Large-Scale Transient Sensitivity Analysis of a Radiation-Damaged Bipolar Junction Transistor via Automatic Differentiation

  • Eric T. Phipps
  • Roscoe A. Bartlett
  • David M. Gay
  • Robert J. Hoekstra
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 64)

Summary

Automatic differentiation (AD) is useful in transient sensitivity analysis of a computational simulation of a bipolar junction transistor subject to radiation damage. We used forward-mode AD, implemented in a new Trilinos package called Sacado, to compute analytic derivatives for implicit time integration and forward sensitivity analysis. Sacado addresses element-based simulation codes written in C++ and works well with forward sensitivity analysis as implemented in the Trilinos time-integration package Rythmos. The forward sensitivity calculation is significantly more efficient and robust than finite differencing.

Keywords

Sensitivity analysis radiation damage bipolar junction transistor forward mode Trilinos Sacado Rythmos 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Trilinos packages Sacado, Rythmos, NOX, Thyra, Stratimikos, AztecOO and Ifpack are available at the Trilinos web site http://trilinos.sandia.gov
  2. 2.
    Abrahams, D., Gurtovoy, A.: C++ Template Metaprogramming. Addison-Wesley, Boston (2005)Google Scholar
  3. 3.
    Aubert, P., Di Césaré, N., Pironneau, O.: Automatic differentiation in C++ using expression templates and application to a flow control problem. Computing and Visualisation in Sciences 3, 197–208 (2001)MATHCrossRefGoogle Scholar
  4. 4.
    Bartlett, R.A., Gay, D.M., Phipps, E.T.: Automatic differentiation of C++ codes for large-scale scientific computing. In: V.N. Alexandrov, G.D. van Albada, P.M.A. Sloot, J. Dongarra (eds.) Computational Science – ICCS 2006, Lecture Notes in Computer Science, vol. 3994, pp. 525–532. Springer, Heidelberg (2006)Google Scholar
  5. 5.
    Feehery, W.F., Tolsma, J.E., Barton, P.I.: Efficient sensitivity analysis of large-scale differential-algebraic systems. Appl. Numer. Math. 25(1), 41–54 (1997)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gay, D.M.: Semiautomatic differentiation for efficient gradient computations. In: H.M. Bücker, G. Corliss, P. Hovland, U. Naumann, B. Norris (eds.) Automatic Differentiation: Applications, Theory, and Tools, Lecture Notes in Computational Science and Engineering. Springer (2005)Google Scholar
  7. 7.
    Hennigan, G.L., Hoekstra, R.J., Castro, J.P., Fixel, D.A., Shadid, J.N.: Simulation of neutron radiation damage in silicon semiconductor devices. Tech. Rep. SAND2007-7157, Sandia National Laboratories (2007)Google Scholar
  8. 8.
    Heroux, M., Bartlett, R., Howle, V., Hoekstra, R., Hu, J., Kolda, T., Lehoucq, R., Long, K., Pawlowski, R., Phipps, E., Salinger, A., Thornquist, H., Tuminaro, R., Willenbring, J., Williams, A., Stanley, K.: An overview of the Trilinos package. ACM Trans. Math. Softw. 31(3) (2005)Google Scholar
  9. 9.
    Hindmarsh, A.C., Brown, P.N., Grant, K.E., Lee, S.L., Serban, R., Shumaker, D.E., Woodward, C.S.: Sundials: Suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw. 31(3), 363–396 (2005)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Hughes, T.J.R., Franca, L.P., Balestra, M.: A new finite element formulation for computational fluid dynamics: V. Cicumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accomodating equal order interpolation. Computer Methods in Applied Mechanics and Engineering 59, 85–99 (1986)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hughes, T.J.R., Franca, L.P., Hulbert, G.M.: A new finite element formulation for computational fluid dynamics: VIII. the Galerkin/least-squares method for advective-diffusive equations. Computational Methods Applied Mechanics and Engineering 73, 173–189 (1989)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Sze, S.M.: Physics of Semiconductor Devices, 2nd edn. Wiley & Sons (1981)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Eric T. Phipps
    • 1
  • Roscoe A. Bartlett
    • 1
  • David M. Gay
    • 1
  • Robert J. Hoekstra
    • 1
  1. 1.Sandia National LaboratoriesAlbuquerqueUSA

Personalised recommendations