Fourier Spectral Methods PDF Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486141926
Category : Mathematics
Languages : en
Pages : 688
Book Description
Completely revised text applies spectral methods to boundary value, eigenvalue, and time-dependent problems, but also covers cardinal functions, matrix-solving methods, coordinate transformations, much more. Includes 7 appendices and over 160 text figures.

Spectral Methods

Spectral Methods PDF Author: Claudio Canuto
Publisher: Springer Science & Business Media
ISBN: 3540307281
Category : Mathematics
Languages : en
Pages : 596
Book Description
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.

Time-Domain Scattering

Time-Domain Scattering PDF Author: P. A. Martin
Publisher: Cambridge University Press
ISBN: 1108835597
Category : Mathematics
Languages : en
Pages : 267
Book Description
The first thorough synthesis of methods for solving time-domain scattering problems, covering both theoretical and computational aspects.

Spectral Methods and Their Applications

Spectral Methods and Their Applications PDF Author: Benyu Guo
Publisher: World Scientific
ISBN: 9789810233334
Category : Mathematics
Languages : en
Pages : 349
Book Description
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/hp Element Methods for Computational Fluid Dynamics

Spectral/hp Element Methods for Computational Fluid Dynamics PDF Author: George Karniadakis
Publisher: Oxford University Press
ISBN: 0199671362
Category : Mathematics
Languages : en
Pages : 676
Book Description
Revision of: Spectral/hp element methods for CFD. 1999.

Quasi-spectral Finite Difference Methods

Quasi-spectral Finite Difference Methods PDF Author: Tristan Kremp
Publisher: Cuvillier Verlag
ISBN: 3736936850
Category : Mathematics
Languages : en
Pages : 240
Book Description
The doctoral thesis „Quasi-spectral finite difference methods: Convergence analysis and application to nonlinear optical pulse propagation“ by Tristan Kremp addresses the theory and application of so-called quasi-spectral finite differences. Contrary to the common Taylor approach, these are by construction exact for trigonometric instead of algebraic polynomials. With any fixed discretization spacing, this allows for a higher accuracy, e.g., when differencing functions that have a band-pass like Fourier spectrum. In this dissertation, the convergence of such quasi-spectral finite differences is proven for the first time. It is shown that the highest possible order of convergence is the same as for the Taylor approach, i.e., it is basically identical to the total number of summands in the finite difference. This order is achieved if all frequencies, for which the quasi-spectral finite difference is exact, vanish sufficiently fast in comparison to the discretization spacing. This condition can be easily incorporated in the finite difference weights construction, which can be achieved by spectral interpolation or least-squares optimization, respectively. Employing previously unknown Haar (or Chebyshev) systems that consist of combinations of algebraic and trigonometric monomials, the equivalence of both methods of construction is proven. In a semidiscretization framework, these finite differences are, for the first time, combined with exponential split-step integrators for an efficient solution of linear or nonlinear evolution equations. It is shown that a simple modification of the common symmetric split-step integrator guarantees its second-order convergence even in the presence of general nonlinearities. An important example of such a partial differential equation is the nonlinear Schrödinger equation (NLSE). In contrast to the standard literature, the NLSE is derived here directly from Maxwell’s equations, without the common assumption that the second spatial derivative in the direction of the propagation can be neglected, and without the assumption that the multiplicative nonlinear term behaves as a constant with respect to the Fourier transformation. A practically relevant application is the propagation of wavelength division multiplexing (WDM) signals in optical fibers. Compared to other semidiscretization techniques such as finite elements, wavelet collocation and the pseudo-spectral methods (split-step Fourier method) that are mostly employed by the industry, the quasi-spectral finite differences allow, at the same accuracy, for a substantial reduction of the computation time.

Spectral/hp Element Methods for CFD

Spectral/hp Element Methods for CFD PDF Author: George Karniadakis
Publisher: Oxford University Press on Demand
ISBN: 0195102266
Category : Mathematics
Languages : en
Pages : 390
Book Description
This book is an essential reference for anyone interested in the use of spectral/hp element methods in fluid dynamics. It provides a comprehensive introduction to the field together with detailed examples of the methods to the incompressible and compressible Navier-Stokes equations.

High-Order Methods for Incompressible Fluid Flow

High-Order Methods for Incompressible Fluid Flow PDF Author: M. O. Deville
Publisher: Cambridge University Press
ISBN: 9780521453097
Category : Mathematics
Languages : en
Pages : 499
Book Description
This book covers the development of high-order numerical methods for the simulation of incompressible fluid flows in complex domains.

Computational Methods for Nanoscale Applications

Computational Methods for Nanoscale Applications PDF Author: Igor Tsukerman
Publisher: Springer Science & Business Media
ISBN: 0387747788
Category : Technology & Engineering
Languages : en
Pages : 532
Book Description
Positioning itself at the common boundaries of several disciplines, this work provides new perspectives on modern nanoscale problems where fundamental science meets technology and computer modeling. In addition to well-known computational techniques such as finite-difference schemes and Ewald summation, the book presents a new finite-difference calculus of Flexible Local Approximation Methods (FLAME) that qualitatively improves the numerical accuracy in a variety of problems.

Computational Solid Mechanics

Computational Solid Mechanics PDF Author: Marco L. Bittencourt
Publisher: CRC Press
ISBN: 1439860017
Category : Science
Languages : en
Pages : 680
Book Description
Presents a Systematic Approach for Modeling Mechanical Models Using Variational Formulation—Uses Real-World Examples and Applications of Mechanical Models Utilizing material developed in a classroom setting and tested over a 12-year period, Computational Solid Mechanics: Variational Formulation and High-Order Approximation details an approach that establishes a logical sequence for the treatment of any mechanical problem. Incorporating variational formulation based on the principle of virtual work, this text considers various aspects of mechanical models, explores analytical mechanics and their variational principles, and presents model approximations using the finite element method. It introduces the basics of mechanics for one-, two-, and three-dimensional models, emphasizes the simplification aspects required in their formulation, and provides relevant applications. Introduces Approximation Concepts Gradually throughout the Chapters Organized into ten chapters, this text provides a clear separation of formulation and finite element approximation. It details standard procedures to formulate and approximate models, while at the same time illustrating their application via software. Chapter one provides a general introduction to variational formulation and an overview of the mechanical models to be presented in the other chapters. Chapter two uses the concepts on equilibrium that readers should have to introduce basic notions on kinematics, duality, virtual work, and the PVW. Chapters three to ten present mechanical models, approximation and applications to bars, shafts, beams, beams with shear, general two- and three-dimensional beams, solids, plane models, and generic torsion and plates. Learn Theory Step by Step In each chapter, the material profiles all aspects of a specific mechanical model, and uses the same sequence of steps for all models. The steps include kinematics, strain, rigid body deformation, internal loads, external loads, equilibrium, constitutive equations, and structural design. The text uses MATLAB® scripts to calculate analytic and approximated solutions of the considered mechanical models. Computational Solid Mechanics: Variational Formulation and High Order Approximation presents mechanical models, their main hypothesis, and applications, and is intended for graduate and undergraduate engineering students taking courses in solid mechanics.