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Mathematics > Optimization and Control

arXiv:2210.08220 (math)
[Submitted on 15 Oct 2022 (v1), last revised 16 Nov 2022 (this version, v3)]

Title:Min max method, shape, topological derivatives, averaged Lagrangian, homogenization, two scale convergence, Helmholtz equation

Authors:Mame Gor Ngom, Ibrahima Faye, Diaraf Seck
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Abstract:In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem is formulated by introducing cost functional. We derive first by considering the lagradian method the shape derivative of the functional. It is also proven a topological derivative with the same approach. An application to several unconstrained shape functions arising from differential geometry are also given.
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA)
Cite as: arXiv:2210.08220 [math.OC]
  (or arXiv:2210.08220v3 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.08220

Submission history

From: Ibrahima Faye [view email]
[v1] Sat, 15 Oct 2022 08:09:21 UTC (32 KB)
[v2] Sun, 23 Oct 2022 17:13:17 UTC (31 KB)
[v3] Wed, 16 Nov 2022 15:31:49 UTC (31 KB)
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