Robert L. Higdon

Professor of Mathematics
Oregon State University


Office: Kidder 294B
Phone: (541) 737-5150
Fax: (541) 737-0517
E-mail: higdon@math.oregonstate.edu

Postal address:
Department of Mathematics
Oregon State University
Kidder Hall 368
Corvallis, Oregon 97331-4605
Education:
Univ. of Missouri - Columbia, B.A., Dec. 1975
Stanford University, Ph.D., Aug. 1981


Teaching

Spring 2008
Math 623, Differential and Integral Equations of Mathematical Physics, 1:00-1:50 MWF.
Office hours: Monday 2:00-3:00, Wednesday 3:00-4:00, Friday 11:00-11:50, or by appointment.
Matlab notes
Notes on Computational Mathematics: Matlab, by R. L. Higdon. (PDF, 225 K.) These notes describe the basics of Matlab, plus some mathematical topics. The notes were last revised in 1996, but the contents are still valid.

Research

Research interests
Applied mathematics, numerical solution of partial differential equations. Current activity is related to the numerical modeling of ocean circulation. Earlier, I worked on absorbing boundary conditions and initial-boundary value problems.
Example

The figure to the right was produced from a numerical computation that tested a timestepping method and other algorithms for solving a system of partial differential equations that describes large-scale ocean circulation. It is similar to a black-and-white figure in the 2005 JCP paper listed below. The curves and varying colors represent a contour plot of the height of the free surface at the top of the fluid, and the arrows represent the horizontal fluid velocity. In the color bar, the units are centimeters. Due to the effects of the earth's rotation, the horizontal velocity is approximately perpendicular to the horizontal pressure gradient, which means that the fluid flows along curves of constant elevation.

A larger version of this plot can be obtained here. This test computation was performed on a square spatial domain; a black-and-white contour plot for the entire fluid domain is given in the next figure.

Recent publications

R. L. Higdon, A two-level time-stepping method for layered ocean circulation models: further development and testing (PDF, 4 Mb), Journal of Computational Physics, vol. 206, pp. 463-504, 2005. Due to copyright restrictions, the final published version cannot be posted here. This is a personal version, which has the same contents.

R. L. Higdon, Numerical modelling of ocean circulation (PDF, 3.3 Mb), Acta Numerica 2006, pp. 385-470. Acta Numerica is an annual volume, published by Cambridge University Press, that contains invited surveys on topics in numerical analysis and scientific computing.

This page was last updated: April 4, 2008.