Automatic Differentiaion of an Eulerian Hydrocode
by
Rudy Henninger
Los Alamos National Lab
Coauthors: Alan Carle (Rice University), Paul Maudlin (Los Alamos National Laboratory)

Automatic differentiation (AD) is applied to a two-dimensional Eulerian hyrodynamics computer code (hydrocode) to provide gradients that will be used for design optimization and uncertainty analysis. We examine AD in both the forward and reverse mode using Automatic DIfferentiation of FORtran (ADIFOR, version 3.0) and the Tangent-linear and Adjoint Compiler (TAMC). Setup time, accuracy, and run times are described for three problems. The test set consists of a one-dimensional shock-propagation problem, a two-dimensional metal-jet-formation problem and a two-dimensional shell-collapse problem. Setup time for ADIFOR was approximately one month starting from the original code. ADIFOR produced accurate (as compared to finite difference) gradients in both modes for all of the problems. TAMC required additional work (measured in months) to successfully produce reverse mode gradients and accurate gradients were produced only in the forward mode and for the one-dimensional problem in the reverse mode. These test problems had 17 independent variables. We find that the forward mode is up to 30% slower than finding the gradient by means of finite differences. The adjoint mode run time is longer, but problems of real interest will certainly have more independent variables.

http://www-xdiv.lanl.gov/XHM/personnel/Henninger/summaries/AD2000/AD2000_Summary.ps

Date received: December 22, 1999