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A Shape Optimization Algorithm for Interface Identification Allowing Topological Changes

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  • Martin Siebenborn

    (Universität Hamburg)

Abstract

In this work, we investigate a combination of classical optimization techniques from optimal control and a rounding strategy based on shape optimization for interface identification for problems constrained by partial differential equations. The goal is to identify the location of pollution sources in a fluid flow represented by a control that is either active or inactive. We use a relaxation of the binary problem on a coarse grid as initial guess for the shape optimization with higher resolution. The result is a computationally cheap method, where large shape deformations do not have to be performed. We demonstrate that our algorithm is, moreover, able to change the topology of the initial guess.

Suggested Citation

  • Martin Siebenborn, 2018. "A Shape Optimization Algorithm for Interface Identification Allowing Topological Changes," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 306-328, May.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:2:d:10.1007_s10957-018-1279-4
    DOI: 10.1007/s10957-018-1279-4
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    References listed on IDEAS

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    1. Falk Hante & Sebastian Sager, 2013. "Relaxation methods for mixed-integer optimal control of partial differential equations," Computational Optimization and Applications, Springer, vol. 55(1), pages 197-225, May.
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