A FAST METHOD FOR ESTIMATING DISCRETE FIELD VALUES IN EARLY ENGINEERING DESIGN

Much of the analysis done in engineering design involves the solution of partial differential equations (PDEs) that are subject to initial-v alue or boundary-value conditions; generically these are called ''fiel d problems.'' Finite-element and finite-difference methods (FEM, FDM) are the predominant solution techniques, but these are often too expen sive or too tedious to use in the early phases of design. What's neede d is a fast method to compute estimates of field values at a few criti cal points that uses simple and robust geometric tools. This paper des cribes such a method. It is based on an old technique-integrating PDEs through stochastic (Monte Carlo) sampling-that is accelerated through the use of ray representations. In the first (pre-processing) stage, the domain (generally a mechanical part) is coherently sampled to prod uce a ray-rep. The second stage involves the usual stochastic sampling of the field, which is now enhanced by exploiting the semi-discrete c haracter of ray-reps. The method is relatively insensitive to the comp lexity of the shape being analyzed, and it has adjustable precision. I ts mechanics and advantages are illustrated by using Laplace's equatio n as an example.