MA 721: Selected Topics in Numerical Analysis:

Mathematical Models of Physical Problems

Professor C. C. Douglas Fall, 1998

Class Meets on Tuesdays and Thursdays at 2:00 in 327 McVey Hall

Mathematics Graduate Handbook Description:

Review of current research in numerical analysis. May be repeated to a maximum of nine credits.
Prerequisite: Consent of instructor

Course Description

This course will take an in depth study into several physical problems which are relevant today (and in the forseeable future). These include

Ocean modeling, including coastal water flow and water flow in the Pacific Ocean.
Movement of underground media, including oil, gas, and pollutants.
Flames, including simple flames found in jet engines, candles, heat pumps, and burning buildings or forests.
Semiconductor devices, including standard memory chips and nanodevices.
Adaptive grid coarsening.

Students will have to read some papers and talk about them in the class.

The topics have some common mathematical bases. During the course we will see how different fields have or have not mastered the obstacles that have to be surmounted in order to simulate the underlying physical problem.

Each of the topics is a current, hot topic in its field. Theses are areas that attract funding from the NSF, DOE, NASA, DARPA, and DoD grant agencies in high performance computing and/or new technologies. Grab the gold: The $1,000,000,000 US government initiatives in high performance computing are driven by these topics.

If you are interested, please contact Professor Craig Douglas at douglas@ccs.uky.edu or +1-606-257-2326 for more information or permission to take the course. Due to the choice of the classroom, the time of the course can be changed through mutual choice of the students and instructor.

See http://www.ccs.uky.edu/~douglas/ma721 for further information.

Coursework

The course will consist of two parts. In the first part, students will be given one or more related papers. Students will give a series of lectures on the topics ranging from very short talks to one hour, in depth talks. Some computing may be necessary.

In the second part of the course, one or two class projects will be done as a group effort. A problem will be described in general terms. The class will have to come up with a specific model, demonstrate why the model is appropriate, and provide numerical results. The projects will be result in group written, journal quality paper.

Grading

Letter grades only will be given. No pluses and minuses will be given as a final grade. The two parts of the course will count equally. In the group part of the course, stronger students will have to cope with weaker students in order for the whole group to get a good grade.