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Primal-Dual Newton-Type Interior-Point Method for Topology Optimization

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Abstract

We consider the problem of minimization of energy dissipation in a conductive electromagnetic medium with a fixed geometry and a priori given lower and upper bounds for the conductivity. The nonlinear optimization problem is analyzed by using the primal-dual Newton interior-point method. The elliptic differential equation for the electric potential is considered as an equality constraint. Transforming iterations for the null space decomposition of the condensed primal-dual system are applied to find the search direction. The numerical experiments treat two-dimensional isotropic systems.

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Authors and Affiliations

  1. Institute of Mathematics, University of Augsburg, Augsburg, Germany

    R.H.W. Hoppe (Professor)

  2. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria

    S.I. Petrova (Assistant Professor)

  3. Department of Mathematics, University of Trier, Trier, Germany

    V. Schulz (Professor)

Authors
  1. R.H.W. Hoppe
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  2. S.I. Petrova
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  3. V. Schulz
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Hoppe, R., Petrova, S. & Schulz, V. Primal-Dual Newton-Type Interior-Point Method for Topology Optimization. Journal of Optimization Theory and Applications 114, 545–571 (2002). https://doi.org/10.1023/A:1016070928600

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