Title: AD-based perturbation methods for uncertainties and errors

Authors: M. Martinelli, A. Dervieux, L. Hascoet, V. Pascual, A. Belme

Addresses: Institut National de Recherche en Informatique et en Automatique, INRIA Sophia Antipolis – Mediterranee, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France. ' Institut National de Recherche en Informatique et en Automatique, INRIA Sophia Antipolis – Mediterranee, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France. ' Institut National de Recherche en Informatique et en Automatique, INRIA Sophia Antipolis – Mediterranee, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France. ' Institut National de Recherche en Informatique et en Automatique, INRIA Sophia Antipolis – Mediterranee, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France. ' Institut National de Recherche en Informatique et en Automatique, INRIA Sophia Antipolis – Mediterranee, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France

Abstract: The progress of automatic differentiation (AD) and its impact on perturbation methods is the object of this paper. AD studies show an important activity for developing methods addressing the management of modern CFD kernels, taking into account the language evolution and intensive parallel computing. The evaluation of a posteriori error analysis and of resulting correctors will be addressed. Recent works in the AD-based construction of second-derivatives for building reduced-order models based on a Taylor formula will be presented on the test case of a steady compressible flow around an aircraft.

Keywords: automatic differentiation; second-order derivatives; uncertainty; error correction; design; CFD; systems modelling; simulation; perturbation methods; errors; compressible flow; aircraft; CFD; computational fluid dynamics.

DOI: 10.1504/IJESMS.2010.031872

International Journal of Engineering Systems Modelling and Simulation, 2010 Vol.2 No.1/2, pp.65 - 74

Published online: 27 Feb 2010 *

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