2018/03/09 by Alexandre Munnier, Munnier, Alexandre, Karim Ramdani +1
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Electrical and Bioimpedance Tomography #FOS: Mathematics #Geophysical and Geoelectrical Methods #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1803.03519
openalex publication_date 2018/03/09 · openalex created_date 2022/09/04 · openalex updated_date 2026/07/28
In this paper, we address a particular case of Calderón's (or conductivity) inverse problem in dimension two, namely the case of a homogeneous background containing a finite number of cavities (i.e. heterogeneities of infinitely high conductivities). We aim to recover the location and the shape of the cavities from the knowledge of the Dirichlet-to-Neumann (DtN) map of the problem. The proposed reconstruction method is non iterative and uses two main ingredients. First, we show how to compute the so-called generalized Pólia-Szegö tensors (GPST) of the cavities from the DtN of the cavities. Secondly, we show that the obtained shape from GPST inverse problem can be transformed into a shape from moments problem, for some particular configurations. However, numerical results suggest that the reconstruction method is efficient for arbitrary geometries.