Primal-dual Newton-type interior-point method for topology optimization

Authors:
R. H. W. Hoppe;S. I. Petrova;V. Schulz
Affiliations:
Professor, Institute of Mathematics, University of Augsburg, Augsburg, Germany;Assistant Professor, Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria;Professor, Department of Mathematics, University of Trier, Trier, Germany
Venue:
Journal of Optimization Theory and Applications
Year:
2002

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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.