**Adjoint design sensitivity analysis of molecular dynamics in parallel
computing environment**

HL Jang and JH Kim and Y Park and S Cho, INTERNATIONAL JOURNAL OF MECHANICS AND MATERIALS IN DESIGN, 10, 379-394 (2014).

DOI: 10.1007/s10999-014-9253-2

An adjoint design sensitivity analysis method is developed for molecular dynamics using a parallel computing scheme of spatial decomposition in both response and design sensitivity analyses to enhance the computational efficiency. Molecular dynamics is a path-dependent transient dynamic problem with many design variables of high nonlinearity. Adjoint variable method is not appropriate for path- dependent problems but employed in this paper since the path is readily available from response analysis. The required adjoint system is derived as a terminal value problem. To compute the interaction forces between atoms in different spatial boxes, only atomic positions in the neighboring boxes are required to minimize the amount of data communications. Through some numerical examples, the high nonlinearity of the selected design variables is discussed. Also, the accuracy of the derived adjoint design sensitivity is verified by comparing with finite difference sensitivity and the efficiency of parallel adjoint variable method is demonstrated.

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