Download or read book Implementing Spectral Methods for Partial Differential Equations written by David A. Kopriva and published by Springer Science & Business Media. This book was released on 2009-05-27 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Spectral Methods for the Euler Equations written by and published by . This book was released on 1984 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Methods for the Euler Equations written by and published by . This book was released on 1984 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Uniform High Order Spectral Methods for One and Two Dimensional Euler Equations written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1991 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Methods in MATLAB written by Lloyd N. Trefethen and published by SIAM. This book was released on 2000-07-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Spectral Methods for the Euler Equations written by and published by . This book was released on 1984 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Methods for Partial Differential Equations written by Robert G. Voigt and published by . This book was released on 1984 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Methods in Fluid Dynamics written by M. Y. Hussaini and published by . This book was released on 1986 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
Download or read book Implementing Spectral Methods for Partial Differential Equations written by David Kopriva and published by Springer. This book was released on 2009-08-29 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Characteristic Based Asymptotic Perturbation Spectral Method for Th Euler Equations written by T. Michal and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Spectral Methods for Inviscid Compressible Flows written by M. Y. Hussaini and published by . This book was released on 1983 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Development of a Robust Efficient Solver for Spectral and Spectral element Time Discretizations written by Nathan L. Mundis and published by . This book was released on 2014 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines alternative time discretizations for the Euler equations and methods for the robust and efficient solution of these discretizations. Specifically, the time-spectral method (TS), quasi-periodic time-spectral method (BDFTS), and spectral-element method in time (SEMT) are derived and examined in detail. For the two time-spectral based methods, focus is given to expanding these methods for more complicated problems than have been typically solved by other authors, including problems with spectral content in a large number of harmonics, gust response problems, and aeroelastic problems. To solve these more complicated problems, it was necessary to implement the flexible variant of the Generalized Minimal Residual method (FGMRES), utilizing the full second-order accurate spatial Jacobian, complete temporal coupling of the chosen time discretization, and fully-implicit coupling of the aeroelastic equations in the cases where they are needed. The FGMRES solver developed utilizes a block-colored Gauss-Seidel (BCGS) preconditioner augmented by a defect-correction process to increase its effectiveness. Exploration of more efficient preconditioners for the FGMRES solver is an anticipated topic for future work in this field. It was a logical extension to apply this already developed FGMRES solver to the spectral-element method in time, which has some advantages over the spectral methods already discussed. Unlike purely-spectral methods, SEMT allows for bothh - and p -refinement. This property could allow for element clustering around areas of sharp gradients and discontinuities, which in turn could make SEMT more efficient than TS for periodic problems that contain these sharp gradients and would require many time instances to produce a precise solution using the TS method. As such, a preliminary investigation of the SEMT method applied to the Euler equations is conducted and some areas for needed improvement in future work are identified. In this work, it is shown that many if not most periodic problems can be solved more quickly and more precisely (utilizing the current FGMRES solver) using the time-spectral method than the currently state-of-the-art second-order accurate time-implicit methods. Additionally, the potential efficiency gains of the quasi-periodic time-spectral method for strongly-periodic problems, over time-implicit methods for these same types of problems, is demonstrated. Problems with strong, moving shock waves, high reduced frequencies, and/or content in high harmonics (higher than the 20th harmonic) are particularly difficult to solve efficiently using TS, BDFTS, and SEMT, and future work should focus on solver improvements to address these types of problems in particular.
