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arXiv · 2501.15887

A monotonicity-based globalization of the level-set method for inclusion detection

Bastian Harrach·Houcine Meftahi
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Abstract

We focus on a geometrical inverse problem that involves recovering discontinuities in electrical conductivity based on boundary measurements. This problem serves as a model to introduce a shape recovery technique that merges the monotonicity method with the level-set method. The level-set method, commonly used in shape optimization, often relies heavily on the accuracy of the initial guess. To overcome this challenge, we utilize the monotonicity method to generate a more precise initial guess, which is then used to initialize the level-set method. We provide numerical results to illustrate the effectiveness of this combined approach.

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Bastian Harrach, Houcine Meftahi. 2025-01-27. A monotonicity-based globalization of the level-set method for inclusion detection. https://arxiv.org/abs/2501.15887

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