The Study On Numerical Method For Conformal Mapping Of Interior Domain

Conformal mapping,also called conformal transformation,which is one of the important parts in the complex variable function.Using conformal mapping is a good way to solve the complex boundary problem of Laplace delimited.Solve the conformal mapping generally available analytical method and numerical method,because the Riemann uniqueness theorem,the analytical method can only solve the problem of limited.The traditional numerical conformal mapping method includes integral equation method,the series expansion method,variational method,etc.Since the 1980 s,Japan Amano to researchers such as the charge simulation method and the numerical conformal mapping a large amount of research work.On the basis of the uniqueness theorem of electrostatic field.With conductor within a set of discrete charge to replace the continuous distribution of free charge,conductor electrode surface was proposed based on charge simulation method of numerical conformal mapping method,also called Amano method.Compared with the traditional numerical conformal mapping method,by using the method of Amano computing time is shorter,achieve higher precision,the program is relatively easy to write,makes the calculation difficulty is reduced,and to obtain approximate conformal mapping function,the error evaluation of this part is relatively easy.In order to verify the feasibility of the numerical conformal mapping method based on the charge simulation method,and explore the effectiveness of the new method to solve the linear equations in the numerical conformal mapping method,this paper proposes the numerical calculation method of internal conformal mapping,and makes an effective illustration through numerical experiments.At the same times,with more extensive practical needs and more in-depth research,we need to find a way to mapping digital images.The main research work described in this paper is as follows:(1)The concepts and theorems related to conformal mapping are introduced,and the principle of simulated charge method is expounded.(2)Selection of simulated charge points and constraints for a simply connected inner region using a double conjugate ladder Degree stabilization method is used to solve linear equations,and numerical conformal mapping is carried out in both directions.The elliptic region is taken as the research object and numerical experiments are carried out.(3)The conformal mapping of rectangular and elliptical images is carried out,and the experimental results are obtained.(4)Summarize and analyze the experimental results,and prospect the follow-up research.