2022
DOI: 10.48550/arxiv.2202.12136
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A phase-field approach for detecting cavities via a Kohn-Vogelius type functional

Andrea Aspri

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 … Show more

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