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Title: Benefits of Simulation Codes from Automatic Differentiation of Templated C++.


Abstract not provided.

; ;
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
Report Number(s):
DOE Contract Number:
Resource Type:
Resource Relation:
Conference: Proposed for presentation at the Tri-Lab Engineering Conference held May 7-10, 2007 in Albuquerque, NM.
Country of Publication:
United States

Citation Formats

Gay, David M., Bartlett, Roscoe, and Phipps, Eric Todd. Benefits of Simulation Codes from Automatic Differentiation of Templated C++.. United States: N. p., 2007. Web.
Gay, David M., Bartlett, Roscoe, & Phipps, Eric Todd. Benefits of Simulation Codes from Automatic Differentiation of Templated C++.. United States.
Gay, David M., Bartlett, Roscoe, and Phipps, Eric Todd. Tue . "Benefits of Simulation Codes from Automatic Differentiation of Templated C++.". United States. doi:.
title = {Benefits of Simulation Codes from Automatic Differentiation of Templated C++.},
author = {Gay, David M. and Bartlett, Roscoe and Phipps, Eric Todd},
abstractNote = {Abstract not provided.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}

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  • We discuss computing first derivatives for models based on elements, such as large-scale finite-element PDE discretizations, implemented in the C++ programming language.We use a hybrid technique of automatic differentiation (AD) and manual assembly, with local element-level derivatives computed via AD and manually summed into the global derivative. C++ templating and operator overloading work well for both forward- and reverse-mode derivative computations. We found that AD derivative computations compared favorably in time to finite differencing for a scalable finite-element discretization of a convection-diffusion problem in two dimensions.
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  • A Straight-line code, which consists of assignment, addition, and multiplication statements is an abstraction of a serial computer program to compute a function with n inputs. Given a serial straight-line code with N statements, the authors derive an algorithm that automatically evaluates not only the function but also its first-order derivatives with respect to the n inputs on a parallel computer. The basic idea of the algorithm is to marry automatic computation of derivatives with automatic parallelization of serial programs. The algorithm requires O(M{sub N} log of N) scalar operations, where O(M{sub N}) is the time complexity of a parallelmore » multiplication of two dense N x N matrices and it represents a measure of the complexity of the straight-line code. Although it can be exponential in N in the worse case, it tends to be only polynomial in N for many important problems.« less
  • Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown here that sensitivity derivatives can be obtained accurately andmore » efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier-Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g. O(man-week) not O(man-year).« less