The Numerical Conformal Mapping Of Horizontal Slit And Its Image Mapping

In this dissertation,we studied the numerical conformal mapping based on the charge simulation method of horizontal slit.As we all know,the analytic solution of conformal mapping is difficult to solve in most cases,but the numerical conformal mapping based on the charge simulation method translate the approximate conformal mapping problem into an approximation problem of conjugate harmonic function,by approximating a pair of conjugate harmonic functions,the charges of the simulated charge points was obtained.In order to obtain the highly accurate charges,we use the improved Hermitian and skew-Hermitian split-ting method based on(k,j)-Padéiteration to solve the charges,then the numerical solution of conformal mapping is constructed by the charges.In the numerical experiment,we simulated the numerical conformal mapping of simply-connected region and doubly-connected region,and realized image conformal mapping.Experimental results show that the proposed method has highprecision,and the mapping results effectively maintain the corresponding relationship between the pre-mapping angle and the post-mapping angle.