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HYDROCODE SENSITIVITIES BY MEANS OF AUTOMATIC DIFFERENTIATION

Description: The purpose of this project has been to provide sensitivities of results from an Eulerian hydrodynamics computer code (hydrocode) for use in design-optimization and uncertainty analyses. We began by applying an equation-based sensitivity technique used successfully in the early eighties that was applied to reactor-safety thermal-hydraulics problems, which is called Differential Sensitivity Theory (DST). The methodology is as follows: the system of partial differential equations (the forward or physical PDEs) is assembled, and differentiated with respect to the model parameters of interest; the adjoint equations are then determined using the inner-product rules of Hilbert spaces; and finally, the resulting adjoint PDEs are solved using straightforward numerical operators. The forward-variable solutions when needed for the adjoint solutions are provided by the original computer code that solves the physical (or forward) problem. In the present hydrocode application, acceptable results were obtained for one-material, one-dimensional problems. The DST results were then improved by means of ''compatible'' finite difference operators. We have seen, however, that DST techniques do not produce accurate values for sensitivities to all of the parameters of interest and for problems with discontinuities such as a multi-material problem. To obtain accurate sensitivities for arbitrary numerical resolution a more code-based approach was then tried. We attempted to apply automatic differentiation (AD) in the forward mode using Automatic Differentiation of Fortran (ADIFOR, version 2.0) and the Tangent-linear and Adjoint Model Compiler (TAMC) in the forward and adjoint modes. We were successful for one-dimensional problems in both modes but failed to obtain accurate sensitivities in the adjoint mode for two-dimensional problem. Here we present the successful results for two-dimensional problems in both the forward and adjoint modes using ADIFOR, version 3.0. In what follows, we describe AD methods in the context of their use for a hydrocode. We then examine setup time, results, accuracy, ...
Date: January 1, 2001
Creator: HENNINGER, R.; CARLE, A. & MAUDLIN, P.
Partner: UNT Libraries Government Documents Department

AUTOMATIC DIFFERENTIATION OF AN EULERIAN HYDROCODE

Description: Automatic differentiation (AD) is applied to a two-dimensional Eulerian hydrodynamics computer code (hydrocode) to provide gradients that will be used for design optimization and uncertainty analysis. We examine AD in both the forward and adjoint (reverse) mode using Automatic Differentiation of Fortran (ADIFOR, version 3.0). 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 a simplified, fixed-dimension version of the original code. ADIFOR produced accurate (as compared to finite difference) gradients in both modes for all of the problems. These test problems had 17 independent variables. We find that the forward mode is up to 39% slower and the adjoint mode is at least 11% faster than finding the gradient by means of finite differences. Problems of real interest will certainly have more independent variables. The adjoint mode is thus favored since the computational time increases only slightly for additional independent variables.
Date: November 1, 2000
Creator: HENNINGER, R.; CARLE, A. & MAUDLIN, P.
Partner: UNT Libraries Government Documents Department

Automatic differentiation of the TACO2D finite element code using ADIFOR

Description: The need for sensitivities in particular applications is becoming increasingly important in problems such as optimal design or control. In this study, the authors use ADIFOR to generate derivative code for TACO2D, a finite element heat transfer code. The study of TACO2D indicates that ADIFOR-generated derivatives yield accurate derivatives at a fraction of the time requirements of finite difference approximations, and space requirements proportional to the number of variables. The primary focus on TACO2D was for the design of chemical vapor deposition reactors.
Date: April 1, 1996
Creator: Carle, A. & Fagan, M.
Partner: UNT Libraries Government Documents Department

Fortran 77 interface specification to the SparsLinC 1.0 library

Description: The SparsLinC library, written in C, has been developed for exploiting sparsity in automatic differentiation of codes. Issues pertaining to the proper interface to the library from Fortran programs are discussed, including the interpretation of Fortran INTEGERs as C pointers, and the representation of Fortran precisions in C. The Appendix contains the full set of Fortran Interfaces to the SparsLinC library.
Date: May 1, 1995
Creator: Bischof, C. H.; Khademi, P. & Carle, A.
Partner: UNT Libraries Government Documents Department

Algorithms and design for a second-order automatic differentiation module

Description: This article describes approaches to computing second-order derivatives with automatic differentiation (AD) based on the forward mode and the propagation of univariate Taylor series. Performance results are given that show the speedup possible with these techniques relative to existing approaches. The authors also describe a new source transformation AD module for computing second-order derivatives of C and Fortran codes and the underlying infrastructure used to create a language-independent translation tool.
Date: July 1, 1997
Creator: Abate, J.; Bischof, C.; Roh, L. & Carle, A.
Partner: UNT Libraries Government Documents Department

Automatic differentiation: Obtaining fast and reliable derivatives -- fast

Description: In this paper, the authors introduce automatic differentiation as a method for computing derivatives of large computer codes. After a brief discussion of methods of differentiating codes, they review automatic differentiation and introduce the ADIFOR (Automatic DIfferentiation of FORtran) tool. They highlight some applications of ADIFOR to large industrial and scientific codes (groundwater transport, CFD airfoil design, and sensitivity-enhanced MM5 mesoscale weather model), and discuss the effectiveness and performance of their approach. Finally, they discuss sparsity in automatic differentiation and introduce the SparsLinC library.
Date: December 31, 1994
Creator: Bischof, C. H.; Khademi, P. M.; Pusch, G. & Carle, A.
Partner: UNT Libraries Government Documents Department

On automatic differentiation of codes with COMPLEX arithmetic with respect to real variables

Description: We explore what it means to apply automatic differentiation with respect to a set of real variables to codes containing complex arithmetic. That is, both dependent and independent variables with respect to differentiation are real variables, but in order to exploit features of complex mathematics, part of the code is expressed by employing complex arithmetic. We investigate how one can apply automatic differentiation to complex variables if one exploits the homomorphism of the complex numbers C onto R{sup 2}. It turns out that, by and large, the usual rules of differentiation apply, but subtle differences in special cases arise for sqrt (), abs (), and the power operator.
Date: June 1, 1995
Creator: Pusch, G.D.; Bischof, C. & Carle, A.
Partner: UNT Libraries Government Documents Department

ADIFOR 2.0 user`s guide (Revision B)

Description: Automatic differentiation is a technique for computing the derivatives of functions described by computer programs. ADIFOR implements automatic differentiation by transforming a collection of FORTRAN 77 subroutines that compute a function {line_integral} into new FORTRAN 77 suborutines that compute the derivaties of the outputs of {line_integral} with respect to a specified set of inputs of {line_integral}. This guide describes step by step how to use version 2.0 of ADIFOR to generate derivative code. Familiarity with UNIX and FORTRAN 77 is assumed.
Date: April 1, 1995
Creator: Bischof, C.; Khademi, P.; Mauer, A.; Hovland, P. & Carle, A.
Partner: UNT Libraries Government Documents Department

ADIFOR: Automatic differentiation in a source translator environment

Description: The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function f: R{sup n} {yields} R{sup m}. ADIFOR (Automatic Differentiation in FORtran) is a source transformation tool that accepts Fortran 77 code for the computation of a function and writes portable Fortran 77 code for the computation of the derivatives. In contrast to previous approaches, ADIFOR views automatic differentiation as a source transformation problem and employs the data analysis capabilities of the ParaScope Fortran programming environment. Experimental results show that ADIFOR can handle real- life codes and that ADIFOR-generated codes are competitive with divided-difference approximations of derivatives. In addition, studies suggest that the source-transformation approach to automatic differentation may improve the time required to compute derivatives by orders of magnitude.
Date: January 1, 1992
Creator: Bischof, C.; Corliss, G.; Griewank, A. (Argonne National Lab., IL (United States)) & Carle, A. (Rice Univ., Houston, TX (United States). Center for Research on Parallel Computation)
Partner: UNT Libraries Government Documents Department

ADIFOR: Fortran source translation for efficient derivatives

Description: The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function f: R{sup n} {yields} R{sup m}. Both the accuracy and the computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical method. ADIFOR (Automatic Differentiation In FORtran) is a source translation tool implemented using the data abstractions and program analysis capabilities of the ParaScope Parallel Programming Environment. ADIFOR accepts arbitrary Fortran-77 code defining the computation of a function and writes portable Fortran-77 code for the computation of its derivatives. In contrast to previous approaches, ADIFOR views automatic differentiation as a process of source translation that exploits computational context to reduce the cost of derivative computations. Experimental results show that ADIFOR can handle real-life codes, providing exact derivatives with a running time that is competitive with the standard divided-difference approximations of derivatives and which may perform orders of magnitude faster than divided-differences in cases. The computational scientist using ADIFOR is freed from worrying about the accurate and efficient computation of derivatives, even for complicated functions,'' and hence, is able to concentrate on the more important issues of algorithm design or system modeling. 35 refs.
Date: January 1, 1992
Creator: Bischof, C.; Corliss, G.; Griewank, A.; Hovland, P. (Argonne National Lab., IL (United States)) & Carle, A. (Rice Univ., Houston, TX (United States). Center for Research on Parallel Computation)
Partner: UNT Libraries Government Documents Department