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Compiler-based Differentiation of Numerical Simulation Codes

Authors:
Michel Schanen
Michael Foerster
Boris Gendler
Uwe Naumann

Keywords: Algorithmic Differentiation; Source Transformation; C/C++; Optimization; Numerical Simulation

Abstract:
Based on algorithmic differentiation, we present a derivative code compiler capable of transforming implementations of multivariate vector functions into a program for computing derivatives. The resulting values are accurate up to machine precision compared to the common numerical approximation by finite differences. This paper gives a short mathematical background of algorithmic differentiation while focusing on the user’s perspective of applying derivative generation tools on an already implemented code. This process is illustrated by a one dimensional implementation of Burgers’ equation in a generic optimization setting using for example Newton’s method. In this implementation, finite differences are replaced by the computation of adjoints, thus saving an order of magnitude in terms of computational complexity.

Pages: 105 to 110

Copyright: Copyright (c) IARIA, 2011

Publication date: June 19, 2011

Published in: conference

ISSN: 2308-4529

ISBN: 978-1-61208-139-7

Location: Luxembourg City, Luxembourg

Dates: from June 19, 2011 to June 24, 2011