A semi-analytical complex potential method for solving Laplace's equation

The complex potential function method is combined with the semi-analytical method to solve 2D Laplace problems. The semi-analytical method takes advantage of both the high efficiency of analytical techniques and the flexibility of numerical methods. The complex potential function method is an effective method for solving 2D electric and magnetic field. However, its implementation is limited due to the difficulty in finding the complex function from the boundary value problem. The combination of the two methods not only simplifies the formula and the calculation of the semi-analytical method, but also gives a new way for finding the complex functions. Numerical examples verified the validity of the method.