Accuracy Improvement Method For Numerical Conformal Mapping Of Multiply Connected Domains

Conformal mapping is a basic problem of complex function,which is widely used in physics and engineering.As is well known,solutions to conformal mapping can be divided into analytical and numerical calculation method.The theoretical basis of analytical method is the famous Riemann Thorem,which proves the existence of con-formal mapping function but cannot give the expression for a specific function.This implies that we must use numerical calculation method to solve some related problems when the conformal mapping functions are complex and diverse.The current confor-mal mapping is divided into two categories:one is the conformal mapping of the single connected domains and the other is the conformal mapping of the multi-connected re-gion.In this thesis,the numerical conformal mapping method based on the simulated charge method,the main work is shown as follows:(1)The concepts and theorems of conformal mapping are introduced.(2)The place of simulation charge points and collection points of the three connected doamins with the outer line of the heart line and the star line are given.(3)By taking the preconditioned method to its constraint equations,we get a sym-metric positive definite linear system.The new charge points and conformal mapping radius are calculated using the Runge-Kutta method and Pade iteration method,and the approximate conformal mapping function are constructed.(4)The method of numerical conformal mapping of unbounded multi-connected do-main based on simulation charge method is expounded in detail.The method of this paper is applied to fluid mechanics and the flow line around the cylinder is simulated.Finally,numerical experiments are carried out to the accuracy improving method of numerical conformal mapping.The numerical results show that the proposed method can improve the accuracy of numerical conformal mapping.