Mathematics

Research Interests

Software

Journal Publications

  1. Spectral Methods with Postprocessing for Numerical Hyperbolic Heat Transfer.  Numerical Heat Transfer, Part A, vol. 43 no. 7 (2003), p. 717-730.  DOI: 10.1080/713838126
  2. Chebyshev Super Spectral Viscosity method for a Fluidized Bed Model.  Journal of Computational Physics, 186/2, p. 630-651 (2003). DOI: 10.1016/S0021-9991(03)00089-5
  3. Chebyshev Super Spectral Viscosity method for a Two-Dimensional Fluidized Bed Model.  International Journal of Numerical Methods in Fluids, vol. 42, p. 249-263. DOI: 10.1002/fld.485
  4. The Spectral Signal Processing Suite.  ACM Transactions on Mathematical Software, vol. 29, no. 2, June 2003, p. 1-23. DOI: 10.1145/779359.779364
  5. The Method of Characteristics with applications to Conservation Laws.  Journal of Online Mathematics and Applications (JOMA), Volume 3, February 2003. [applet]
  6. Adaptive Radial Basis Function Methods for time dependent Partial Differential Equations.  Applied Numerical Mathematics, vol. 54, issue 1, p. 79-94, June 2005. DOI: 10.1016/j.apnum.2004.07.004
  7. Integrated Multiquadric Radial Basis Function Approximation Methods.  Computers and Mathematics with Applications, vol. 51, no. 8, April 2006, p. 1283-1296.  DOI: 10.1016/j.camwa.2006.04.014
  8. Digital Total Variation Filtering as Postprocessing for Pseudospectral Methods for Conservation Laws.  Numerical Algorithms, vol. 41, p. 17-33, 2006.  DOI: 10.1007/s11075-005-9003-5
  9. Digital Total Variation Filtering as postprocessing for Radial Basis Function Approximation Methods.  Computers and Mathematics with Applications, vol. 52, p. 1119-1130, Sept. 2006.  DOI: 10.1016/j.camwa.2006.02.013
  10. Chebyshev Interpolation: an interactive tour.  Journal of Online Mathematics and Applications, September 2006.
  11. A Numerical Study of the Accuracy and Stability of Symmetric and Asymmetric RBF Collocation methods for Hyperbolic PDEs.  Numerical Methods for Partial Differential Equations, vol. 24, no. 2, p. 670 - 686, 2008.  DOI: 10.1002/num.20290
  12. A Pseudospectral Method with Edge Detection Free Postprocessing for 2d Hyperbolic Heat Transfer.  Numerical Heat Transfer, Part B: Fundamentals,  vol. 54,  no. 1, 2008, p. 52-61.  DOI:  10.1080/10407790802122485
  13. Edge Detection Free Postprocessing for Pseudospectral Approximations.   Journal of Scientific Computing, vol. 51, no. 1, p. 49-61,  2009.  DOI: 10.1007/s10915-009-9287-z
  14. A Random Variable Shape Parameter Strategy for Radial Basis Function Approximation Methods (with D. Sturgill).   Engineering Analysis with Boundary Elements, vol. 33, p. 1239-1245, 2009.  DOI: 10.1016/j.enganabound.2009.07.003
  15. Multiquadric Radial Basis Function Approximation Methods for the Numerical Solution of Partial Differential Equations (with E. J. Kansa).  Advances in Computational Mechanics, volume 2, 2009.  ISSN: 1940-5820. (Matlab m-files, pdf).
  16. Algorithm 899: The Matlab Postprocessing Toolkit.  ACM Transactions on Mathematical Software, vol. 37, no. 1, 2010.  DOI: 10.1145/1644001.1644011
  17. Radial Basis Function approximation methods with extended precision floating point arithmetic.  Engineering Analysis with Boundary Elements, Volume 35, Issue 1, January 2011, Pages 68-76.  DOI:  10.1016/j.enganabound.2010.05.011
  18. Stability properties of a predictor-corrector implementation of an implicit linear multistep method (with C. Meador).  Involve, vol. 4, no. 1, p. 43-51, 2011.  DOI: 10.2140/involve.2011.4.43
  19. On the numerical solution of chaotic dynamical systems using extended precision floating point arithmetic and very high order numerical methods (with C. Meador).  Nonlinear Analysis: Modelling and Control, vol. 16, no. 3, 2011, p. 340-352.
  20. A Linear System-Free Gaussian RBF Method for the Gross-Pitaevskii equation on unbounded domains.  Numerical Methods for Partial Differential Equations, volume 28, number 2, p. 389-401, 2012.  DOI: 10.1002/num.20623
  21. A Local Radial Basis Function method for Advection-Diffusion-Reaction equations on complexly shaped domains.  Applied Mathematics and Computation, volume 218, p. 9853-9865, 2012.  Matlab files.   DOI: 10.1016/j.amc.2012.03.062
  22. Regularized symmetric positive definite matrix factorizations for linear systems arising from RBF interpolation and differentiation.  Engineering Analysis with Boundary Elements, volume 44, p. 76-86, July 2014.  (source code)  DOI: 10.1016/j.enganabound.2014.04.019
  23. Filtered Leapfrog Time Integration with Enhanced Stability Properties (with A. Aluthge,  and R. Estep).  Journal of Applied Mathematics and Physics, 4, p. 1354-1370, 2016. DOI: 10.4236/jamp.2016.47145.  (source code)
  24. An examination of evaluation algorithms for the RBF methods (with S. Cogar).  Engineering Analysis with Boundary Elements, volume 75, p. 36-45, February 2017.  DOI: 10.1016/j.enganabound.2016.11.006,   (source code)
  25. The Matlab Radial Basis Function Toolkit. Journal of Open Research Software, volume 5, issue 1, page 8, 2017.   (software web page)  DOI: 10.5334/jors.131
  26. Radial Basis Function Methods - the case of symmetric domains.  Under review, Numerical Methods for Partial Differential Equations, 2017.
  27. A rational radial basis function method for accurately resolving discontinuities and steep gradients (with Y. Bai).  Under review, Applied Numerical Mathematics, 2017.
Bibtex entries for publications above, ORCID ID: 0000-0003-0989-412X, Researchgate, doi2bib 

Technical Reports

Student Publications


Classes


Current/Past Student Research Group Members

Graduate

Undergraduate

*, #