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On Solution to an Optimal Shape Design Problem in 3-Dimensional Linear Magnetostatics

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Abstract

In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization problem and prove the convergence of the approximated solutions. In the end, we solve the problem for the optimal shape of an electromagnet that arises in the research on magnetooptic effects and that was manufactured afterwards.

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Authors and Affiliations

  1. Department of Applied Mathematics (K457), VŠB-Technical University of Ostrava, 17. listopadu 15, 708 33, Ostrava-Poruba, Czech Republic

    Dalibor Lukáš

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  1. Dalibor Lukáš
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Lukáš, D. On Solution to an Optimal Shape Design Problem in 3-Dimensional Linear Magnetostatics. Applications of Mathematics 49, 441–464 (2004). https://doi.org/10.1023/B:APOM.0000048122.27970.19

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  • DOI: https://doi.org/10.1023/B:APOM.0000048122.27970.19

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