The Study Of The Method Of Numerical Conformal Mapping

Conformal mapping is one of important contents of complex variables; it has been widely applied in the fluid dynamics and many other fields with a strong vitality.The method of solving the conformal mapping generally can be divided into analytic method and numerical method. In a few cases, we can only use elementary function express conformal mapping with analytic method. Due to the complexity of practical problems, it must compute conformal mapping with numerical method. Many researchers have done a lot of research on numerical conformal mapping for its unique advantages.Computing conformal mapping is a very difficult question. But we can gain simple performance and high accuracy for conformal mapping with the charge simulation method. It greatly simplifies the computing complexity. It introduced charge simulation method of numerical conformal mapping, and used four numerical methods to solve constraint equation for the preliminary study in this paper; it compared the accuracy from the four numerical methods. At last, it verifies the effectiveness with the numerical calculation. My main works are:(1)It has comprehensively overviewed state of conformal mapping;(2) It described the theory of conformal mapping and its basic methods in detail;(3)The numerical methods and concept of the charge simulation method was described in detail and made some replaced researches for the solving of constraint equations;(4) It has done some numerical calculation to verify the validity of the methods and comparing the results of several different numerical methods;It has used four kinds of numerical methods to solve the linear equations and test the improved algorithm is effective which is applied in numerical conformal mapping and then we compared experimental results of the four methods in this paper.