Abstract: Anisotropic Electrical Imaging Problems
The low frequency electrical imaging
problem of recovering
a conductivity or permittivity tensor has non-unique solution
due to invariance of the boundary data with respect
to diffeomorphisms of the interior. To solve the inverse
problem using a finite element formulation one
can first find a consistent conductivity tensor in an abstract
coordinate system, then find an embedding of
this abstract manifold which satisfies any constraints
on the conductivity. We will give details of the
implementation of such a method.
At higher frequencies, for materials
permeability, diffeomorphism invariance no longer holds and
we expect a unique solution.
We give some practical applications
of this inverse problem
for time harmonic Maxwell's equations with anisotropic
permittivity at optical frequencies. In particular
integral photoelasticity and finding the director angles
for liquid crystal cells.