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Topology Optimization of Conductive Media Described by Maxwell’s Equations

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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Abstract

The problem of an energy dissipation optimization in a conductive electromagnetic media is considered. The domain is known a priori and is fixed throughout the optimization process. We apply a perturbed and damped interior-point Newton method for the primaldual formulation of the nonlinear programming problem. Nonnegative slack variables are added to the inequality constraints in the optimization problem. Computational results concerning a two-dimensional isotropic system are included.

This work was supported in part by the Alexander von Humboldt Foundation. The second author has also been supported by the Bulgarian Ministry for Education, Science, and Technology under Grant MM-98#801.

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References

  1. El-Bakry, A. S., Tapia, R. A., Tsuchiya, T., Zhang, Y.: On the formulation and theory of the Newton interior-point method for nonlinear programming. Journal of Optimization Theory and Applications, 89 (1996) 507–541.

    Article  MATH  MathSciNet  Google Scholar 

  2. Beck, R., Deuflhard, P., Hiptmair, R., Hoppe, R. H. W., Wohlmuth, B.: Adaptive miltilevel methods for edge element discretizations of Maxwell’s equations. Surveys of Math. in Industry, 8 (1999) 271–312.

    MATH  MathSciNet  Google Scholar 

  3. Bendsøe, M. P.: Optimization of Structural Topology, Shape, and Material. Springer, (1995).

    Google Scholar 

  4. Fiacco, A. V., McCormick, G. P.: Nonlinear Programming: Sequential Uncon-strained Minimization Techniques. John Wiley and Sons, New York, (1968). Re-published by SIAM, Philadelphia, (1990).

    Google Scholar 

  5. Forsgen, A., Gill, P.: Primal-dual interior methods for nonconvex nonlinear pro-gramming. SIAM Journal on Optimization, 8 (1998) 1132–1152.

    Article  MathSciNet  Google Scholar 

  6. Gay, D. M., Overton, M. L., Wright, M. H.: A primal-dual interior method for nonconvex nonlinear programming. Technical Report97-4-08, Computing Science Research Center, Bell Laboratories, Murray Hill, New Jersey, (1997).

    Google Scholar 

  7. Hoppe, R. H. W.: Mortar edge elements in R3. East-West J. Numer. Anal., 7(1999) 159–173.

    MATH  MathSciNet  Google Scholar 

  8. Kojima, M., Mizuno, S., Yoshise, A.: A primal-dual method for linear program-ming. Progress in Mathematical Programming Interior Point and Related Methods, Edited by N. Megiddo, Springer Verlag, New York, (1989).

    Google Scholar 

  9. Maar, B., Schulz, V.: Interior point multigrid methods for topology optimization.Preprint 98-57, IWR, University of Heidelberg, Germany, (1998), Structural Opti-mization(to appear).

    Google Scholar 

  10. Monk, P.: Analysis of finite element method for Maxwell’s equations. SIAM J. Numer. Anal., 29 (1992) 714–729.

    Article  MATH  MathSciNet  Google Scholar 

  11. Wittum, G.: On the convergence of multigrid methods with transforming smoothers. Theory with applications to the Navier-Stokes equations. Numer. Math., 57 (1989) 15–38.

    Article  MathSciNet  Google Scholar 

  12. Wright, M. H.: Ill-conditioning and computational error in interior methods for nonlinear programming. Technical Report97-4-04, Computing Science Research Center, Bell Laboratories, Murray Hill, New Jersey, (1997).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, Universitätsstraße 14, D-86135, Augsburg, Germany

    Ronald H. W. Hoppe & vetozara I. Petrova

  2. Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Mohrenstraße 39, D-10117, Berlin, Germany

    Volker H. Schulz

Authors
  1. Ronald H. W. Hoppe
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  2. vetozara I. Petrova
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  3. Volker H. Schulz
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Hoppe, R.H.W., Petrova, v.I., Schulz, V.H. (2001). Topology Optimization of Conductive Media Described by Maxwell’s Equations. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_48

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  • DOI: https://doi.org/10.1007/3-540-45262-1_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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