AUTOMATIC DIFFERENTIATION APPLICATIONS TO COMPUTER-AIDED PROCESS ENGINEERING

The numerical methods used for solving many scientific computing probl ems, in particular, for computer aided process engineering, require th e computation of derivatives of a function. Both the accuracy and the computational requirements of the derivat:ives are, usually, of critic al importance to ensure the robustness and the efficiency of the numer ical solution. The purpose of this paper is to report on the developme nt and application of computer algebra systems for automating the impl ementation of differentiation into existing computer codes. The so-cal led Automatic Differentiation (AD) Methods have been tested on several examples of thermodynamic property calculation routines. We have used the Odyssee system, developed for the project SAFIR. The various auto matic differentiation algorithms, called forward (direct) mode and rev erse (adjoint) mode, have been compared on these examples. Our results show that Automatic Differentiation algorithms can handle real-life c odes and that the codes generated are competitive in time with calcula tion of derivatives by divided-difference approximations. For some cla sses of programs, the codes generated are much more efficient so as to be competitive with handmade derivatives. Moreover, Automatic Differe ntiation avoids the truncation errors found in finite difference appro ximation Calculation and also the tedious (and error prone) analytical derivation work done by hand.