A method for conformal mapping of a two-connected region onto an annulus

Abstract

This paper presents a method for conformal of a two-connected region onto an annulus. The philosophy of the method is to convert the problem into a Dirichlet problem and to prove the real part of the analytic function transformation should be a harmonic function satisfying certain boundary conditions. According to the theory of harmonic function we can determine the inner radius of the annulus from the condition that the harmonic function defined in two-connected region should be single-valued. It is then easy to see that the imaginary part can directly be obtained with the aid of Cauchy-Riemann conditions. The unknown constants of integration only influence the argument of image points and can easily be derived by using the one-to-one mapping of region onto an annulus. Without loss of generality, the method can be used to conformally map other two-connected regions onto an annulus if they can be subdivided into several rectangulars. The method has been programmed for a digital computer. It is demonstrated that the method is efficient and economical. The corresponding numerical results are shown in the Table.