Applications of the Conjugate Gradient FFT method in scattering and radiation including simulations with impedance boundary conditions.

Abstract

The theoretical and computational aspects related to the application of the Conjugate Gradient FFT (CGFFT) method in computational electromagnetics are examined. The advantages of applying the CGFFT method to a class of large scale scattering and radiation problems are outlined. The main advantages of the method stem from its iterative nature which eliminates a need to form the system matrix (thus reducing the computer memory allocation requirements) and guarantees convergence to the true solution in a finite number of steps. Moreover, since the CGFFT algorithm is highly vectorizable, it can be efficiently implemented on supercomputers and multiprocessor machines. Results are presented for various radiators and scatterers including thin cylindrical dipole antennas, thin conductive and resistive strips and plates, as well as dielectric cylinders. Solutions of integral equations derived on the basis of generalized impedance boundary conditions (GIBC) are also examined. These boundary conditions can be used to replace the profile of a material coating by an impedance sheet or insert, thus, eliminating the need to introduce unknown polarization currents within the volume of the layer. Moreover, by applying these surface boundary conditions, the difficulties associated with the calculation of the Green's function are avoided. Impedance boundary conditions of up to the third order are employed and shown to be compatible with the basic CGFFT formulation, allowing an efficient simulation of large coated structures and filled cavity-backed apertures by further reducing the memory demand. For the purpose of validation of these simulations, a general full-wave analysis of two- and three-dimensional rectangular grooves and cavities is presented which will also serve as reference for future work.