Antenna's shape optimization and reconstruction by level-set 3D

The inverse scattering problem in electromagnetic is studied through the minimisation of the functional Jscr = frac12 int
_thetas
(|E-E
_id
|)
²
dgamma, where Eoarr is the solution of the classical exterior Maxwell problem, Eoarr
_id
the measure of the electrical ideal field and thetas is a fixed region of the open domain Omega. Considering this inverse problem, we compute the shape derivative of the functional Jscr for a smooth surface using an original min max formulation. After solving the state problems and computing the shape gradient by the integral equation, we introduce the level set optimization method. This method, based on the implicit representation of the boundary of Omega
_t
(where t is the evolution parameter) and the speed method, allows to reconstruct a homogenous surface triangular mesh at each iteration to decrease the value of the functional, notably performing several topological changes. We present here some original case of 3D reconstruction in full illumination and pure underconstrained configuration. We present notably the reconstruction of singular geometry. Finally we apply the techniques on a parabolic antenna and present the optimized diagram