Fast alternating direction iterative method for poisson equation of potential

Abstract

A fast alternating direction iterative (ADI) method is presented for solving Poisson equation of potential. The method has all right-hand sides (RHS) free of differential operator with the forcing function to be included in one step only. The derivation of Poisson equation is carried out based on Gauss’s law and Coulomb gauge for inhomogeneous media. The formulation of classical ADI method is also considered whereby the RHS still contain differential operators. Introducing the temporary auxiliary variable and manipulating the RHS terms lead to formulation of the fast ADI method. The computational efficiency is discussed in terms of flops count and memory requirement. Compared to the classical method, the fast ADI method has led to substantial flops count reduction and both methods require the same amount of memory space. Numerical results are illustrated with considerable simplification of each iteration using the fast ADI method having operator-free RHS.