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arXiv · 2308.08133

Integrating the probe and singular sources methods

Masaru Ikehata
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Abstract

The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by the Laplace equation in a bounded domain as a prototype case, an integrated theory of the probe and singular sources methods is proposed. The theory consists of three parts: (i) introducing the singular sources method combined with the notion of the probe method; (ii) finding a third indicator function whose two ways decomposition yields the indicator functions in the probe and singular sources methods; (iii) finding the completely integrated version of the probe and singular sources methods.

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Masaru Ikehata. 2023-08-16. Integrating the probe and singular sources methods. https://doi.org/10.1515/jiip-2024-0006

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