Sensitivity analysis for 3D Maxwell's equations and its use in the resolution of an inverse medium problem at fixed frequency
| Autor: | Stephanie Lohrengel, Jérémy Heleine, Marion Darbas |
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| Rok vydání: | 2019 |
| Předmět: |
Physics
Permittivity Human head Applied Mathematics Mathematical analysis General Engineering Inverse Boundary (topology) 010103 numerical & computational mathematics Numerical Analysis (math.NA) 01 natural sciences Integral equation Computer Science Applications 010101 applied mathematics symbols.namesake Maxwell's equations Electric field symbols FOS: Mathematics Sensitivity (control systems) Mathematics - Numerical Analysis 0101 mathematics |
| DOI: | 10.48550/arxiv.1911.02409 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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