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Title: Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures

Abstract

An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.

Authors:
;  [1];  [1]
  1. National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)
Publication Date:
OSTI Identifier:
22233570
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 240; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; DEGREES OF FREEDOM; DESIGN; FINITE DIFFERENCE METHOD; FUNCTIONS; KERNELS; LANGEVIN EQUATION; NONLINEAR PROBLEMS; PERIODICITY; SENSITIVITY ANALYSIS; SYMMETRY

Citation Formats

Kim, Min-Geun, Jang, Hong-Lae, and Cho, Seonho, E-mail: secho@snu.ac.kr. Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures. United States: N. p., 2013. Web. doi:10.1016/J.JCP.2013.01.020.
Kim, Min-Geun, Jang, Hong-Lae, & Cho, Seonho, E-mail: secho@snu.ac.kr. Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures. United States. doi:10.1016/J.JCP.2013.01.020.
Kim, Min-Geun, Jang, Hong-Lae, and Cho, Seonho, E-mail: secho@snu.ac.kr. 2013. "Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures". United States. doi:10.1016/J.JCP.2013.01.020.
@article{osti_22233570,
title = {Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures},
author = {Kim, Min-Geun and Jang, Hong-Lae and Cho, Seonho, E-mail: secho@snu.ac.kr},
abstractNote = {An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.},
doi = {10.1016/J.JCP.2013.01.020},
journal = {Journal of Computational Physics},
number = ,
volume = 240,
place = {United States},
year = 2013,
month = 5
}
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