A technique for organizing large moment calculations for use with iterative solution methods

Through a specific choice of evenly spaced basis and testing functions, one can construct a moment matrix formulation wherein significant redundancy is embodied in the matrix. A scheme that exploits this redundancy to effect substantial computer storage reduction in an iterative field solution, such as the conjugate-gradient method is described. The expense incurred is a modest increase in computation time. The redundancy results from translational similarity features of specific classes of geometries and leads to matrix equations that may be interpreted as discrete convolutions. For illustration, the analysis here is carried out on a planar scatterer, but the strategy can be applied to spherical or cylindrical scatterers.