Adjoint design sensitivity analysis of molecular dynamics in parallel computing environment

  • Hong-Lae Jang
  • Jae-Hyun Kim
  • Youmie Park
  • Seonho Cho
Article
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Abstract

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.

Keywords

Adjoint design sensitivity analysis Molecular dynamics Parallel computation Path-dependent problem Terminal value problem Lennard–Jones potential 
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References

  1. Black, J., Bopp, P.: The vibration of atoms at high miller index surfaces: face centred cubic metals. Surf. Sci. 140(2), 275–293 (1984). doi: 10.1016/0039-6028(84)90733-7
  2. Cho, S., Choi, KK.: Design sensitivity analysis and optimization of non-linear transient dynamics. Part I: Sizing design. Int. J. Numer. Meth. Eng. 48(3):351–373 (2000). doi: 10.1002/(SICI)1097-0207(20000530)48
  3. Cho, S., Choi, KK.: Design sensitivity analysis and optimization of non-linear transient dynamics. Part II: Configuration design. Int. J. Numer. Meth. Eng. 48(3):375–399 (2000). doi: 10.1002/(SICI)1097-0207(20000530)48
  4. Choi, K., Kim, N.: Structural Sensitivity Analysis and Optimization, vol. 1. Springer, New York (2005)Google Scholar
  5. Farrell, D.E., Park, H.S., Liu, W.K.: Implementation aspects of the bridging scale method and application to intersonic crack propagation. Int. J. Numer. Meth. Eng. 71(5), 583–605 (2007). doi: 10.1002/nme.1981 CrossRefMATHGoogle Scholar
  6. Gao, Z., Ma, Y., Zhuang, H.: Optimal shape design for the time-dependent Navier–Stokes flow. Int. J. Numer. Meth. Fluid 57(10), 1505–1526 (2008). doi: 10.1002/fld.1673 MathSciNetCrossRefMATHGoogle Scholar
  7. Hsieh, C., Arora, J.: Design sensitivity analysis and optimization of dynamic response. Comput. Meth. Appl. Mech. Eng. 43(2), 195–219 (1984). doi: 10.1016/0045-7825(84)90005-7
  8. Kadowaki, H., Liu, W.K.: Bridging multi-scale method for localization problems. Comput. Meth. Appl. Mech. Eng. 193(30–32), 3267–3302 (2004). doi: 10.1016/j.cma.2003.11.014 CrossRefMATHGoogle Scholar
  9. Kim, MG., Jang, H., Kim, H., Cho, S.: Multiscale adjoint design sensitivity analysis of atomistic-continuum dynamic systems using bridging scale decomposition. Model. Simul. Mater. Sci. Eng. 21(3):035,005 (2013)Google Scholar
  10. Kim, M.G., Jang, H.L., Cho, S.: Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures. J. Comput. Phys. 240(0), 1–19 (2013). doi: 10.1016/j.jcp.2013.01.020 MathSciNetCrossRefGoogle Scholar
  11. Lamb, J.S.W., Roberts, J.A.G.: Time-reversal symmetry in dynamical systems: a survey. Phys. D 112(1–2), 1–39 (1998). doi: 10.1016/S0167-2789(97)00199-1
  12. Leach, A.R.: Molecular Modelling: Principles and Applications. Pearson Education, Prentice Hall (2001)Google Scholar
  13. Liu, W.K., Karpov, E.G., Park, H.S.: Nano Mechanics and Materials. Wiley, New York (2006)CrossRefGoogle Scholar
  14. Mendelev, M., Han, S., Srolovitz, D., Ackland, G., Sun, D., Asta, M.: Development of new interatomic potentials appropriate for crystalline and liquid iron. Philos. Mag. 83(35), 3977–3994 (2003)CrossRefGoogle Scholar
  15. Park, H.S., Karpov, E.G., Klein, P.A., Liu, W.K.: Three-dimensional bridging scale analysis of dynamic fracture. J. Comput. Phys. 207(2), 588–609 (2005). doi: 10.1016/j.jcp.2005.01.028 CrossRefMATHGoogle Scholar
  16. Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117(1), 1–19 (1995). doi: 10.1006/jcph.1995.1039 CrossRefMATHGoogle Scholar
  17. Spohr, E., Heinzinger, K.: Molecular dynamics simulation of a water/metal interface. Chem. Phys. Lett. 123(3), 218–221 (1986). doi: 10.1016/0009-2614(86)80016-1
  18. Strogatz, S.H.: Nonlinear Dynamics and Chaos, 1st edn. Perseus Books Group, Cambridge (1994)Google Scholar
  19. Tadmor, E.B., Phillips, R., Ortiz, M.: Mixed atomistic and continuum models of deformation in solids. Langmuir 12(19), 4529–4534 (1996). doi: 10.1021/la9508912 CrossRefGoogle Scholar
  20. Tortorelli, D.A., Haber, R.B., Lu, S.C.Y.: Design sensitivity analysis for nonlinear thermal systems. Comput. Meth. Appl. Mech. Eng. 77(1–2), 61–77 (1989). doi: 10.1016/0045-7825(89)90128-X MathSciNetCrossRefMATHGoogle Scholar
  21. Tsay, J., Arora, J.: Nonlinear structural design sensivitity analysis for path dependent problems. Part 1: General theory. Comput. Meth. Appl. Mech. Eng. 81(2), 183–208 (1990). doi: 10.1016/0045-7825(90)90109-Y MathSciNetCrossRefMATHGoogle Scholar
  22. Tuckerman, M., Berne, B.J., Martyna, G.J.: Reversible multiple time scale molecular dynamics. J. Chem. Phys. 97(3), 1990–2001 (1992). doi: 10.1063/1.463137 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Hong-Lae Jang
    • 1
  • Jae-Hyun Kim
    • 1
  • Youmie Park
    • 1
    • 2
  • Seonho Cho
    • 1
  1. 1.Department of Naval Architecture and Ocean Engineering, National Creative Research Initiatives (NCRI) Center for Isogeometric Optimal DesignSeoul National UniversitySeoul Korea
  2. 2.College of PharmacyInje UniversityGyeongnam Korea

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