A System for Performance Evaluation of Partial Differential Equations Software

Abstract

This paper describes a system to systematically compare the performance of various methods (software modules) for the numerical solution of partial differential equations. We discuss the general nature and large size of this performance evaluation problem and the data one obtains. The system meets certain design objectives that ensure a valid experiment: 1) precise definition of a particular measurement; 2) uniformity in defimition of variables entering the experiment; and 3) reproducibility of results. The ease of use of the system makes it possible to make the large sets of measurements necessary to obtain confidence in the results and its portability allows others to check or extend the measurements. The system has four parts: 1) semiautomatic generation of problems for experimental input; 2) the ELLPACK system for actually solving the equation; 3) a data management system to organize and access the experimental data; and 4) data analysis programs to extract graphical and statistical summaries from the data.