January 2002

Visualizing Arbitrary Basis Functions for Advanced Engineering Analysis and Simulation

Kitware, Inc. has won a Small Business Innovation Research Phase I project to address the lack of visualization technology for advanced engineering simulation tools. Such tools routinely depend on interpolation and approximation (basis) functions for a variety of purposes, including modeling geometry via CAD/CAM tools, or for computational techniques such as the finite element method. What distinguishes advanced tools from earlier, less sophisticated tools is their dependence on higher-order basis functions, as compared to the linear functions typical of early tools.

While modern simulation tools have moved to more sophisticated basis functions, visualization technology has lagged behind. This technology plays a vital role in understanding, communicating and steering computational design, but has not moved beyond supporting linear basis functions, with a few special exceptions (e.g., quadratic). This situation poses a significant problem for engineering computation, since advanced techniques of high accuracy are coupled with lower-accuracy display of results. Such an approach is error prone, and introduces significant penalties in terms of time and computer resources required.