Sensitivity analysis for 3D Maxwell's equations and its use in the resolution of an inverse medium problem at fixed frequency

• Published in: Inverse problems in science and engineering Vol. 28; no. 4; pp. 459 - 496
• Main Authors: Darbas, Marion, Heleine, Jérémy, Lohrengel, Stephanie
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02-04-2020
• Subjects: 3D Maxwell equations; computer science; edge finite elements; Gâteaux derivative; integral equation; Inverse medium problem; Mathematics; Numerical Analysis; small-amplitude inhomogeneities
• ISSN: 1741-5977; 1741-5985
• DOI: 10.1080/17415977.2019.1588896

This paper deals with the reconstruction of small-amplitude perturbations in the electric properties (permittivity and conductivity) of a medium from boundary measurements of the electric field at a fixed frequency. The underlying model is the three-dimensional time-harmonic Maxwell equations in the electric field. Sensitivity analysis with respect to the parameters is performed, and explicit relations between the boundary measurements and the characteristics of the perturbations are found from an appropriate integral equation and extensive numerical simulations in 3D. The resulting non-iterative algorithm allows to retrieve efficiently the centre and volume of the perturbations in various situations from the simple sphere to a realistic model of the human head.