The spectral signal processing suite

Authors:
Scott A. Sarra
Affiliations:
Marshall University, Huntington, WV
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2003

Citing 16
Cited 3

Spectral and finite difference solutions of the Burgers equation

Computers and Fluids
Convergence of spectral methods for nonlinear conservation laws

SIAM Journal on Numerical Analysis
Non-oscillatory central differencing for hyperbolic conservation laws

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Numerical solution of a hyperbolic system of conservation laws with source term arising in a fluidized bed model

Journal of Computational Physics
Family of spectral filters for discontinuous problems

Journal of Scientific Computing
On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function

Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
A modified Chebyshev pseudospectral method with an O(N–1) time step restriction

Journal of Computational Physics
On the Gibbs phenomenon IV: recovering exponential accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic function

Mathematics of Computation
On the Gibbs phenomenon III: recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function

SIAM Journal on Numerical Analysis
A Legendre pseudospectral viscosity method

Journal of Computational Physics
On the Gibbs Phenomenon and Its Resolution

SIAM Review
Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws

SIAM Journal on Numerical Analysis
Spectral methods in MatLab

Spectral methods in MatLab
Enhanced spectral viscosity approximations for conservation laws

Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Detection of Edges in Spectral Data II. Nonlinear Enhancement

SIAM Journal on Numerical Analysis
Chebyshev super spectral viscosity method for a fluidized bed model

Journal of Computational Physics

Chebyshev super spectral viscosity method for a fluidized bed model

Journal of Computational Physics
Digital Total Variation Filtering as Postprocessing for Radial Basis Function Approximation Methods

Computers & Mathematics with Applications
Algorithm 899: The Matlab postprocessing toolkit

ACM Transactions on Mathematical Software (TOMS)

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Abstract

A software suite written in the Java programming language for the postprocessing of Chebyshev approximations to discontinuous functions is presented. It is demonstrated how to use the package to remove the effects of the Gibbs-Wilbraham phenomenon from Chebyshev approximations of discontinuous functions. Additionally, the package is used to postprocess Chebyshev collocation and Chebyshev super spectral viscosity approximations of hyperbolic partial differential equations. The postprocessing method is the Gegenbauer reconstruction procedure. The Spectral Signal Processing Suite is the first publicly available package that implements the procedure. State-of-the-art techniques are used to implement the algorithms with efficiency while reducing round-off error.