Noel J. Walkington

Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
noelw@cmu.edu

Professional Experience:

Professor Carnegie Mellon University. (7/00-Present)

Associate Professor Carnegie Mellon University. (7/95-6/00)

Assistant Professor Carnegie Mellon University. (9/89-6/95)

Post Doctoral Fellow and Lecturer, University of Texas at Austin. (9/88-8/89)

Engineering Consultant, Winbe Products, Austin, Texas. (9/87-8/89)

Teaching Assistant and Assistant Instructor, University of Texas at Austin. (9/84-5/88)

Post Doctoral Fellow, University of Missouri - Rolla. (9/83-9/84)

Research Assistant, University of Missouri - Rolla. (3/79-9/84)

Education:

Ph.D. (Mathematics) The University of Texas at Austin, May 1988.
Dissertation: Resolution of a Diffusion Problem Arising in the Flow of Fluids.
Thesis Advisor: Ralph E. Showalter.

Ph.D. (Mechanical Engineering) University of Missouri-Rolla, December 1983.
Dissertation: A Numerical Model for Subsonic Acoustic Choking.
Thesis Advisor: Walter Eversman.

M.S. (Mechanical Engineering) University of Missouri-Rolla, May 1981.
Thesis Advisor: Walter Eversman.

B.E. (Mechanical, first class honors), University of Canterbury, Christchurch, New Zealand, December 1978.

Selected Talks and Presentations:
Phase Field/Level Set Methods for Flows Containing Elastic Membranes, BIRS workshop on Interfacial Dynamics in Complex Fluids, Bamff 5/06.

Phase Field/Level Set Methods for Problems Involving Elastic Membranes, Oberwolfach, Germany, 2/05.

Simulating Fluids Exhibiting Microstructure, Plenary talk at the Workshop on Analysis and Numerics of Non-Newtonian Fluids, Kirchzarten Germany, 4/03.

Numerical Approximation of the Ericksen Lesslie Equations, SAMSI workshop on Multiscale Challenges in Soft Matter, Raleigh, NC, 2/04.

Selected Publications:

• Chrysafinos, K., and Walkington N. J., Lagrangian and Moving Mesh Methods for the Convection Diffusion Equation, accepted M2AN April 2007.
• Liu, C., and Walkington, N. J. Convergence of Numerical Approximations of the Incompressible Navier Stokes Equations with Variable Density and Viscosity SINUM, Vol 45, No. 3, 2007, pp 1287-1304.
• Walkington N. J., Convergence of the Discontinuous Galerkin Method for Discontinuous Solutions, SINUM, Vol. 42, No. 5, Feb 2005 pp. 1801-1817.
• Liu, C., and Walkington, N. J. An Eulerian Description of Fluids Containing Visco-hyperelastic Particles, Archive for Rational Mechanics and Analysis, Vol. 159, No. 3, pp 229-252, 2001.
• Kinderlehrer, D. and Walkington, N. J., Approximation of Parabolic Equations Using the Wasserstein Metric, Math. Modeling and Numer. Anal., Volume 33, Number 4, August 1999.
• Rulla J. and Walkington N. J., Optimal Rates of Convergence for Degenerate Parabolic Problems in Two Dimensions, SIAM J. Numer. Anal., Volume 33, Number 1, pp 56-67, February, 1996.
• R. E. Showalter and N. J. Walkington, Diffusion of Fluid in a Fissured Medium with Microstructure, SIAM J. Math. Anal., Vol 22, No. 6, pp. 1702-1722, November 1991.
• R. E. Showalter and N. J. Walkington, Microstructure Models of Diffusion in Fissured Media, J. Math. Anal. and Appl. Vol. 155, No. 1, February 1991, pp. 1-20.

Recent Funding:

NSF grant RTG-0635983 (Co PI) 4/07-4/11 Center for Nonlinear Analysis: Research and Training in Applied Mathematics

NSF grant DMS-0208586 7/02-7/05, Algorithms for Simulating Flows of Complex Fluids: Fluid-Solid Mixtures and Liquid Crystals

NSF Grant ITR-0086903, 8/00-7/04, (with G. Blelloch, O. Ghattas, and G. Miller), Simulation of Flows with Dynamic Interfaces on Multi-Teraflop Computers.

NSF Grant CISE-9972541, 8/99-7/01, (with G. Miller), Automatic and Adaptive Mesh Generation with Applications to Scientific Computing.

NSF grant DMS-9973285, 8/99-7/01, Numerical Approximation of Liquid Crystal Flows.

Graduate Students and Postgraduate Advisees:

Ph.D. Students: A. Rand, C. Arama (current), S. Pav (graduated 2003)

Postdoctoral Students: J. Howell, K. Chrysafinos

Co-sponsored Postdoctoral Students: R. Jordan, G. Dolzmann, R. Jerard, C. Liu.

Co-advised Ph.D. Students: D. Talmor, J. Hill, C. Kadow.