2020/01/15 by Doosung Choi, Choi, Doosung, Junbeom Kim +3
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #Geophysical and Geoelectrical Methods #math.AP
paper · pdf · doi:10.48550/arxiv.2001.05147
29 pages, 6 figures
arxiv created 2020/05/11 · arxiv updated 2020/05/12
A conductivity inclusion, inserted in a homogeneous background, induces a perturbation in the background potential. This perturbation admits a multipole expansion whose coefficients are the so-called generalized polarization tensors (GPTs). GPTs can be obtained from multistatic measurements. As a modification of GPTs, the Faber polynomial polarization tensors (FPTs) were recently introduced in two dimensions. In this study, we design two novel analytical non-iterative methods for recovering the shape of a simply connected inclusion from GPTs by employing the concept of FPTs. First, we derive an explicit expression for the coefficients of the exterior conformal mapping associated with an inclusion in a simple form in terms of GPTs, which allows us to accurately reconstruct the shape of an inclusion with extreme or near-extreme conductivity. Secondly, we provide an explicit asymptotic formula in terms of GPTs for the shape of an inclusion with arbitrary conductivity by considering the inclusion as a perturbation of its equivalent ellipse. With this formula, one can non-iteratively approximate an inclusion of general shape with arbitrary conductivity, including a straight or asymmetric shape. Numerical experiments demonstrate the validity of the proposed analytical approaches.