Adaptive finite element method for a coefficient inverse problem for Maxwell's system

Abstract

We consider a coefficient inverse problem for Maxwell's system in 3-D. The coefficient of interest is the dielectric permittivity function. Only backscattering single measurement data are used. The problem is formulated as an optimization problem. The key idea is to use the adaptive finite element method for the solution. Both analytical and numerical results are presented. Similar ideas for inverse problems for the complete time dependent Maxwell's system were not considered in the past.

Keywords:

• time-dependent inverse electromagnetic scattering
• adaptive finite element methods
• a posteriori error estimation

AMS Subject Classifications::

• 65M15
• 65M32
• 65M50
• 65M60

Acknowledgements

The research was partially supported by the Swedish Foundation for Strategic Research (SSF) in Gothenburg Mathematical Modelling Center (GMMC) and by the Swedish Institute, Visby Program.