A Shape Optimization Algorithm for Interface Identification Allowing Topological Changes

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...

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Veröffentlicht in:Journal of optimization theory and applications 2018-05, Vol.177 (2), p.306-328
1. Verfasser: Siebenborn, Martin
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1279-4