NUMERICAL CONFORMAL MAPPING BASED ON THE GENERALIZED CONJUGATION OPERATOR

An iterative procedure for numerical conformal mapping is presented wh ich imposes no restriction on the boundary complexity. The formulation involves two analytically equivalent-boundary integral equations esta blished by applying the conjugation operator to the real and the imagi nary parts of an analytical function. The conventional approach is to use only one and ignore the other equation. However, the discrete vers ion of the operator using the boundary element method (BEM) leads to t wo non-equivalent sets of linear equations forming an over-determined system. The generalised conjugation operator is introduced so that bot h sets of equations can be utilised: and their least-square solution d etermined without any additional computational cost, a strategy largel y responsible for the stability and efficiency of the proposed method. Numerical tests on various samples including problems with cracked do mains suggest global convergence, although this cannot be proved theor etically. The computational efficiency appears significantly higher th an that reported earlier by other investigators.