Research

Research

INTERESTS

In recent years, my academic career has been more focused on administration, but I am still very interested in several research areas, including

  • Scientific computing
  • Parallel algorithms
  • Numerical analysis
  • Nonlinear differential equations
  • IT system administration
  • Computer architecture
  • Computational humor
  • Applications of humor and improvisation

PUBLICATIONS

  1. Humor Applied to STEM Education, with Ludovice, P. and Hu, D. submitted to Systems Research and Behavioral Science, Dec. 2015.

  2. Optimal Numerical Flux of Power Law Fluids in Some Partially Full Pipes, co-author D. Wei, Y. Liu, International Journal of Computational Fluid Dynamics, (2014) 1-12.

  3. Humorous Improvisation Tailored for Technical Innovation, with Ludovice, P., Catrambone, R., Conference Proceedings of the ASEE Southeast Section. 2013

  4. Improvisation methods to catalyze engineering creativity. In Frontiers in Education Conference (FIE), 2010 IEEE, pp. F1A-1. IEEE, 2010.

  5. Improvisation for Engineering Education, with Ludovice, P., Catrambone, R., Proc. ASEE National Meeting, Louisville, KY, Paper AC-2010-1650, June 2010.

  6. Non-Traditional Methods to Enhance Creativity for Engineering Innovation, with Ludovice, P., Catrambone, R., AIChE National Meeting, Nashville, TN (paper 88b), November, 2009.

  7. An Introduction to Parallel and Vector Scientific Computing, with Ronald Shonkwiler, Cambridge Texts in Applied Mathematics, Cambridge University Press (2006).

  8. Penalty finite element approximations of the stationary power-law Stokes problem,with Dongming Wei, J. Numer. Math. 11 (2003), no. 4, 301322.

  9. A penalty method for approximations of the stationary power-law Stokes problem,with Dongming Wei, Electron. J. Differential Equations (2001), No. 7, 12 pp.

  10. A priori Lr error estimates for Galerkin approximations to porous medium and fast diffusion equations,with Dongming Wei, Mathematics of Computation, 68 (1999), no. 227, 971989.

  11. Uniqueness for small solutions to a superlinear boundary value problem at resonance,Nonlinear Analysis, 29 (1997), no. 8, 927935.

  12. Numerical approximation of the first eigenpair of the p-Laplacian using finite elements and the penalty method,with Dongming Wei, Numer. Funct. Anal. Optim., 18 (1997), no. 3-4, 389399.

  13. Positive solutions for a two-point nonlinear boundary value problem with applications to semilinear elliptic equations,with Jairo Santanilla, Differential Integral Equations, 9, (1996), no. 6, 12931304.

  14. Calculus&Mathematica: An End-User’s Point of View,with Enid Steinbart, PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Volume 5, Number 1, (1995), pp. 8096.

  15. Resonance and quasilinear parabolic partial differential equations,with Victor Shapiro, J. Differential Equations, 101 (1993), no. 1, 148177.

  16. Quasilinear ellipticity and jumping nonlinearities,with Victor Shapiro, Rocky Mountain J. Math. 22 (1992), no. 4, 13851403.

  17. Small Solutions to BVP’s at Resonance with Nonhomogeneous Nonlinearity,in Ordinary Differential Equations and Delay Equations, J. Wiener and J. Hale eds., Pitman Research Notes in Mathematics Series Number 272 (1992), pp. 106110.

  18. Existence of small solutions to a resonant boundary value problem with large nonlinearity,J. Differential Equations, 85 (1990), no. 1, 171185.