A Shape Optimization Algorithm for Interface Identification Allowing Topological Changes

Martin Siebenborn ()
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Martin Siebenborn: Universität Hamburg

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 2, No 3, 306-328

Abstract: 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.

Keywords: Shape optimization; Interface identification; Multigrid methods; 49Q10; 35Q93; 57N25; 65M55 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1279-4

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