Automatic differentiation of the TACO2D finite element code using ADIFOR Page: 4 of 12
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In this report, we describe various aspects of our differentiation project for a radiative heat
transfer code. This code, called TACO2D, models various transient radiative heating effects
for two-dimensional geometries using a finite element method . Our primary focus on
TACO2D was for the design of chemical vapor deposition reactors. Designers at Sandia
National Laboratories were using optimization methods to improve their heating chamber
designs . Consequently, the designers were interested in obtaining accurate derivatives,
and in obtaining them quickly. As we will demonstrate in this report, both objectives are
met by using the ADIFOR automatic differentiation tool.
Our report divides into a few sections. First, we summarize our methodology. Second,
we describe the derivative generation process. Third, we demonstrate the accuracy of the
generated derivative code. Fourth, we discuss the time requirements of the generated deriva-
tive code. Fifth, we discuss the space requirements of the generated code. Finally, we close
with a summary of results and some speculation about future investigations.
Whenever feasible, we prefer to study the aspects of ADIFOR-generated derivatives on multi-
ple platforms. For TACO2D, we were able to use both an SGI Power Challenge (SGI/R8000)
platform, as well as an IBM RS 6000 Model 390 platform for our study. We used only one
node (out of four) on the SGI platform. As an additional point of interest, we processed the
source code on Sun workstations. So, our methodology consisted of these steps:
" Obtain the SGI platform source and copy it to the Sun platform.
" Port the code to the IBM RS6000 platform.
" Run ADIFOR on the Suns, correcting all inconsistencies in the original code.
" Port the ADIFOR-generated derivative code to the IBM RS6000.
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Carle, A. & Fagan, M. Automatic differentiation of the TACO2D finite element code using ADIFOR, report, April 1, 1996; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc665861/m1/4/: accessed October 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.