Fast Integral Equation Solver for Propagation of Electromagnetic Pulses thru Inhomogeneous Irregularly Shaped Dispersive Media

The objective is to develop a new algorithm which can be used as a reliable and efficient tool in the analysis of such aspects of interaction of electro-magnetic radiation with biological tissue as: a) wideband pulse propagation through highly dispersive medium, b) medium response to the pulse, c) inverse scattering problems, d) localization of the energy deposited in the medium. The proposed algorithm will solve Maxwell's equations in their integral form in the frequency domain. A complete solution of the time-dependent scattering problem will be constructed as a superposition of a set of harmonic (fourier) components. The underlying algorithm discretization is designed to : (1) assure its ability to model accurately highly inhomogeneous, irregularly shaped dispersive media, (2) reduce significantly its memory and execution time requirements with respect to conventional method of moments and partial differential equation solvers. These features are of crucial impotance in applications involving electrically large 3-dimensional volumetric scatterers with frequency dependent material properties.