The Study On Bidirectional Method For Numerical Conformal Mapping

Conformal mapping is one of the most important concepts in complex analysis.It comes from physics and still being widely used in many fields.Conformal mapping is a crucial way to solve many practical problems in most kinds of dynamics,electromagnetic theory and other aspects in physics.In 1980 s,Amano in Japan and other mathematicians started to consider the method of charge simulation and firstly find a way to use it in dealing with the numerical conformal mappings(Amano's method).Compared with the classic methods such as integral equation and series expansion in solving the problems of numerical conformal mappings,Amano's method did good work in accuracy,speed,error analysis and realization of procedures.Based on the basic theory of numerical conformal mapping in the way of charge simulation method,the following research work has been done on the method of numerical conformal mapping in the exterior of the single connected region and the numerical conformal mapping of double connected regions.1.The principle of simulation charge method are introduced,the method of numerical conformal mapping in the single connected region based on the simulation charge method is studied,and the method of numerical conformal inverse mapping in the exterior of the single connected region based on the LSQR method is proposed.2.The method of numerical conformal mapping in bidirectional region is studied,and the method of numerical conformal inverse mapping in bidirectional region based on QMR method is proposed.3.The numerical results show that the proposed method can improve the accuracy of numerical conformal mapping by using classical closed Jordan.