A Fast Direct Solution of Poisson's Equation Using Fourier Analysis

The demand for rapid procedures to solve Poisson's equation has led to the development of a direct method of solution involving Fourier analysis which can solve P0isson's equation in a square region covered by a 48 X 48 mesh in 0,9 seconds ca the IBM 7090.This compares favorably with the best iterative methods which would require about 10 seconds to solve the same problem.The method is applicable to rectangular regions with simple boundary conditions and the maximum observed error in the potential for several random charge distributions is 5 X i0 -r of the maximum potentiM change in the region. * Computation Center.Computation times given in this paper will be for this machine except where specified.95