Numerical solution of an inverse initial boundary-value problem for the full time-dependent Maxwell's equations in the presence of imperfections of small volume

Abstract

We consider the numerical solution, in a three-dimensional bounded domain, of the inverse problem for identifying the location of small electromagnetic imperfections in a medium with homogeneous background. Our numerical algorithm is based on the coupling of a discontinuous Galerkin method for the time-dependent Maxwell's equations, on the exact controllability method and on a Fourier inversion. Several numerical results are given with one and two imperfections and the robustness and accuracy of the numerical method used for the dynamic detection problem are shown.

Keywords:

• electromagnetic inhomogeneities
• Maxwell's equations
• inverse problem
• control problem
• Fourier transform

AMS Subject Classifications::

• 35R30
• 35B40
• 35B37
• 78M35