Abstract
A direct method was designed to solve the Poisson equation for an arbitrarily shaped domain with the boundary conditions of Dirichlet or Neumann. The present method is essentially an extension of the one-dimensional “sweep-out method„ to the two-dimensional case by using the matrix calculus.
The procedure of the present method consists of two parts, i.e., (1) the calculation of the residual maxtrix R and its inverse matrix R-1, and (2) the correction of the initial guess matrix Φ by the use of R-1. Since R depends only on the shape of the domain, this method is powerful in repeating to solve the equation for the same domain but with different boundary conditions and load functions.
An estimate of the number of arithmetic operations required for solving the equation indicates that the present method requires less machine time than those of other methods. Some remarks on the practical computations are also given.
