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Mathematics > Analysis of PDEs

arXiv:2202.12136 (math)
[Submitted on 24 Feb 2022 (v1), last revised 23 Jul 2022 (this version, v2)]

Title:A phase-field approach for detecting cavities via a Kohn-Vogelius type functional

Authors:Andrea Aspri
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Abstract:We deal with the geometrical inverse problem of the shape reconstruction of cavities in a bounded linear isotropic medium by means of boundary data. The problem is addressed from the point of view of optimal control: the goal is to minimize in the class of Lipschitz domains a Kohn-Vogelius type functional with a perimeter regularization term which penalizes the perimeter of the cavity to be reconstructed. To solve numerically the optimization problem, we use a phase-field approach, approximating the perimeter functional with a Modica-Mortola relaxation and modeling the cavity as an inclusion with a very small elastic tensor. We provide a detailed analysis showing the robustness of the algorithm through some numerical experiments.
Subjects: Analysis of PDEs (math.AP); Optimization and Control (math.OC)
Cite as: arXiv:2202.12136 [math.AP]
  (or arXiv:2202.12136v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2202.12136
Related DOI: https://doi.org/10.1088/1361-6420/ac82e4

Submission history

From: Andrea Aspri [view email]
[v1] Thu, 24 Feb 2022 14:57:23 UTC (1,438 KB)
[v2] Sat, 23 Jul 2022 10:37:58 UTC (1,650 KB)
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