B4.1.1 Overview

B4.1.1.b The Intermediate Workshop: Modifying Models

Once faculty have a basic understanding of what computers can and cannot do in formulating and solving models, we find that most want to go deeper and understand the details. Usually this is necessitated by the desire to significantly modify an existing numerical model. The model for this workshop is NASCAR stock car racing: the rules say you have to start with a "production model" of the car, but then you are allowed, within certain limits, to modify the tires, the suspension, the steering, the engine, the gear ratios, and so forth, for various track conditions and to help the car run faster. Often, the resulting car looks very little like the model one started with. Even small changes, sometimes, can affect performance enough over a long enough race to gain a half a second in a 3 hour race (about 1 part in 20,000), the average margin of victory. Recently, for instance, NASCAR officials used a NASA airfoil model to demonstrate that adding a small camera to the top of a car changed the lift properties of the roof sufficiently so as to give a slight advantage to cars who had the cameras over cars that didn't.

This workshop presents a complete interdisciplinary course in computational science, presented to the participants as a model of how we want them to teach such a course themselves: team-taught emphasizing the interdisciplinary nature of the subject.

The following topics are covered in this more advanced workshop: (Re)Introduction to Computational Science, Floating Point Models and Machine Precision, Introduction to Numerical Analysis, Functional Approximation, Conditioning and Error Propagation, Physical Model Specification, Parallelism in Nature and Computing, Numerical Quadrature, Introduction to Ordinary Differential Equations, Monte Carlo and Molecular Dynamics Methods, and optimization Methods.

The SCSI staff has prepared case studies in a variety of science, engineering, and education areas. Introductory case studies will be presented in common, but worked on with different teams emphasizing the implementation and classroom use of the examples appropriate to that discipline.

Homework assignments similar to those given in undergraduate courses will be given to the participating faculty to handle as interdisciplinary teams. Each assignment will be written up by the teams as a lab report. In-class presentations will be required of all participants. Extensive course notes and supplementary materials will be supplied to participants to take back to their schools for incorporation into their own courses.

Our overall focus is "Simple Problems Done Well." The introductory problems do not need a supercomputer for their solution, but supercomputers can be used to compare the solution of these problems on different machines. An example we have used is the calculation of the length of a pole perpendicular to the earth's surface that will keep taut a string whose length is the circumference of the earth plus ten feet. The challenge is to compute the answer to the precision of a given machine. In a recent pilot workshop, three interdisciplinary teams of three faculty generated four different "answers" to this problem before coming to agreement by applying the correct numerical analysis and taking the details of computer arithmetic into account. We stress the absolute reliance of the science or engineering application on the correctness of the computation. Therefore, emphasis is placed on forming a prior error bounds or at least in making a posteriori error measurements.