Forward and Inverse Electromagnetic Scattering


When electromagnetic waves impinge on an object, they are
scattered and the electromagnetic field differs from the 
background field in the absence of the object. One the one 
hand, for the forward scattering problem, we are interested 
to compute the effects of the object (the scatterer) on the
known background or incident field. This problem is well-posed 
and linear. I shall present a finite element method for 
approximating this problem in the frequency domain and discuss 
some of the issues that influence the choice of algorithm. On 
the other hand, acoustic or electromagnetic waves are often 
used to try to determine properties of an inaccessible scatterer 
(for example radar). This problem, in which the incident and 
resulting scattered field are known, but the scatterer is unknown, 
is an inverse scattering problem. Such problems are ill-posed and 
non-linear However, I shall present an algorithm called the Linear
sampling Method for the problem and show some computational results.