Journal ArticleDOI
The Accurate Solution of Poisson's Equation by Expansion in Chebyshev Polynomials
Dale B. Haidvogel,Thomas A. Zang +1 more
TLDR
In this article, a Chebyshev expansion technique was applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions, and the spectral equations were solved in two ways - by alternating direction and by matrix diagonalization methods.About:
This article is published in Journal of Computational Physics.The article was published on 1979-02-01. It has received 257 citations till now. The article focuses on the topics: Chebyshev equation & Chebyshev polynomials.read more
Citations
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Spectral Methods in Fluid Dynamics
M. Y. Hussaini,Thomas A. Zang +1 more
TL;DR: Spectral methods have been widely used in simulation of stability, transition, and turbulence as discussed by the authors, and their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed.
Journal ArticleDOI
Efficient spectral-Galerkin method I: direct solvers of second-and fourth-order equations using Legendre polynomials
TL;DR: This paper presents some efficient algorithms based on the Legendre–Galerkin approximations for the direct solution of the second- and fourth-order elliptic equations using matrix-matrix multiplications for discrete variational formulations.
Journal ArticleDOI
Advances in global linear instability analysis of nonparallel and three-dimensional flows
TL;DR: A summary of physical insights gained into three-dimensional linear instability through solution of the two-dimensional partial-differential-equation-based nonsymmetric real or complex generalised eigenvalue problem is presented in this article.
Journal ArticleDOI
Accurate solutions to the square thermally driven cavity at high Rayleigh number
TL;DR: In this article, a pseudo-spectral Chebyshev algorithm was used to solve the equations of natural convection in a 2D differentially heated cavity with adiabatic top and bottom walls for values of Ra up to 108.
References
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Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Book
Matrix iterative analysis
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
MonographDOI
Numerical analysis of spectral methods : theory and applications
David Gottlieb,Steven A. Orszag +1 more
TL;DR: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of algebraic stability analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Method as discussed by the authors.