A concise Conjugate Gradient computation of plats problems with many excitations

A major difficulty in the application of tha Conjugate Gradient algorithm [1-3] for tha analysis of electromagnetic scattering problama is tha necessity to carry out tha calculation separately for each incidant wava. Moreover, tha rates of conversance can differ significantly between different incoming waves and are usually unpredictable. It haa been pointed out in the literature that the speed advantages of the CO algorithm as compared with conventional inversion of the moment method matrix is seriously hampered when a large number of excitations are to be evaluated [4]. Speed up schemes such as the use of preconditioners may also be useful for a single excitiktion at a time [5]. A partially successful process for treating jointly several angles of plane wave incidence haa been proposed recently by Smith et al [6]. where a composite system of equations. including all the excitationa, was generated and treated first. After obtaining a preacrlbed Joint residual error, the procedure goes through a succession of restarts of the algorithm. each time at the system of equations with the worst error. Several restarts are thus used. Eleven excitations are treated in [6]. resulting in appreciable saving of iteration steps.