Improved charge-density method for studying circular-plate multipole systems

A general algorithm for computing the potentials of a circular plate multipole system is developed based on the charge-density method. An efficient numerical integration algorithm for the superposition integrals is derived from integral asymptotic concepts. Utilization of system symmetry to reduce computation time and memory requirement is discussed in detail, particularly for storing the superposition integral matrix and for solving the charge-density vector. The Levinson algorithm for solving Toeplitz matrices is generalized to unravel the huge superposition matrices, yielding orders of magnitude savings in computational steps over the generic N³ matrix inversion schemes. Modification of the algorithms for studying ring multipole systems is considered. Sample computations are presented for demonstration and verification.