Scott A. Sarra

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Radial basis function (RBF) methods have shown the potential to be a universal grid free method for the numerical solution of partial differential equations. Both global and compactly supported basis functions may be used in the methods to achieve a higher order of accuracy. In this paper, we take advantage of the grid free property of the methods and use(More)
Digital total variation filtering is analyzed as a fast, robust, post-processing method for accelerating the convergence of pseudospectral approximations that have been contaminated by Gibbs oscillations. The method, which originated in image processing, can be combined with spectral filters to quickly post-process large data sets with sharp resolution of(More)
ii Preface Radial Basis Function (RBF) methods have become the primary tool for interpolating multidimensional scattered data. RBF methods also have become important tools for solving Partial Differential Equations (PDEs) in complexly shaped domains. Classical methods for the numerical solution of PDEs (finite difference, finite element, finite volume, and(More)
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(More)
Several variable shape parameter methods have been successfully used in Radial Basis Function approximation methods. In many cases variable shape parameter strategies produced more accurate results than if a constant shape parameter had been used. We introduce a new random variable shape parameter strategy and give numerical results showing that the new(More)
Spectral methods approximate functions by projection onto a space PN of orthogonal polynomials of degree ≤ N . When the underlying function is periodic trigonometric (Fourier) polynomials are employed while a popular choice for non-periodic functions are the Chebyshev polynomials. Legendre polynomials are another option in the non-periodic case but are not(More)
Gaussian Radial Basis Function (RBF) interpolation methods are theoretically spectrally accurate. However, in applications this accuracy is seldom realized due to the necessity of solving a very poorly conditioned linear system in order to evaluate the methods. Recently, by using approximate cardinal functions and restricting the method to a uniformly(More)