#### Filter Results:

- Full text PDF available (16)

#### Publication Year

2002

2012

- This year (0)
- Last 5 years (1)
- Last 10 years (12)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Scott A. Sarra
- 2004

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)

- Scott A. Sarra
- Numerical Algorithms
- 2005

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)

- Scott A. Sarra
- 2003

Under the governing equations of Hyperbolic Heat Transfer, energy propagates through a medium as a wave with sharp discontinuities at the wave front. The use of spectral methods to solve such problems numerically results in a solution in which strong numerical oscillations are present due to the Gibbs-Wilbraham Phenomenon. It is demonstrated that a… (More)

- Scott A. Sarra
- ACM Trans. Math. Softw.
- 2003

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)

- Scott A. Sarra
- 2002

A Chebyshev super spectral viscosity method and operator splitting are used to solve a hyperbolic system of conservation laws with a source term modeling a fluidized bed. The fluidized bed displays a slugging behavior which corresponds to shocks in the solution. A modified Gegenbauer postprocessing procedure is used to obtain a solution which is free of… (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)

- Scott A. Sarra
- 2009

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)

- Scott A. Sarra
- Applied Mathematics and Computation
- 2012

- Scott A. Sarra
- 2010

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)