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Walkington
Noel J. Walkington, Professor
Ph.D., The University of Texas at Austin
E-mail: noelw@andrew.cmu.edu
Office: Wean Hall 7117
Phone: 412-268-6291


Research:

Walkington's research centers around the analysis of numerical schemes to approximate solutions of (systems of) partial differential equations. These equations are used ubiquitously in science and engineering to simulate virtually every macroscopic system and form the corner stone of predictive design capability. Examples include response of liquid crystals, ground flow in heterogeneous media, and plastic deformation of crystalline materials.

Algorithms to approximate the solution of partial differential equations involve mesh generation (computational geometry), (non) linear solvers (computational linear algebra), and a numerical kernel (numerical analysis). The major focus of Walkington's work is on the later component; in particular, the development of numerical schemes which faithfully inherit as many of the properties of the (partial differential) equations as possible. Tools from analysis continue to play an increasingly important role in the modeling, simulation, and understanding of complex physical systems. His research together tools from partial differential equations, continuum mechanics, and numerical analysis, to analyze numerical schemes to simulate these systems.


Selected Publications:

  • Walkington, N. J. and Rulla, J., "Optimal Rates of Convergence for Degenerate Parabolic Problems in Two Dimensions," SINUM, Volume 33, Number 1, February 1996, pp. 5667.
  • Nicolaides, R. A. and Walkington, N. J., "Strong Convergence of Numerical Solutions to Degenerate Variational Problems," Math. Comp., Volume 64, Number 209, January 1995, pp. 117127.
  • Ma, L. and Walkington, N. J., "On Algorithms for Non-Convex Optimization," SIAM J. Numer. Anal. , Volume 32, Number 3, June 1995, pp. 900923.

Recent CNA Publications: