Finite Element Solution of Optimal Control Problems Arising in Semiconductor Modeling

  • Pavel Bochev
  • Denis Ridzal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4818)


Optimal design, parameter estimation, and inverse problems arising in the modeling of semiconductor devices lead to optimization problems constrained by systems of PDEs. We study the impact of different state equation discretizations on optimization problems whose objective functionals involve flux terms. Galerkin methods, in which the flux is a derived quantity, are compared with mixed Galerkin discretizations where the flux is approximated directly. Our results show that the latter approach leads to more robust and accurate solutions of the optimization problem, especially for highly heterogeneous materials with large jumps in material properties.


Optimal Control Problem State Equation Mixed Method Galerkin Method Semiconductor Device 
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  1. 1.
    Abraham, F., Behr, M., Heinkenschloss, M.: The effect of stabilization in finite element methods for the optimal boundary control of the oseen equations. Finite Elements in Analysis and Design 41, 229–251 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Babuška, I., Miller, A.: The post processing approach in the finite element method, part 1: calculation of displacements, stresses and other higher derivatives of the displacements. Internat. J. Numer. Methods. Engrg. 34, 1085–1109 (1984)CrossRefzbMATHGoogle Scholar
  3. 3.
    Berggren, M., Glowinski, R., Lions, J.L.: computational approach to controllability issues for flow-related models (II): Control of two-dimensional, linear advection-diffusion and Stokes models. INJCF 6(4), 253–274 (1996)Google Scholar
  4. 4.
    Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer, Berlin (1991)CrossRefzbMATHGoogle Scholar
  5. 5.
    Brezzi, F., Hughes, T.J.R., Süli, E.: Variational approximation of flux in conforming finite element methods for elliptic partial differential equations: a model problem. Rend. Mat. Acc. Lincei ser. 9 12, 159–166 (2001)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Burger, M., Pinnau, R.: Fast optimal design of semiconductor devices. SIAM Journal on Applied Mathematics 64(1), 108–126 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Collis, S.S., Heinkenschloss, M.: Analysis of the Streamline Upwind/Petrov Galerkin method applied to the solution of optimal control problems. Technical Report CAAM TR02-01, CAAM, Rice University (March 2002)Google Scholar
  8. 8.
    Hinze, M., Pinnau, R.: Optimal control of the drift-diffusion model for semiconductor devices. In: Hoffmann, K.H., et al. (eds.) Optimal Control of Complex Structures. ISNM, vol. 139, pp. 95–106. Birkhäuser, Basel (2001)CrossRefGoogle Scholar
  9. 9.
    Ridzal, D., Bochev, P.: A comparative study of Galerkin and mixed Galerkin discretizations of the state equation in optimal control problems with applications to semiconductor modeling. Technical Report SAND2007, Sandia National Laboratories (2007)Google Scholar
  10. 10.
    Wheeler, J.A.: Simulation of heat transfer from a warm pipeline buried in permafrost. In: Proceedings of the 74th National Meeting of the American Institute of Chemical Engineers (1973)Google Scholar
  11. 11.
    Wheeler, M.F.: A Galerkin procedure for estimating the flux for two-point boundary value problems. SIAM Journal on Numerical Analysis 11(4), 764–768 (1974)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pavel Bochev
    • 1
  • Denis Ridzal
    • 1
  1. 1.Computational Mathematics and Algorithms DepartmentSandia National LaboratoriesAlbuquerqueUSA

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