SC 740 SEMINAR REVIEW

By Deborah Dent

 

Elephants and Numerical Modeling Methods

Presented by

Louise Perkins

Department of Computer Science and Statistics

University of Southern Mississippi

Friday, January 30, 1998

 

Dr. Perkins arrived in a unique manner. Her attire and attitude clearly stated that she had the intentions of starting a rebellion! She stated that she has been misled for many years when working with the data used in modeling, simulations, and research into believing the errors in simulation results were due to factors such as round-off. One of the real culprits is the slow time drift of non-constant coefficients which introduces serious simulation errors. After presenting visuals of analysis results, she stated that the analysis results were "lies" and that we really don't know the entire solution. Dr. Perkins is now at the point of not believing in classic analysis methods such as Taylor series and finite differences. She emphasized that much of the blame for simulation errors has always been attributed to truncation error, which she says is meaningless.

 Dr. Perkins stated that she has found problems in the data and has even experienced cases where the initial conditions contained instrument error. She also questions the methods and conditions that the scientist use to collect data. When the problem is in the data, convergence and accuracy, two cornerstones of numerical analysis, are shown to be misleading indicators of the performance of a simulation. Dr. Perkins says that in order to avoid some of the pitfalls discussed, the focus for determining error conditions when performing numerical modeling needs to be re-directed. Modelers need to question the quality of the data and abandon the tradition methods, which quickly attribute error conditions to discretization or convergence error. We should also disregard the methods of analyzing and controlling them as taught by our college professors. There is no doubt that she no longer believes in the current state of numerical methods for realistic simulations. She is currently performing research on methods designed to produce accurate results.