Advanced Numerical Methods for the Electromagnetic Modeling of Complex Communications and Sensing Scenarios

Review of electromagnetic theory and various methods for modeling of scattering and propagation. High frequency techniques: Geometrical Optics, Physical Optics, Gaussian Beam Summation vs. numerically rigorous differential and integral equation-based methods.
Scattering problem definition. Formulation of surface integral equations for scattering from perfectly conducting and piecewise homogeneous bodies. Formulation of volumetric integral equations. Discretization of integral equations: method of moments.
Solution of integral equations for two-dimensional problems: TM and TE polarizations. Accuracy and stability. Alternative formulations: Combined Field and Combined Source equations and proof of uniqueness. Method of fictitious sources.
Solution of large systems of linear equations: direct and iterative methods. Computational complexity of solving integral equations. Sparsification of matrices by designing basis and testing functions: impedance matrix localization and complex multipole beam approach. Fast field evaluation algorithms: FFT, fast multipole method and non-uniform grid approach.
Surface integral equations for three-dimensional problems. Discretization using RWG basis functions.